- -^ « » V "* ,0 "> x^q. a' > .\ . A^- -i.^ ^^'i%^,- ^v" ^ ct- ^ t, ^ C3 '^ '' ^ oV' ■^' y ''^:i''.-^ '^^ ^ c; -^ o s <- , ^^ \ 0^ > " : " ^. -^^ ^^^^-^^y^'^^^ " ' ^ ^0*^'' c « ^ ^' . . '^. ^ -^ .0 0, ^>*' o . '^^ ^ ft « •^ .\ . 1 a A. y ' / 7. \ ^,Q>.^„..-Hi-*— * ^-cr"'^ . /..... .^ ^ y^.-i.-^.^-'^^"^^"^ ' METHODS IN EDUCATION METHODS IN EDUCATION BY THOMAS J. McEVOY Price, $1.50 PUBLISHED BY THE AUTHOR 306 FULTON STREET, BROOKLYN. N. Y. 1911 v4' Covyright, 1908, 1911 By Thomas J. McEvoy First edition, September, 1908 Reprinted, May, 1911 THE • PLIMPTON • PRESS • NORWOOD • MASS • U • S • A (gCI.A292240 ^ ^ PREFACE This book is a working guide for students and teachers who are striving for unity in education. Content, arrange- ijient, and style are determined by existing needs, and the ^ treatment as a whole conforms to modern educational thought. The first edition was announced as the cumulative product of contributions from pupils, students, and teachers. It embodied the results of experience in normal schools, summer schools, teachers' institutes, and the elementary schools of New York City. Immediate public acceptance was a gratifying indication of the demand for terse, prac- tical, and specific presentation. This second edition has the same characteristics, but the revision of subject-matter carries the benefit of three years more of experience in working with hundreds of graduates from the leading pedagogical schools of America. Personal gratitude is expressed for all sources of help in making this book a true exposition of what has been done and should be done in systematic education. New York City, May, 1911. 9 10 11 CONTENTS [References are to pages] CHAPTER I Introduction: The Scope of this Book of educa- The purpose tion 3 Our general view or plan 3 3. Meaning of pedagogics 4. Scope of methods in edu- cation CHAPTER II The Curriculum 5. Curriculum and course of study distinguished 5 6. The teacher and the course of study 5 7. The pupils and the course of study 5 8. Principles determining course of study 6 Butler on the course of study 6 An eclectic course of study 7 Contrast of courses of study 7 12. 13. 14. 15. 16. 17. 18. Enriching the course of study The culture epoch theory in relation to course of study .... Correlation of studies . Report of the Commit- tee of Fifteen on cor- relation of studies . . Concentration of studies Co-ordination of studies Correlation, concentra- tion, and co-ordina- tion distinguished . . . CHAPTER III Maxwell on the Course of Study 19. A modern type 20. Principles and methods 21. Object of education . . 22. Harmony with environ- ment: intellectual . . 23. Harmony with environ- ment : moral and ethical 24. Harmony with environ- ment: physical .... 25. Summary 26. Extent of intellectual inheritance 27. Literary inheritance . . 28. Aesthetic inheritance . . 15 29 15 30 16 31 32 16 33 34 35 16 36 17 37 17 38 18 39 18 40 18 9 10 11 13 14 14 Scientific inheritance . 19 Institutional inheritance 19 Religious inheritance . 19 Assimilation by child . 20 Variety 20 Quantity of matter ... 21 Objectivity 21 Continuity, correlation, variety 22 Objectivity 22 Logical unity or con- tinuity 23 Correlation 26 Substitution or variety. 33 vu vm CONTENTS CHAPTER IV Principles of Education 41. Justification of this chapter 35 42. Limitations and options 35 43. Consciousness 36 44. Mind 36 45. Kno^\■ing 36 46. Feehng 36 47. WilUng 36 48. WiU 36 49. Faculties 36 50. Object, action, product of a faculty 36 51. Attention 37 52. Interest 37 53. Apperception 37 54. Sensation 38 55. Sense-perception: the gathering of percepts 38 56. Observation 38 57. Memory: storing con- cepts 39 58. Imagination: building concepts 39 59. Conception: holdingcon- cepts 39 60. Concept 61. Judgment: connecting concepts 62. Reasoning: deriving con- cepts 63. Self -activity 64. Habit Training the Mind The plan simplified . . . The plan outlined Explanation of the plan Classification of Principles or 68. Lack of agreement .... The principle of sense- perception The principle of motor reaction The principles of atten- tion and interest .... The principle of apper- ception The principle of self- activity Other principles 65. 66. 67. 69 70 71 72. 73. 74. 39 39 39 39 39 40 40 40 Laws 41 42 42 43 43 44 44 CHAPTER V Methods in School Econoihy 75. Meaning 45 76. Space 45 77. Light 45 78. Doors and windows ... 46 79. Air shafts 46 80. Indirect method 46 81. Gra\-ity system 47 82. Fireplace 47 83. Seating: adjustable equipment 47 84. Decoration: relation to school spirit 47 85. Grounds: suggestions from England 48 CHAPTER VI Methods in School Management 86. Opinions 87. Principles 88. Definite responsibility 89. Free discussion 50 50 50 50 90. Spontaneity and origi- nality 51 91. Qualifications of teachers 52 92. Maxwell on marking teachers 52 CONTENTS IX How to Estimate a Teacher's Value 93. Important things in teaching ability .... 52 94. Signs of poor teaching ability 52 95. Personality of teacher . 53 96. Control of class 53 97. Suggestion 53 98. Teaching by suggestion 54 99. The law of habit 54 100. The law of change or • variety 54 Opening Exercises 101. Justification 54 102. Value of habit 55 103. Memory gems 55 104. Desire 56 105. Interest in songs 56 106. Expectancy: declama- tion 56 107. Monitors 56 108. Motives 56 109. Anecdotes 56 lir. The teacher an ex- ample 56 111. Honor roll 56 112. Fellowship 56 113. Our platform 56 114. Grading 58 115. Promotion 58 116. Class teaching 59 117. Group teaching 59 118. General use 60 119. Adapted to each pupil 60 120. Vigorous teaching .... 60 121. Study periods 60 122. Concentrated attention 60 123. Promotion facilitated . 60 124. No tiresome repetition 60 125. Difficulties and advan- tages 61 126. Individual teaching . . 61 127. The Batavia plan 62 Examinations 128. For pupils 62 129. Methods of conducting examinations 63 130. Advantages of written tests 68 131. Disadvantages of writ- ten tests 63 132. Advantages of oral ex- aminations 63 133. Disadvantages of oral examinations 63 134. Reviews 63 135. Home lessons 64 136. Advantages of home study 64 137. Disadvantages of home study 64 Moral Education 138. A contribution from New York City 65 139. Moral aim 65 140. Personality of teacher 65 141. Reverence 65 142. Self-respect 65 143. Principle in character 66 144. Spirit of school 66 145. Social membership ... 66 146. Self-government 67 147. Moral values of studies 67 148. Contemporary civiliza- tion 68 149. Topics for moral les- sons • . 68 Principles of Moral Instruction 150. Development 69 151. Cultivation of imagi- nation 69 152. Employ self-activity . 69 153. Positive vs. negative . . 69 154. Supremacy of law ... 70 155. Discipline 70 156. Authority 70 157. Co-operation of par- ents 70 Punishment 158. Definition 71 159. Detention 71 160. Assignment of extra tasks 72 CONTENTS 161. Demerit marks 72 162. Expulsion 72 163. Incentives 73 164. Self-government of pupils 73 165. Public opinion in school 74 166. Evils 74 167. Virtues 74 168. Affiliated interests ... 74 169. Adolescence 74 170. Fatigue 75 171. Devices in manage- ment 75 CHAPTER VII Methods of Teaching 172. Definition 76 173. Classification 77 174. Conversational method 77 193 175. Development method . 77 194. 176. Lecture method 78 195. Questioning 196. 177. Bases 78 178. Consecutive question- 197. ine 79 179. Promiscuous question- 198 ing 79 180. Simultaneous question- 199 ing 79 200 181. Development questions and review questions 201 distinguished 80 202. 182. Rules 80 183. Positive rules 80 184. Negative rules 81 185. Weak questioning .... 81 186. Socratic method 82 203. 187. Value of the Socratic method 82 204 188. Irony in Socratic 205 method 82 206 189. Limitations in use of 207 Socratic method . . . 82 208 190. Illustration of Socratic questioning in 209 mathematics 82 210 191. Illustration of Socratic questioning in gram- 211 mar 84 212 192. Another illustration of Socratic questioning 84 213. Answers The kind wanted .... 85 The educational value of answers 85 Characteristics of good answers 85 What answers should be received 85 What answers should be rejected 86 From the particular to the general 86 Simple to complex ... 87 Concrete to abstract . . 88 From the known to the related unknown ... 88 Observation before reasoning; processes before rules ; facts before definitions or principles 89 From the empirical to the rational 89 Heuristic method .... 90 Prussian method 91 Inductive method .... 91 Deductive method ... 92 The inductive-deduc- tive method 92 Analytic method 93 Synthetic method .... 93 Comparison of analy- sis and synthesis ... 94 Individual things vs. classes 94 Topical method 95 CONTENTS XI 214. 215. 216. 217. Discussion in class .... 95 Advantages of discus- sion in class 95 Dangers in discussions in class 96 Directions for creating 218. 219. and profitably con- ducting a discus- sion 96 Characteristics of effec- tive discussion 96 Text-book method ... 96 CHAPTER VIII General Method 220. Device, method, gen- 229. • eral method 98 230. 221. Herbartian view of the order of the mind . . 99 231. 222. Justification of the for- mal steps 100 232. 223. Preparation 100 224. Presentation 101 233. 225. Comparison or associa- tion 101 226. Generalization 101 234. 227. Application or drill . . . 101 235. 228. Aims 102 Rein on aim 102 Dr. Hervey on formal steps of instruction 103 Dr. Hervey's conclu- sion 104 Colegrove on formal steps of instruction . 104 Illustrative lesson on attribute comple- ment 105 Method-whole 108 Definition of method- whole 109 OTAPTER IX _ ' Spelling 236. Accuracy a worthy aim 110 237. Value of spelling 110 238. Psychology of spelling . 110 239. The problem Ill Difficulties in Suhject-M alter 240. Composite language . . Ill Difficulties in Pupils 241. Not knowing how to study 112 242. Failure in observation 112 243. Carelessness 113 Difficulties in Teachers 244. Defective teaching ... 113 245. Using eye alone 113 246. Rote work 114 247. Neglect of spelling as a subject 114 248. Abuse of dictation ... 114 249. Indistinct concepts ... 115 250. Lapses 115 251. Unscientific classifica- tion 115 252. Interruption 115 253. Lack of variety 115 254. Excuses for failure ... 115 255. What words shall pu- pils spell? 115 Arguments for Text-book 256. Convenience 116 257. System 116 258. Breadth and utility . . 116 259. Accuracy 116 260. Stimulus 116 Arguments for Lists of Selected Words 261. Specific utility 116 262. Interest 117 263. Adaptation 117 264. Economy of efTort ... 117 265. Correlation 117 266. Summary of arguments 117 Xll CONTENTS 267. Combination of book and lists 117 268. Three ways of con- ducting recitations . 117 269. Advantages of oral spelling 118 270. Disadvantages of oral spelling 118 271. Advantages of written spelling 118 272. Disadvantages of writ- ten spelling 118 Directions for Studying Spelling Lessons 273. Physical conditions . . 118 274. Responsibility a stimu- lus 118 275. Concentration 119 276. Reproduction 119 277. Comparison 119 278. Repetition 119 279. Rowe quoted 119 280. Difficulties 120 281. The old way 120 Experiments in Studying Spelling 282. In Germany 120 283. Suggestions to the teacher 122 284. Rules for spelling 122 285. Classification of words 123 286. How to teach synonyms 124 287. How to teach homo- phones 129 288. How to teach homo- nyms 129 How to Teach the Meaning of Words 289. Associative or objec- tive process 130 290. By imitation 130 291. By the context 130 292. By etymology 131 293. By the history of words 132 294. By finding synonyms . 132 295. How pupils may show their knowledge of the meaning of words 133 296. Means of learning pro- nunciation 133 297. Uses of the dictionary 133 298. Devices in word-build- ing 133 299. Grouping words by comparison 134 300. Grouping by contrast . 135 301. Correlation through dictation 135 302. "Make every lesson a spelling lesson" .... 136 303. Pronunciation of each syllable 136 304. Repetition in writing misspelled words . . . 136 305. Combination plan .... 136 306. Self-correction 136 307. Interchange 137 308. Monitor 137 309. Group criticism 137 310. Individual responsi- bility 137 311. Class responsibility .. . 138 312. Alertness 138 313. Choosing sides 138 314. Spelling down 138 315. Pupils as examiners . . 138 316. Pupils as reviewers . . . 138 317. Pupils as critics 138 318. Pupils as friends 139 CHAPTER X Composition 319. Utility and culture ... 140 320. General aims 140 321. The pupils' motives: pleasure, sponta- neity, interest 141 322. Principles determining selection of matter for compositions . . . 141 323. Suggestions for the teacher 142 CONTENTS Xlll 324. 325. 326. 327. 328. 329. 330. 331. 33S. 333. 334. 335. 336. 337. 338. 339. 340. 341. 342. 343. 344. 345. 346. 347. 374. 375. 376. 377. 378. 379. 380. 381. 382. Kinds of composition exercises 143 Oral composition .... 143 In primary grades .... 143 Dr. Maxwell on oral composition 143 Optional classification. 144 Transcription or copy- ing 144 Dictation 145 Forms of expressions . . 145 Reproduction 145 Paraphrase 145 Abstract 146 Elaboration 146 Kinds of written com- position 146 Problems 146 Selection of subjects . . 146 Some suitable subjects 147 The model as a prepa- ration for writing . . 148 The selection of a model 148 The study of the model 148 Imitation of the model 149 The model in criticism 150 Outlines 150 Purposes of outlines . . 150 Composition without model 150 348. Criticism of composi- tions 151 349. Suggestions on criti- cisms 151 350. Too many rules 152 351. The sentence 152 352. The paragraph 153 Pertinent Questions Answered 353. Rewriting composi- tions 153 354. Occasional rewriting . . 153 355. Original drafts 154 356. Ink or pencil 154 357. Envelopes 154 358. Consulting references . 154 359. Choice of model 154 360. Cause of errors 154 361. Time before criticism . 154 362. Effect of criticism .... 155 363. No criticism 155 364. Signature of -critic ... . 155 365. Coloried pencil used . . 155 366. Errors indicated .... 155 367. Self-correction 155 368. Time limits 155 369. Pupils choose subjects. 156 370. Reading best work ... 156 371. Writing poetry 156 372. General progress .... 156 373. Question answered . . 156 CHAPTER XI Grammar Value of technical grammar 159 Scope of this chapter . 160 A habit of thinking . . 160 Facts before conclu- sions 100 The syllogism 161 Fundamental facts in grammar 161 Development based upon fundamental facts 162 Types 164 Independent elements. 164 383. Simple sentence first . 164 384. Maxims applied .... 164 385. Content of illustrative sentences 164 386. Oral analj'sis 165 387. Diagrams 165 388. Drill 166 389. Parsing literary mas- terpieces 167 390. False syntax 168 '391. Types of lessons .... 169 392. Parts of speech 169 393. Development lesson on the noun 170 XIV CONTENTS 394. Development, lesson on attribute complement 171 395. Predicate, adjective, and adverb modifiers distinguished 171 396. Personal pronoun and relative pronoun .... 173 Shall and Will 397. Meaning and us 174 398. Rule 175 399. Rule 175 400. Rule 175 Should and Would 401. Applications 176 402. Modes 176 403. Drill on Modes 177 Participles and Infinitives 404. The meaning of terms used 178 Participles 405. Lesson on participle used as an adjective . 179 406. Uses of participles ... 181 407. Distinctions required . 181 408. Drill on participle used as adjective; verbal, or verbal adjective . 183 409. Drill on participles used as nouns; gerunds, or verbal nouns .... 184 410. Drill on participle used as a mere adjective . 184 411. Drill on participle used as a mere noun .... 185 Infinitives 412. Uses of infinitives .... 186 413. Drill on infinitives used as nouns 186 414. Drill on infinitives used as adjectives 187 415. Drill on infinitives used as adverbs 187 416. The infinitive without to 187 417. Words, phrases, clauses 188 418. Drill on adjective clauses 189 419. Development: Con- cord of relative pro- noun and antecedent 190 420. Development: The noun clause 191 421. Drill on noun clauses . 193 422. Connectives: Explana- tion and drill 194 423. Distinctive uses of con- nectives illustrated . 197 424. Synthetic drill on con- nectives 197 425. Assignment 198 426. Exercises in false syn- tax 198 CHAPTER XII Geography 427. The old and the new . . 201 428. The old way 201 429. The new way 202 430. Definitions of geog- raphy 202 431. Broader educational use 203 432. The courses of study . 203 433. Introductory note . . . 203 434. Practical purposes . . . 204 435. Intellectual purposes . 205 436. Ethical purposes 206 437. Col. Parker quoted . . 207 438. Home geography .... 208 439. Fundamental facts ... 208 440. Early lessons 208 441. Points of compass .... 209 442. Distance 209 443. Maps 209 444. Models 210 445. Constructive imagina- tion 211 446. Analytic and synthetic methods 211 CONTENTS XV 447. Synthetic method 212 448. Both methods com- bined 212 449. Excursions 213 450. McMurry on excur- sions 214 Committee of Ten Quoted 451. Order of treatment . . , 214 452. Representative geog- raphy 214 453." Derivative or descrip- tive geography .... 215 454. Rational geography . . 215 455. Observational geog- raphy 216 456. Concentric circles .... 217 457. Illustration of concen- tric arrangement . . 218 458. Causal relations 219 459. Causal series 219 460. Man and nature 219 461. Types in geography. . . 221 462. Home city a type 222 463. Comparison 224 How to Study 464. A plan suggested .... 225 465. Continents as wholes . 225 466. Plan for studying a country 225 467. The recitation 226 468. Use of pictures 227 469. OutHnes by pupils ... 228 470. Aids 228 471. Dr. Maxwell on geog- raphy 228 472. Suggestions to princi- pals 228 473. Results that are essen- tial 229 Suggestions for Devices 474. Concrete aids 229 475. Outline maps 229 476. Product maps 230 477. Scrap-book 230 478. Pupils as examiners . . . 230 479. Class discussion 230 480. Debates 231 481. Commercial trips .... 231 482. Geographical cards ... 231 483. Competition 231 484. The globe an essential . 232 485. Uses of the globe 232 486. The shape of the earth 233 Climate 487. Extension of the term . 235 488. Conditions affecting climate 236 489. Forms of moisture .... 237 490. Rain 238 491. Glaciers 240 492. Icebergs 242 493. The seasons 242 494. Zones 244 495. Isotherms . . .* 244 Latitude and Longitude 496. A lesson outlined 245 497. International date line. 247 498. Standard time 248 499. Volcanoes: concrete presentation 248 500. Winds 250 501. Trade winds 251 How to Study a Map 502. Importance 252 503. The process of studying a map 253 How to Study the Text 504. Difficulties 254 505. The process of study- ing the text 255 506. Suggestions for the aid of pupils in studying the text 255 507. Characteristics of mod- ern text-books 256 XVI CONTENTS CHAPTER XIII History and Civics 508. An institutional sub- ject 257 509. Early work in history . 257 510. Geographical back- ground 257 511. Current events, anni- versaries, excursions 258 512. 513. 514. 515. 516. 517. 518. 519. 520. 521. 522. 523. 524. 525. 526. Civics 258 Members of society. Topics for discussion in all grades 258 Importance of local or- dinances 259 Government by the people 259 Aim of history and civics 259 Result sought 260 Habituation to civic requirements 260 Definition of history . . 260 Value of the study of history 261 The historical sense . . 262 Extent of history .... 261 Method of teaching history 263 Method in the lower grades 263 The teacher's prepara- tion 264 Topical method 266 527. Text-book method . . 267 528. Source method 267 529. Collateral reading .... 268 530. Open text-book recita- tion 269 531. Cause and effect 269 532. What should be memo- rized? 270 533. Verbal repetition .... 270 534. Correlation 271 535. Reviews 271 536. Use of outlines 273 537. Note books 273 538. The use of maps 273 539. Progress maps 274 540. Debates 274 541. Questions prepared by pupils 274 542. The use of illustrations 275 543. Collection of prints and pictures 275 544. Excursions 275 545. Dramatization of his- toric events 275 546. Use of mnemonics .... 276 547. How to arouse interest 276 548. Civics 276 549. Local government .... 276 550. Process of legislation . 277 551. Institutional study of history and civics . . 277 552. Common mistakes in teaching history and civics 277 CHAPTER XIV Reading 553. Value 279 554. Characteristics of books formerly used 279 555. Complete works vs. selections 280 556. Guiding principle to- day 281 557. 558. 559. 560. Types of reading mat- ter used at present . 281 Principles determining the selection of read- ing matter 282 Analytic method .... 282 Word method 282 CONTENTS xvii 561. Sentence method .... 283 562. Meaning of synthetic method 283 563. Alphabet method 283 564. Phonic method 284 565. Advantages of phonic training 284 Analytic-Synthetic Methods 566. Distinction not ac- . cepted 284 567. Combination method . 285 568. Dramatization 285 569. Arguments for drama- tization 286 570. Features 287 Ward Method 571. Self-help 289 572. Sight reading and drill 289 573. Features 289 Aldine Method 574. A general outline .... 290 575. The method justified . 291 576. Summary of advan- tages claimed 294 McCloskey and Aldine Combined 577. Eclectic tendency . . . 578. Good reading defined 579. Physical difficulties . 580. Mental difficulties . . 581. Reading to pupils . , . 582. Meaning of words . . . 294 296 296 296 297 297 How to Arouse Interest in Reading 583. Information and drill . 297 584. Removing difficulties . 298 585. Enlarging native inter- ests 299 586. Appreciative reading . 299 587. Oral reports 300 588. Memorizing 300 589. Silent reading . . .• 300 590. Violations of articula- tion 301 591. Definitions of accent and Cimphasis 301 592. Emphasis illustrated . 301 593. Meaning and kinds of inflection 302 594. Monotone 302 595. Rising inflection 302 596. Falling inflection .... 303 597. Circumflex for under- scored words 303 598. Kinds of modulation: pitch, quantity, quality 303 599. Meaning of quality of tone 304 600. Pure tone 304 601. Orotund 304 602. Aspirated tone 305 603. Guttural quality 305 604. Grammatical and rhe- torical pauses 305 605. Control of the breath . 306 606. Extensive and inten- sive reading 306 607. Home reading 307 608. Literature and char- acter 307 609. Patriotic selections . . . 308 610. Biography 308 How to Memorize a Selection 611. The selection 308 612. Copy in sight 309 613. Biography of author . 309 614. Occasion of writing . . . 309 615. Business-like attack . . 309 616. Physical comfort 309 617. The memorizing 309 618. Unifying review 309 619. Rhetorical exercises . . 310 620. Adaptation 310 621. Variety 310 622. Correlation 310 623. Memory gems: limi- tations 311 XVlll CONTENTS CHAPTER XV Akithmetic 624. 625. 626. 627. 628. 629. 630. 631. 632. 633. 634. 635. Changing points of view 316 Quantity, measure- ment, mathematics 316 Definition of number . 316 Counting and measur- ing 320 Arithmetic and its aim 321 Utility of arithmetic . . 322 Important historical facts 323 Method in arithmetic . 325 Methods of teaching the concept of num- ber 327 Concrete number oper- ations, order of suc- cession 328 Summary of modes of concrete number operations 329 The use of a book by pupils 330 Devices for Drill in Primary Grades 636. A distinction repeated 330 637. Cards 331 638. Charts 331 639. Mimeograph work ... 331 640. Text-books 331 641. Board 331 642. Circle 331 643. Square 331 644. Drawing 331 645. Dictation 331 646. Competition 332 647. Decimation 332 648. How to mark papers . . 332 649. The nature of the prob- lems 333 650. Opinions on drill 334 651. The fundamental oper- ation 334 652. Hint from experience of the race 334 Addition 653. A kind of counting . . 335 654. The forty-five combi- nations 336 655. Automatic habits .... 336 656. Two fundamental facts 337 657. Decomposition 337 658. Algorisms 338 659. Laws or principles of addition 339 Subtraction 660. Relation to addition . . 339 661. Decomposition to ex- plain borrowing . . . 339 662. Equal additions to ex- plain borrowing . . . 340 663. Complementary addi- tion in subtraction . 340 664. Four ways of perform- ing subtraction .... 341 665. Principles of subtrac- tion 341 666. Proof of subtraction . . 342 Multiplication 667. Special case of addition 342 668. Counting 342 669. Decomposition 342 670. Justification 343 671. Multiplication by fac- tors 344 672. Justification by com- mutative law 344 673. Commutation, associa- tion, distribution . . 344 674. Multiplication tables: mode and order of learning 345 675. Principles of multipli- cation 346 676. Proof of multipHcation 346 677. Concrete and abstract numbers in multipli- cation . . . . ^ 346 CONTENTS XIX Division 678. Nature of division .... 347 679. Measurement and par- tition 347 680. Short division; long division 348 681. Division by factors (associative law) . . . 349 682. Laws or principles of division 349 683. Proof of division 349 6SJ:. Grube method: char- acteristics, advan- tages 349 685. Objections to the Grube method 349 686. Speer method 350 687. Graphic methods .... 350 Properties of Number for Primary Grades 688. Extent of work 351 689. Odd and even 351 690. Prime and composite . 351 691. Divisibility 352 Properties of Number for Higher Grades 692. Induction and deduc- tion 693. Commutative, associa- tive, and distributive laws 694. Other general proper- ties 695. References 696. Application: tests of divisibility 353 697. Types of demonstra- tion 354 698. Test by 3 354 699. Frequent use of syllo- gism 355 700. Common divisors and factors; highest common factor .... 356 701. By observation 357 702. By product of prime factors 357 703. By continued division . 358 352 352 352 353 704. Definitions of multiples 360 705. First method 360 706. By multiplying prime factors 360 707. Factoring by inspec- tion 361 708. Actual division 361 709. ByaidofG. C. D 361 Fractions 710. Common fractions . . . 362 711. Principles or laws of fractions 363 712. Three conceptions of fractions 364 713. Changing to equivalent fractions 365 714. Reduction to lowest terms 366 715. Whole or mixed num- bers 366 716. Addition 366 717. Subtraction 366 718. Multiphcation 366 719. Multiphcation: frac- tion by fraction. . . . 367 720. Faulty arrangement. . . 369 721. Division: fraction by integer 369 722. Division: fraction by a fraction 370 723. Equation introduced . 372 724. Division: integer by fraction 372 Decimal Fractions 725. Relation to common fractions 372 726. Suggestions of early lessons 373 727. The decimal point 373 728. Principles 374 729. Development lesson: notation and nu- meration 374 730. Addition and subtrac- tion 375 731. Division: related to common fractions . . 377 XX CONTENTS 732. Division: Austrian method 377 733. Division: inverse of abbreviated multi- plication 378 Denominate Numbers 734. Turn to use 379 Percentage 735. Relation to fractions . . 380 736. Method of common fractions 380 737. Method of decimal fractions 381 738. The method of the equation 381 Simple Interest 739. Terms used 383 740. Methods 383 741. Faulty arrangement . . 383 Miscellaneous Topics 742. Algebra used in arith- metic 384 743. Ratio 384 744. Short process and busi- ness methods 384 745. Unitary analysis 386 746. Variable unit 386 747. Series 386 748. Arithmetical comple- ment 387 749. Problems 387 750. Proof, verification, or checking 387 751. Rule 387 Text-Books in Arithmetic 752. Guiding principles 388 753. Elimination of subject- matter 389 754. Content of the prob- lems 390 755. Types of books 390 New York City Point of View 756. Suggestions 392 757. General directions . . . 392 758. The combinations .... 392 759. Addition and miilti- plication 393 760. Subtraction and di- vision 394 761. Constructive " and in- ventional exercises . 394 762. Problems 395 763. What to look for in the solution of problems 395 764. Analysis in solution . . 395 765. Rote work criticised . . 395 766. Progressive advance in difficulties by grades 396 767. Problems illustrating progressive order of difficulties 399 768. Methods applied in New York City 401 Addition 769. Grade lA 401 770. Grade IB 402 771. Grade 2A 403 772. Grade 3A 404 Subtraction 773. Grade lA 404 774. Grade IB 404 775. Grade 2A 405 776. Grade 2B 405 777. Grade 3A 408 Multiplication 778. Grade 2B 408 779. Grade 3A 410 780. Grade 3B 410 Division 781. Grade 2B 412 782. Grade 3A 413 783. Grade 3B 413 CHAPTER XVI Questions on the Text, page 417 Index 427 METHODS IN EDUCATION METHODS IN EDUCATION CHAPTER I INTRODUCTION: THE SCOPE OF THIS BOOK 1. The purpose of education. — It is not necessary to try to construct a new definition of education. By examining a few of the definitions we find that the best modern thinkers consider that education should give to each individual a full development of all his powers. This means physical power, intellectual power, and moral power. It is a threefold harmonious development that enables each individual to know, feel, and do his duty to himself and to the civilized community in which he lives. This meaning of education implies culture, eflficiency, discipline, knowledge, development, charac- ter, and citizenship, — the seven ideals found in the history of education in western civilization. 2. Our general view or plan. — The purpose of edu- cation expresses an aim or ideal. It gives us a criterion for educative effort. The second desirable considera- tion is the subject-matter suitable in attaining the ideal, a consideration relating to the curriculum or course of study. The use of the course of study brings up the consideration of procedure or methods. As we take these considerations one by one or together, we must think of the child or the one to be educated. This fourth topic necessitates the application of psychological prin- ciples of education in justifying methods of teaching. 3 4 METHODS IN EDUCATION Thus a serviceable comprehension of methods in educa- tion impHes a blending of these five considerations: 1. Ideals, aims or purpose in education. 2. Subject-matter in education: the curriculum. 3. The mind to be educated: psychology. 4. Method in education: the processes.' 5. General organization: school management and discipline. 3. Meaning of pedagogics. — As an illustration of the tendency toward comprehensive treatment of topics in education, many schools are classifying their educational courses under the term pedagogics. The word peda- gogics is derived from two Greek words meaning the training or guiding of boys. Its larger signification at present covers the theory and the practice of teaching as a profession, embracing the application of history and principles of education, methods of teaching, school management, psychology, and ethics. 4. Scope of methods in education. — The treatment of methods of teaching is usually restricted to particular ways of presenting arithmetic, geography, grammar, and other subjects in the curriculum. But the larger con- ception in modern educational thought requires the teacher to see and feel that the presentation of daily lessons is only one methodical act in habit-formation; all the other educative acts in and out of school are sub- ject to the laws governing methods of teaching. This book aims, therefore, as outlined in section 2, to treat under methods in education many aspects of school work not usually discussed under methods of teaching. This view is defended on the ground that education is a unified or blended result rather than an aggregate of a series of independent acts. CHAPTER II THE CURRICULUM §. Curriculum and course of study distinguished. — By many writers these terms are considered interchange- able, but the following quotation gives a good distinction: ''By the curriculum is meant the logical, complete, and unified conception of the studies and exercises of the schools regardless of their administration, while by the course of study is meant the arrangement and grouping of these studies and exercises for the purpose of bringing them effectively to the learners." For an elaboration of this conception, see Ruediger's The Principles of Education, page 225. 6. The teacher and the course of study. — The average teacher has little to do in making a course of study, but every teacher has much to do in carrying out the requirements of prescribed courses. It is necessary, therefore, to know the underlying principles so that the mutual rights of the child and the curriculum may be wisely adjusted. 7. The pupils and the course of study. — In the first place, a course of study is not a rigid standard of work, irrespective of pupils, teacher, and methods; it is, on the other hand, conditioned by those three factors, and all four must yield to satisfy the needs of each. When Rousseau insisted upon a curriculum of natural material, adapted to the nature of the child, he directed attention 5 6 METHODS IN EDUCATION to what has recently been recognized, namely, that the needs of the child must determine the course of study, and not vice versa. 8. Principles determining course of study. — Our conception of education embodies' the. reciprocal rela- tions of the individual and society. It is not enough to know our civic duties; right thinking must pass into right action. So the first principle is a sociological one; the second, psychological. The former shows what subject-matter will tend to develop broad, useful, effi- cient knowledge; the latter indicates the manner of adapting the chosen subjects to the capacities of indi- vidual minds. 9. Butler on the course of study. — An application of the principles mentioned in section 8 is found in the course of study outlined by President Butler of Columbia University. In defining education he says: ''What does the term mean? I answer, it must mean a gradual adjustment to the spiritual possessions of the race. Those possessions are at least five-fold. The child is entitled to his scientific inheritance, to his literary inheritance, to his aesthetic inheritance, to his insti- tutional inheritance and to his religious inheritance." The scientific inheritance is found in geography, nature study, mathematics, and physics; the literary inheritance includes all forms of literary composition and interpretation; the aesthetic inheritance includes drawing, music, and all other kinds of art that may aid in forming a higher conception of life; the institutional inheritance is found in all kinds of civic training, includ- ing political geography, history, civics, and all the sub- ordinate forms of government represented in state and municipal organizations; and the religious inheritance THE CURRICULUM 7 includes all forms of training that are conducive to spiritual perfection. The course of study in New York City is in agreement with the requirements mentioned by Butler. 10. An eclectic course of study. — Modern courses of study are said to be eclectic because they embody the chosen culture products of civilization. To complete the. five inheritances mentioned in the last section, it is suggested that a sixth, industrial inheritance, be added to satisfy the recognition of industrial training as a part of systematic education. As an interesting study in development, recall what was taught in the oriental nations and then trace the history of courses of study. The following courses are suggested, with references to McEvoy's Epitome of History and Principles of Education: 1. Greece — Music and Gymnastics, pages 38 and 58. 2. Rome — Utilitarian Tendencies, pages 60 and 70. 3. Monasticism — Seven Liberal Arts, page 86. 4. Early Christian Universities — Law, Medicine, Philosophy, Theology, page 102. 5. Sturm — Classical High School Course, page 128. 6. Jesuits — Ratio Studiorum, page 130. 7. Comenius — Nature, page 154. 8. Spencer — Science, page 216. 9. Modern — Eclectic. See opinions of Harris, Dewey, DeGarmo, Butler, and others. 11. Contrast of courses of study. — Twenty-five years ago the elementary school taught reading, writing, spelling, grammar, geography, United States history, and what was called civics. In order to fill in the time arithmetical rules of no possible use in life were taught 8 METHODS IN EDUCATION and the children's wits were exercised or blunted by out- landish mathematical puzzles; a manual of United States history and the constitution of the United States were learned by heart; long lists of meaningless names were memorized in geography; parsing, with the utmost de- tail, was continuous; drawing, where drawing was taught, was exclusively from flat copies, and the crowning glory of the school was held to be the ability to spell sesqui- pedalian words whose signification had never dawned upon the childish intellect. The additions are nature study, intended to train what President Ehot calls the '^ capacities for productiveness and enjoyment" through the progressive acquisition of an elementary knowledge of the outside world; algebra, chiefly as an aid, through the equation, to the solution of arithmetical problems; inventional geometry; litera- ture, studied as such, distinct from the ordinary reading lesson; language and composition, as the act of expres- sion; drawing from objects; and manual training and other physical exercises. This seems a long list, and yet every subject is justified and required by the fundamen- tal assumption that the school exists for the progressive adaptation of the child's mind to its spiritual environ- ment. In other words, each child has a right to the acquisition not only of the tools of knowledge, but at least to the beginnings of a knowledge of literature, of science, of art, of institutions, and of ethics, so that when he leaves school he may be able to continue along the road on which he has started. — W. H. Maxwell, N. E. A. Address, St. Louis, 1904. 12. Enriching the course of study. — This expres- sion is an indication of an effort to frame a curriculum that will satisfy the majority of pupils. The first para- THE CURRICULUM 9 graph in section 11 mentions a rigid course formerly used; but as a large number of pupils must leave school before completing the elementary course, it is desirable to give them some knowledge of the advanced subjects which bear directly upon the affairs of life. It has been found, too, that for all pupils the elements of advanced subjects may be taught long before technical words are understood. This effort to give breadth, utility, and interest to all elementary work is called enriching the course of study. For illustration see second paragraph in section 11. 13. The culture epoch theory in relation to course of study. — This theory may be expressed in these words: **The individual mind in its development repeats the order of development of the race mind." The history of civilization presents certain stages or epochs as the pastoral epoch, the nomadic epoch, the stone age, the bronze age, the hunting stage, the agri- cultural epoch, and so on. It is believed that each stage of race development shows certain culture products in rehgion, history, Hterature, etc., and that such culture products should be arranged in the course of study for the corresponding epochs or stages in child development. Opinion hy Roark Any attempt to apply the theory closely must be futile, for only the most general correspondence can be found between the periods of the child's development and the epochs of race growth. Even if it were possible to estabhsh exact correspondence, it would be unwise to plan a course of study and methods of teaching in strict conformity therewith, for the sufficient reason that, in 10 METHODS IN EDUCATION his recapitulation, the average child exhibits some char- acteristics it is highly desirable to eliminate. The child, as the heir of the race, should be put in posses- sion of only the best which the race has gained for him. And he should be trained to adapt himself to the actual conditions of modern life, not to those of bygone eras. — Economy in Education, page 211. The American View In America this theory has not been generally ac- cepted. The experiments that have been made here are based upon the manumental arts in recognition of the efforts of the race to adjust itself to its material environments. We do, however, admit that there should be an adaptation of subject-matter in a course of study, and the culture epoch theory has given some aid in making this adaptation. We may broadly clas- sify the elementary period of school life under the imag- inative stage, the memory stage, and the reasoning stage. The general divisions of subject-matter are in harmony with these phases of mental activity. The following quotation aptly expresses the thought: '' Fairy- tales for the child, history for the youth, philosophy for the man." 14. Correlation of studies. — Correlation is putting such subjects side by side at a given time in the course as will help to bring to view the universal relations involved in the study of any one of them. — Tompkins, Philosophy of Teaching, page 263. Correlation Illustrated " In treating the Hudson river as a type we come upon the mountains, forests, water power, and manufactur- THE CURRICULUM 11 ing of its upper course; the navigation, cities, railroads, and scenery of its lower course; its commercial connec- tions by canal with the coal fields of Pennsylvania, with the forests of the north by canal to Lake Champlain, with the Great Lakes by the Erie canal along the Mohawk to Buffalo. The harbor and city of New York and their easy connections with the Great Lakes and the upper Mississippi Valley, are on one side, with the Atlantic coast and the marts of Europe on the other. Historically, the Hudson is very attractive; Hudson and his contact with the Indians, Washington and his cam- paigns, the old forts and the battle scenes, Arnold and Andre, Burgoyne's invasion. In Uterature Irving has made certain spots on its banks as famous as the old battle grounds. From a purely scientific standpoint, the great drowned valley, its palisades, mountains, and incoming ocean tides are at once suggested. Thus we have the relations of geography to history, literature, and natural science." 15. Report of the Committee of Fifteen on correla- tion of studies. — Your Committee understands by correlation of studies : I. Logical order of topics and branches First, the arrangement of topics in proper sequence in the course of study, in such a manner that each branch develops in an order suited to the natural and easy prog- ress of the child, and so that each step is taken at the proper time to help his advance to the next step in the same branch, or to the next steps in other related branches of the course of study. 12 METHODS IN EDUCATION II. Symmetrical whole of studies in the world of human learning Second, the adjustment of the branches of study in such a manner that the whole course at any given time represents all the great divisions of human learning, as far as is possible at the stage of maturity at which the pupil has arrived, and that each allied group of studies is represented by some one of its branches best adapted for the epoch in question; it .being implied that there is an equivalence of studies to a greater or less degree within each group, and that each branch of human learning should be represented by some equivalent study; so that, while no great division is left unrepre- sented, no group shall have superfluous representatives and thereby debar other groups from a proper repre- sentation. III. Psychological symmetry — the whole mind Third, the selection and arrangement of the branches and topics within each branch considered psycholog- ically with a view to afford the best exercises of the fac- ulties of the mind, and to secure the unfolding of those faculties in their natural order, so that no one faculty is so overcultivated or so neglected as to produce abnormal or one-sided mental development. IV. Correlation of pupiVs course of study with the world in which he lives — his spiritual and natural en- vironment Fourth and chiefly, your Committee understands by correlation of studies the selection and arrangement in orderly sequence of such objects of study as shall give THE CURRICULUM 13 the child an insight into the world that he lives in, and a command over its resources such as is obtained by a helpful co-operation with one's fellows. In a word, the chief consideration to which all others are to be sub- ordinated, in the opinion of your Committee, is this requirement of the civilization into which the child is born, as determining not only what he shall study in school, but what habits and customs he shall be taught in the family before the school age arrives; as well as that he shall acquire a skilled acquaintance with some one of a definite series of trades, professions, or voca- tions in the years that follow school; and, furthermore, that this question of the relation of the pupil to his civiUzation determines what political duties he shall assume and what religious faith or spiritual aspirations shall be adopted for the conduct of his hfe. — Pages 40, 41. 16. Concentration of studies. — A curriculum based upon concentration of studies has one study as the centre or core, and other related studies are grouped around the core. Ziller, a disciple of Herbart, used Uterature and history as the core; Colonel Parker used geography; and John Dewey advocates manual training. Concentration favors a strict interpretation of the culture epoch theory. Germany favors concentration, but America does not. Ziller used Robinson Crusoe as the central study. All language lessons were based upon it; arithmetic measured the voyage, the time on the island, the number of sheep and goats, etc.; geog- raphy became vivid by tracing the routes and locating the island*; constructive powers were exercised in imitat- ing Robinson in making ladders, fish-hooks, tools, and other equipments; moral lessons were learned from Rob- 14 METHODS IN EDUCATION inson's patience, kindness, and perseverance. In Amer- ica, Hiawatha has been used in making similar typical lessons. 17. Co-ordination of studies, -r- The arrangement of studies in groups of equal rank is co-ordination of studies. See Butler's views in section 9. 18. Correlation, concentration, and co-ordination dis- tinguished. — Observe that concentration makes use of one central study with radiating lines of related knowl- edge; that co-ordination makes use of more than one study, — five in the scheme of Harris, such groups being of equal value; and that correlation utilizes the general lines of related knowledge running through and unifying all the subjects and all the groups of subjects in the course of study. Correlation is a general term including concentration and co-ordination. CHAPTER III MAXWELL ON THE COURSE OF STUDY 1^. A modem type. — The New York City Course of Study has been widely discussed as an illustration of recent efforts in the organization of subject-matter. Theoretically, it is ideal for a typical American city like New York; practically, it is requiring modification especially on the quantitative side. Such changes are expected, however good the course of study may be, on account of the varying needs of the community and the changing viewpoints in education. This chapter deserves consideration by students who desire to have a practical discussion of a course of study as a whole. Principles and methods are clearly exempli- fied in this address, which was delivered by Dr. William H. Maxwell, City Superintendent of Schools, before the New York City Teachers' Association and the Society for the Study of Practical School Problems. 'His sub- ject was Some Phases of the New Course of Study. The address was reported by E. F. Smith and printed in the Metropolitan Teacher in May, 1904. The pub- lishers of that magazine gave us permission to publish the address. The Address by Dr. Maxwell 20. Principles and methods. — In discussing some phases of the new course of study, I shall deal princi- 15 16 METHODS IN EDUCATION pally with the foundation, the principles of education that seem to underlie it, and I shall take occasion inci- dentally to illustrate some of my points by referring to methods of teaching. 21. Object of education. — The first thing to be con- sidered in making a course of study is that exceedingly difficult and exceedingly complex, but always extremely interesting question. What is the object of educating the child at all? In looking for this object, in trying to determine the aim of elementary school education or of any education, there is nothing better to be found than that very comprehensive statement which appears in the report of the Committee of Fifteen, namely, that the object of education is to bring the child into har- mony with his environment. Now what does this ex- pression mean? What is meant by saying that the child is to be brought into harmony with his environment? 22. Harmony with environment : intellectual. — First, it means that in so far as our time, our ability, and his aptitude will permit, the child is to be put into pos- session of the intellectual inheritance of the race. He belongs to the human race, whose history has been that of many -great achievements, and therefore it must be assumed that education involves a knowledge of some of the things by which the race has made progress in the past. Some of the things, because the range of human knowledge is now so enormous that no one human mind can compass it. There are, however, certain of these things that any one of ordinary intelligence can compre- hend, can take in, and these the child should compre- hend if he is to be in harmony with his environment. 23. Harmony with environment: moral and eth- ical. — Second, the bringing of a child into harmony MAXWELL ON THE COURSE OF STUDY 17 with his environment impUes the development of cer- tain moral or ethical qualities; these may b-^ summarized under three great heads: Reverence, Courage, Simple- minded Devotion to Duty. The development of these virtues is necessary because without them no one will build surely and steadfastly upon the former achievements of the race. In other words, a man may know many things that are very use- ful, pleasant, and ornamental; he may know them well and thoroughly; but if he has no reverence, if he has no courage, if he has not simple-minded devotion to duty, his knowledge will be of little avail. 24. Harmony with environment: physicaL — The third consideration in the adjustment of the child to his environment is the development of his physical powers. He must have health, strength, and agility of body, and skill of hand. A man may have knowledge, he may have these great ethical qualities of reverence and cour- age and simple-minded devotion to duty, yet if he has not health and bodily strength and some skill of hand, he will accomplish little. What will a man give in exchange for health? No amount of study, no amount of intellectual attainment, no amount of accomplish- ment in the purely intellectual sphere will ever compen- sate anybody for the loss of health. 25. Summary. — These three things, then, are neces- sary to bring a child into harmony with his environment : 1. Putting him into possession of his intellectual inheritance. 2. Developing the three great moral qualities of rev- erence, courage, and simple-minded devotion to duty. 3. Developing his health, strength, and agihty of body, and giving him the use of his hands. 18 METHODS IN EDUCATION 26. Extent of intellectual inheritance. — What things are included under the intellectual achievements of the human race? What is our intellectual inheritance? If this be determined, then the subjects that should be included in the curriculum of a school are known. And here we may follow a great thinker and fellow citizen, President Butler, of Columbia University. You will agree that his classification of the intellectual inheri- tance of the race is a comprehensive one: Literary inheritance, aesthetic inheritance, scientific inheritance, institutional inheritance, religious inheri- tance. Literature, art, science, institutions, religion, compre- hend the intellectual inheritance of the race. In the new course of study, each one of these great departments of our intellectual inheritance is represented. (Butler, The Meaning of Education, pages 3-34.) 27. Literary inheritance. — Literature is represented, even in the very lowest grade, by the fables, and the folk stories, and the memory gems; in higher grades by the readers — and in the highest grades by masterpieces of literature. 28. Aesthetic inheritance. — Aesthetics is repre- sented by the study of pictures, by drawing, by water- color sketches, and by music. In all classes, as is the case in a great many classes, photographs of fine pic- tures should be on the walls. They should, however, be there for some other purpose than simply to hang on the walls. They should not be pictures and nothing more to the pupils, but even so they just make some impression, if, as we fondly believe, the children are trained to some sense of beauty by merely looking on what is beautiful. MAXWELL ON THE COURSE OF STUDY 19 Drawing, water-color sketches, and music serve to cultivate the aesthetic sense of the children, and the city itself presents also great opportunities for teaching children something of what is fine in architecture. A great deal can be done for this city by including some- thing of a taste for fine architecture. Examples of what is fine in architecture exist here side by side with ex- amples of what is most atrocious. For instance, the Flatlron Building is one of the most hideous structures in America, while only a few steps away from it may be seen one of the most beautiful buildings in this coun- try, a perfect gem of architecture, the Court House of the Appellate Division, at the corner of Madison Avenue and 25th Street. Many of our schoolhouses are speci- mens of good architecture, and those who live in other boroughs should take a journey up to the Bronx to see that beautiful building, the new Morris High School, which, situated on a hill, dominates the landscape. 29. Scientific inheritance. — Our scientific inheri- tance is represented in the course of study by nature study, by mathematics, under which is included arith- metic, algebra, and inventional geometry, by physical geography, and by physics. 30. Institutional inheritance. — Our institutional in- heritance is represented by political geography and by history, and it will be still better represented in the near future, when we come to study municipal govern- ment with more care than we do now. 31. Religious inheritance. — Lastly, our religious inheritance is represented by ethical training, although the doctrines of any particular sect cannot be taught. This training comes partly from the habits built up through the administration of a well-ordered school, 20 METHODS IN EDUCATION and partly from the study of all the subjects, particularly literature and history. 32. Assimilation by child. — Now, if these five divi- sions of our intellectual inheritance should all be rep- resented somewhere in the course of study, the next question that comes up is, should something of each of them be taught from the very start, or should some of them be taken up later in the course? That is a nice question — a question upon which opinion will possibly differ, but for my part I have come to the conclusion, along with my colleagues, that some part of each one of these five great divisions of knowledge should be represented in every grade of the course. The opinion now held of a child's nature is more rational than that of years ago. In the little child, not more than four or five years of age when he first comes under your guidance, in that little body there is included the promise and potency of everything that afterwards develops into the full grown man or woman, just as a bud contains, in rudimentary form, the fully developed flower. The little child has a right to what- ever part of his inheritance he can assimilate; he is en- titled to have all of his powers developed from the start. Some of them will develop more rapidly than others, but all will develop more or less, provided they are supplied with the proper nourishment. 33. Variety. — In the second place, the child mind, particularly in the beginning, craves variety. There can be nothing more dull and deadly, nothing more likely to check the development of a child's mind, than to occupy it all the time with one kind of work, or even with two or three kinds of work, particularly upon the formal sides of reading, writing, and arithmetic. If you MAXWELL ON THE COURSE OF STUDY 21 would stupefy the child's faculties, if you would prevent his latent powers from developing, occupy him during his first years of school with a dull, monotonous routine. Only when the child has grown into a man does l\e de- vote all his time to one or two subjects. In the earlier stages he needs variety and he needs a broad founda- tion to support the edifice of specialization. Like the pyramids, the educational structure must be broad at tfie base and gradually taper to the top. 34. Quantity of matter. — Some objection has been made to teaching so many subjects to young children. It has been said that they are given more than they can assimilate. The person who makes such a statement, either wil- full}^ misleads, or does not understand what is being done in the schools. In the primary schools, science is not taught as science, mathematics is not taught as mathematics, institutions are not taught as institutions. The child does not study these subjects separately. The child does not know the divisions of knowledge; he simply learns facts as facts. To put a flower into a child's hand and direct attention to its colors and parts, is to give him a lesson in botany; and this lesson is just as easily comprehended by the child as is a lesson on reading the word cat. Only very gradually he learns to classify and arrange facts in the separate departments of knowledge. Principles in Teaching 35. Objectivity. — The next question arises as to the principle upon which the facts to be observed and taught should be selected and arranged. The first of these principles is familiar because it has been expressed in 22 METHODS IN EDUCATION books upon principles of education and methods of teaching over and over again. Sometimes the expres- sion is ''from the known to the unknown, from the simple to the complex;" sometimes ''from the concrete to the abstract." The meaning underlying these expressions may be reduced to a form that will be our first principle: Select those parts of a subject that can be presented objectively or that will appeal immediately to the imag- ination of the child, for perception and imagination are the strongest powers in the young child's mind. 36. Continuity, correlation, variety. — The second principle is the principle of logical unity or continuity in each of the studies; the third is the principle of correlation of studies, and the fourth is that of variety, or substitution. Application of Principles 37. Objectivity. — The principle of objectivity is illustrated by presenting in the lowest grade arithmetic in the form of counting, objects of nature, birds, home geography, and striking anecdotes of great men with history. Just one word here, incidentally, upon a sub- ject that does not receive sufficient attention, home geography. While it is in one of the grades, 4A, home geography should not be limited to this grade, but should be used in illustrations wherever possible throughout the whole course. In lessons in geography, often no reference is made to things at the very door, and there are many who come out of our schools knowing very little about their own surroundings. A boy on the roof playground of one of the schools when asked, after the East and North rivers were pointed out to him, what waters he MAXWELL ON THE COURSE OF STUDY 23 was looking at, said he saw the Atlantic and Pacific Oceans. Do not confine this home geography to one grade, but bring it in whenever it will illustrate the matter in hand. For instance the gutter in front of the school- house or the rivers that flow past this island will always illustrate the very interesting subject of river drainage, and the excavations being made in the city will illustrate the strata of the earth's surface. When you speak of forests, Prospect Park, Central Park, and Bronx Park furnish magnificent illustrations. By referring to Union Square, the plain may be illustrated; ask the children to imagine the square stretching out for hundreds of miles. Some of the parks downtown will give a fine opportunity to illustrate a desert. The usual way of illustrating a mountain by making a little sand heap on the sand tables amounts to little, because the propor- tion is lost; but if some of our Manhattan and Brooklyn friends could take their children down to Staten Island, for instance, and let them take a look at St. George, they would get a far better idea of what a mountain is than by the sand heap. Even by taking them to Morn- ingside Heights or by showing them the Palisades your object will be accomphshed. But objectivity is not then to be dropped. While geography lends itself particularly to illustrations, use illustrations in every subject — illustrations that are near and familiar to the child. 38. Logical unity or continuity. — In arranging the various subjects in the course of study, the next thing to be considered after objectivity is the logical unity or continuity of these subjects; that is, the arranging of topics in such a way that one shall spring out of what 24 METHODS IN EDUCATION goes before. With each advance, if possible, the rela- tion of cause and effect should be brought out, as in the production of wind through the expansion of air by heat, or the relation between the war of the Revolution and the French and Indian war. In this way alone can be established that wonderful connection between facts which make them part of the very texture of the mind. It is only when rational links of associations are estab- lished that knowledge stored away in the mind of the child will remain at its service. Teaching without establishing these links of association has resulted in very great harm to many characters. It has resulted in a lack of decision, simply because, when the decision was necessary, the link of association which would have enabled the individual to deal with the situation was not there. There is no more important work to do than to establish these links of association, which will bind together the masses of matter arranged under each topic from the beginning to the end of the course of study, and in so doing the very best possible means of insuring interest in the work has been taken as well. Compare for a moment two teachers. One of them takes no pains to establish the link of association, either by speaking of cause and effect, which is the best way, or by any other means. She simply says, '' I am going to hammer that knowledge into that boy's head if it takes me all summer;" and she hammers and hammers. What is the result? The child is not interested, and while she is doing her hammering he is thinking of his marbles or of his play. His mind is far away; he is pay- ing no attention, is getting into mischief, and perhaps the teacher thinks, in a moment of weakness — and per- haps the principal too — what a fine thing it would be MAXWELL ON THE COURSE OF STUDY 25 if the inattentive boy could be sent to the principal for a walloping; and all because the teaching has not been done in the right way, for if the teacher were bringing out the relations between cause and effect, every child would be interested. Why is this true? Because this desire to know the cause of things, the desire to know the answer of the question, " Why? " is one of the pri- mary instincts of the human race. The child's mind cries aloud for the satisfaction of that instinct, and unless that satisfaction be given, the attention of the children will not be gained, and their minds will be with their games and play. Think of such questions as these, and the interest they may awaken: Why does the water rise in a pump when we lower the handle? Why does the mercury fall in the thermometer as the weather grows colder? Why does the dew gather on the grass at night? Why are railroads and rivers important in military operations? Why does dividing the denominator of a fraction multiply its value? By setting such problems and working at their solu- tion, interest is aroused and maintained because of the appeal to one of the most deep-seated instincts of our human nature. Such teaching is interesting and profit- able to children. But this is not all. By it is cultivated the habit of seeking for the cause* of events throughout Hfe. That is always the supreme test of good teaching. It is not whether the average is highest on the immedi- ate subject of study, but whether the child has acquired a habit which will be of use to him in life. Make him put the question, and make him try to answer the ques- 26 METHODS IN EDUCATION tion, ''Why?" Then a habit is being estabhshed that increases enormously not only the efficiency of every kind of labor, but enhances the pleasure of living. Con- trast the laborer, for instance, who strings the electric wires, according to a rule, with a trained intelligence like that of Edison, which never rests without ascertaining the cause of every step in that operation. Which of them leads the more profitable and useful life? Con- trast the mind of a vender or seller of flowers in the street with that of an Agassiz or an Asa Gray. Which of them gets the most pleasure out of his work? Con- trast the mind of the navigator at sea who ascertains his position by rule of thumb with that of the naviga- tor skilled in the art of navigation who, by means of observations made on the heavenly bodies and the aid of trigonometry, can determine the position of the ship at any moment. Contrast the mind of the teacher who simply sets the task and listens, book in hand, to the recitation; contrast the mind of that teacher with that of the teacher who asks herself the reason for every step she takes and who sees in every mood that mirrors itself in her pupils' faces the manifestations of some all-pervading physiological or psychological law. By keeping the links of the chain tightly bound to- gether, by asking and inciting the pupils to answer the question, ''Why?" the links of association are being forged that enable the child to call up and use knowl- edge when it is needed; a perennial source of interest is being drawn upon that will enliven all school work, and a habit of mind is being cultivated that enhances the pleasure of life and increases its efficiency. 39. Correlation. — The next principle is that of cor- relation of studies. We in America have not resorted MAXWELL ON THE COURSE OF STUDY 27 to that form of correlation which is known as concentra- tion, in whose name so many educational sins have been committed. By concentration is meant the selection of some one subject, usually history, as the core of the course of study, every other study being arranged with reference to this core. While that principle has not been adopted anywhere in ^America, correlation is a very important and very useful principle. Correlation is not the teaching of two things at the same time — that is not the meaning at all, but it is using a fact or principle learned in one study, to illuminate or demonstrate something difficult of apprehension in another. Thus, grammar may be made to elucidate obscure or involved sentences in the reading lesson; stories from history brighten the details of geography, and the facts of geography explain, as nothing else can, the movements of history; while the knowledge acquired in arithmetic may be and should be used for quantitative work in every other subject, but particularly in science, civics, and geography. The difference between lessons based on correlation and those wherein no account is taken of this principle may, perhaps, be made clearer by the following illustra- tions. The Rose The teacher takes a rose from the hand of some little child who brings it into the classroom. She talks to the children about roses; they begin to get interested, when suddenly the lesson stops short, and from talking about roses they come to the reading lesson. How interesting it must be for that little child-mind in love with nature to be called upon to read ''See the dog has the rat! I 28 METHODS IN EDUCATION see the rat. Does the cat see the rat? Can the rat see the cat?" There is not even a Httle variation in the way of an answer, such as, ''No, he can't unless he turns round." After a Httle while this is stopped, and the drawing lesson begins. No reference is made to what was done in the reading lesson. One child is drawing a square plinth, another is cutting out a dog, and so on. Such lessons as these are offences against correlation. How differently this work would go on with the help of a little correlation. The nature study begins as be- fore with the rose. Can any more beautiful object be used? Is there anything better to do than to place the rose in the hand of the child, and talk to him about its leaves and petals? He will learn to love it and learn to observe it. He will want to know something about it and find out what its various parts are. At all events, the teacher has interested the children in the rose. When the reading lesson begins, she does not begin to talk of the dog or the rat, but gets the children talking about the beautiful rose. And as the children talk she has taken some sentences that seem appropriate and pretty and has written them on the blackboard, and by the time they are through with their nature study lessons she has her blackboard covered with things they have said. What better reading lesson can there be than that? What could there be more in- teresting to the children? But the teacher notices that the things the children have said are not in very good order. There is no beginning or end. She says: ''Why, here is something about the color of the rose, and here is something about the perfume of the rose. Now, sup- pose we write these over." The children dictate, and the teacher puts the sentences together in order on the MAXWELL ON THE COURSE OF STUDY 29 blackboard. She is letting the children talk instead of talking herself. They are simply dictating to her and she is writing. She makes no paragraphs. Something new comes up again about the shape of the rose, the number of petals, two or three statements about them, perhaps. She gathers these two or three statements together. They read the description again, and that is the^end of the reading lesson. Observe what has been done. The teacher has given the children the very best possible lesson. They have composed and she has written down. She has simply been their amanuensis, and without giving them any formal instruction she has got them to do the work. Then comes the drawing lesson, and the httle boxes of water colors are passed around with paper. What shall they draw? After this combined reading and nature lesson, would not the children like to make a picture of that rose, and would they not like to get one or two sentences from the board and write them under their picture? That is correlation. Is it not possible? In the higher grade the teacher was giving a read- ing lesson describing a place in England. Then she passed to the geography lesson; this was about Russia. Then she had the children reproduce something about Africa. The history lesson was about the French and Indian war, and the drawing was something that was not in the likeness of anything in the heavens above or the earth beneath. That is an example of lack of correlation in a higher grade. Here are a few examples of what seems to be legitimate, wise, and proper cor- relation: 30 METHODS IN EDUCATION History and Geography In the first place, correlate history and geography, and don't do it by trying to teach two things in one lesson; but when giving the history lesson, use the knowledge of geography that the children have already acquired to fix every prominent place in the history. Correlate your geography lesson with the history les- son, for unless the child's historical knowledge is rooted to his geographical knowledge he will not retain it. Teachers make children memorize long lists of names over and over again. Of what use is it? The teacher should, however, be able to tell the story of any name associated with any great historical event. Tell some historical stories about Rome, Boston, Salem, New York, Concord, Vicksburg, Philadelphia, instead of trying to make the children memorize the names. Then again arithmetic should be taught with other subjects. Do not try to teach arithmetic when teaching nature subjects, but, whenever possible, correlate the work. It is a good thing to count the petals of the flower in nature study. Arithmetic There used to be an examination for graduation from grammar school. The children in most of the schools were splendidly drilled in arithmetic, but they had no idea of applying it outside of the arithmetic hour. This question was once given to a class: Supposing a piece of property — a house and lot — had an assessed valuation of $6000, and a tax of $26 per $1000, what should the annual tax be upon that house? All they had to do was to multiply the tax by six. Yet these children MAXWELL ON THE COURSE OF STUDY 31 thought there was something wonderful about it, and covered pages in trying to get a wrong answer; and what was the reason? The teacher had not done quan- titative work, had not apphed their arithmetic and made them work out practical problems. Drawing Another proper method of correlation is to use draw- ing whenever possible. Use it whenever the child can better express his meaning in that way. Let him make a sketch right in the middle of his composition. I saw very recently a letter from a little girl who was taught in a school where this custom had been followed. This little girl — she is ten years of age — was describing to a little girl friend — she never knew I would see the letter — how another friend fixed her hair, and she found it hard to get the right words to express her ideas, so she drew a little pen and ink sketch. The little sketch was very good, and showed just how the hair was arranged. Use drawing whenever possible, and particu- larly in nature study, for there can be no proper study of nature without the objects, and no proper study of these objects unless they are drawn. This is absolutely essential. Language Work Another place where correlation may be apphed is in language work. To illustrate this, take the type sentences in one of the primary grades. It is an impor- tant thing for the teacher to know that all sentences can be reduced to five primary types, and it is impor- tant to the child — not to be told that there are five types — that information is not of any use to him; but 32 METHODS IN EDUCATION it is important for him to know how to make sentences according to those five types. The first type of sentence is simplified by the expression, what things do, as, The dog barks, Birds fly; the second, what things are, as. Men and dogs are animals. The third indicates what quality things are; the fourth, what things do to things; and the fifth, what is done to things. All the material used in other studies can be introduced in the making of sentences after these models. All thought must be expressed by one or the other of these five forms, and in thus correlating the study of the sentence the work done in the other subjects is being reviewed, while at the same time the foundation for future grammar studies is being laid. Memory Gems There is another form of correlation by means of the memory gem — the thing the child memorizes. Corre- late this with the spelling lessons. Instead of dictating to the children every day, once in a while ask them to write from memory a few lines that they have learned. The selection of gems of poetry and prose laid down in the course of study was very wisely made by the com- mittee of principals. The children should learn these, and then write them from memory once in a while instead of taking dictation. Formal and Content Studies But here a very important question arises, one about which there is a great deal of discussion. Shall the for- mal studies, such as penmanship and the beginnings of arithmetic, be correlated with the content studies? Certainly, for it is the only way to make the child begin MAXWELL ON THE COURSE OF STUDY 33 to recognize the symbols used for expressing the words in written form. Yet there can be no doubt that the best results cannot be obtained by teaching the formal studies only as incidental to the content studies. A lady who had quite a reputation as a teacher, and who loves her work, once said that when a child was learning to read she paid no attention to the formal side, but fixed all her attention on the content side, and that when the child did not know a new word she told him the meaning. The objection to that is that it does not develop power in the child. The child must be given some means by which he can determine the meaning of a new word when the teacher is not present to tell it. Literature cannot be enjoyed if the words are not under- stood, and no student enjoys the reading of a great work if he has to look up every word in the dictionary; no one can apply grammar to the correction of his own composition unless he has learned the classifications, the rules, and the definitions. In the first stage, there must be some reading, and the child will enjoy the study if it is well taught, if you will give him a reason for enjoying it. He enjoys a story, and if the story is read to him, he will show that he appreciates and enjoys it. He will want the book to get that beautiful story. By reading to him he gets the motive to read for himself. 40. Substitution or variety. — The reason the prin- ciple of variety has been introduced is, first, that the children get tired of one subject. when they are kept at it too long, grade after grade. The new course prevents monotony. In the second place, the new matter is really easier for the child than the more difficult parts of an older subject. The beginnings of more than one part of the main divisions of study may be necessary 34 METHODS IN EDUCATION in order to enable the child who no longer goes to school to adapt himself to his environment and to enable him to pursue his studies by himself. Enghsh history has been introduced in the seventh year, in the first place because the children get very tired of American history; and in the second place, because they understand and appreciate American history much better after studying English history for a year. Algebra and geometry have been put in the seventh year, so that the children may not get utterly tired of arithmetic, and may be able to use equations in solving the more difficult problems of arithmetic. These, very briefly, are the reasons for these substitutions. CHAPTER IV PRINCIPLES OF EDUCATION 41. Justification of this cbJapter. — If any educator is inclined to question the appropriateness of a chapter on psychology in a text-book on methods in education, let him consider the necessity of giving a reason for every process in teaching. Reasons based on personal opin- ion or local success may be good, but the only reasons strong enough to command general acceptance are those supported by psychological principles of education. A knowledge of approved methods does presuppose famil- iarity with elementary text-books on psychology and principles of education, but surely there is no valid objec- tion to an attempt to unify the essentials of acquired knowledge in a book of this kind. The argument for convenience alone might be made a justification, but a better reason is the purpose of helping students who are trying to harmonize definitions of education, courses of study, psychology, and methods under a modern con- ception of effectual education. 42. Limitations and options. — The terse presenta- tion of essentials in this chapter is intended as a guide to the interpretation of subsequent chapters, but no student is expected to consider these few pages a substi- tute for an approved text-book on psychology. In this matter, as in all other decisions on collateral study, the judgment of an earnest student is a safe criterion. 35 36 METHODS IN EDUCATION Other definitions may be preferred, too, but these are chosen on account of simphcity, directness, and brevity. Definitions 43. Consciousness. — Consciousness is the name given to all possible mental operations. — Dexter and Garlick^s Psychology, page 2. Consciousness is that indefinable characteristic of mental states which causes us to be aware of them. — Halleck, Psychology and Psychic Culture, page 44. 44. Mind. — Mind is a spiritual force that manifests itself in knowing, feeling, and willing. 45. Knowing. — Knowing is the act of affirming the certainty of states of consciousness. 46. Feeling. — Feeling is a term that indicates pleas- ant or painful states of consciousness. 47. Willing. — Wilhng is the act of the mind in making a choice of desires. 48. Will. — The will is the power which operates in the mind in willing. 49. Faculties. — A faculty is a mental power which acts upon objects, external or internal, and discriminates them from one another. We must not, however, think of the mind as composed of separate faculties. The mind is a unit, but it can manifest itself in different ways; and for convenience we shall use the word faculties to indicate the different manifestations of power. 50. Object, action, product of a faculty. — That on which the mind acts in the exercise of any faculty is termed the object of that faculty. I hear a peal of thunder; the sound so heard is the object of the faculty of hearing. The action of this faculty is called listen- PRINCIPLES OF EDUCATION 37 ing; the product of such action on the object referred to is a notion or idea of the sound of thunder. — Welch, Teachers' Psychology, page 4. In teaching, the subject-matter of instruction is the object; the principles of education are appHed in the action; and the product is the ultimate purpose of all education. 51. Attention. — Attention is the centring of the act of'any faculty upon its object, by an impulse of the will. — Welch, page 5. Consciousness occupying itself with an object is atten- tion. — Home, Psychological Principles of Education, page 314. Attention is that act of the mind by which we bring into clear consciousness any subject or object before the mind. — Gordy, New Psychology, page 111. Attention is concentrated ' consciousness. Attention is not a faculty of the mind; it is simply a concentra- tion of consciousness upon some particular object, external or internal. 52. Interest. — Interest is the name given to the pleasurable or painful feelings which are evoked by an object or an idea, and which give that object the power of arousing and holding the attention. — Dexter and Garlick, page 31. 53. Apperception. — Apperception is the process by which a mass of presentations assimilate relatively new elements, the whole forming a system. The new material assimilated may be either given in sensation or reproduced by the internal working of the psycholog- ical mechanism; and attention, in the broad sense of noticing an object, coincides in the main, but not altogether, with the apperceptive process. 38 METHODS IN EDUCATION Apperception is the interpretation of new knowledge in the hght of that previously obtained: mental assimilation. 54. Sensation. - — A sensation is a state of conscious- ness resulting from nerve action. — Halleck, page 59. A sensation is a simple mental state resulting from the stimulation or excitation of the outer or peripheral extremity of an incarrying or sensitive nerve. — Sully. 55. Sense-perception : the gathering of percepts. — Perception is the general name of a faculty through whose action the mind gains knowledge, whether of things without or within ourselves. Sense-perception is the faculty which supplies the mind with knowledge of external objects through the action of the senses of touch, sight, and hearing. In exposure to a storm I see, hear, and feel the driving rain. In this act of sense-percep- tion the senses employed are those of touch, sight, and hearing. The object is the driving rain; the acts put forth are feeling, seeing, and hearing; and the product of these acts, while in progress, is a notion or percept of the rain. The percept in this case unites in itself the elements gained from feeling, seeing, and hearing. If the object of my sense-perception had been a thing which was visible but not tangible, or audible, as a pic- ture, a cloud, or a rainbow, the percept would have contained only the elements gained from the act of a sight. — Welch, page 5. 56. Observation. — The special function of the senses is sensation, a responding to any external stimulus that affects nerve tissue. The corresponding function of the mind in referring these sensations to their external causes is perception. Sensation and perception taken together may be called observation. — Roark, Psychol- ogy in Education, page 68. PRINCIPLES OF EDUCATION 39 Observation is the acquisition of knowledge by direct sense-perception. Observation is the act of looking at a thing closely so as to take note of its several details and parts. 57. Memory: storing percepts. — Memory is the fac- ulty which unconsciously receives, retains, and restores the products or ideas gained through the action of the other faculties. — Welch, page 6. 58. Imagination; building concepts. — The process of making images is imagination. An image is a revived percept. 59. Conception: holding concepts. — Conception is a mental process which results in a concept. — Dexter and Garlick, page 150. 60. Concept. — A concept is a re-presentation in our minds answering to a general name. — Sully. 61. Judgment : connecting concepts. — A judgment is an assertion of agreement or disagreement between two ideas. — Dexter and Garlick, page 163. 62. Reasoning : deriving concepts. — Reasoning is the faculty that derives new truths or concepts from class concepts already known. — Welch, page 11. 63. Self -activity. — Self-activity, as a principle in consciousness, means self-direction. — Home, Philos- ophy of Education, page 171. Conscious effort in the evolution of possibilities is termed self-activity. — Boyer, Principles and Practice of Teaching, page 35. 64. Habit. — A fixed tendency to think, feel, or act in a particular way is a habit. 40 METHODS IN EDUCATION Training the Mind 65. The plan simplified. — This topic is comprehen- sive enough to include the whole field of education. Students are confronted with conflicting the"bries about the possibility or impossibility of training the faculties, and then further conflict is found regarding effectual methods. Let us take it for granted that the term faculty, as defined in section 49, is used to indicate a kind of work done by the mind, without implying a division of mind itself; that each faculty can be trained, and that the general result is mental training. This mental training implies accompanying moral and phys- ical habits. All these habits constitute education. Let us see, then, how the plan can be outlined as a simple guide for our methods of training the mind. 66. The plan outlined. — This working plan shows the faculties of the mind, or the manifestations of mind, which we have to deal with in educating the child; the laws or principles which guide the effort to bring the mind of the child into the desired relation with the mind of the teacher; and the object, aim, or result of all our efforts in education. Working Plan for Training the Mind PRINCIPLES OR LAWS FACULTIES OF EDUCATION RESULTS Sensation. Law of attention. Habit. Perception (Observation). Law of interest. Habituation to Memory. Law of apperception. right thinking, Imagination. Law of self-activity. right feeling, Conception. right willing. Judgment. Reasoning. 67. Explanation of the plan. — Much attention used to be given to the natural order of development of the PRINCIPLES OF EDUCATION 41 faculties. That order is indicated in the first column. In each faculty there are physical factors and psychical factors to be considered. The physical factors are the nerves and other material parts of the body; the psychi- cal factors are the mental or spiritual results of the respective processes. These matters are discussed under reaction. In every educational process there are certain prin- ciples of education to be observed. They are given in the second column. Thus in training any one of the seven faculties, all four of those principles should be used; and the order in which they are used is the order given in the second column. There are many aims in education, but it is possible to summarize all of them in habit. The process of form- ing habits is habituation. School life may only begin the process, but school life should direct the habitua- tion toward the right end. Think of all the purposes of education as you view them, and see if they are not all included under habituation to right thinking, right feeling, and right willing. Classification of Principles or Laws 68. Lack of agreement. — The four laws mentioned in section 66 are not the only ones mentioned by those who have written on the principles of education. Her- bart could make apperception alone include all processes in education; apperception and self-activity can be considered adequate, since both attention and interest are contributing factors in both; others enumerate forty or more as essential laws. The classifications depend somewhat upon the purpose of the respective writers. One classification may be required irji a comprehensive 42 METHODS IN EDUCATION treatment of the science of education, while another may be suited to psychology. The classification in this chapter is made to help students who need a simple but adequate guide for classroom work. While we favor the four given in section 66, others are given to satisfy educators who demand a wider classification. 69. The principle of sense-perception. — This has been expressed by saying that the mind must gain through the senses everything external to itself; or, as Comenius said, " There is nothing in the mind that has not first been in the senses." As a principle in element- ary teaching, it is axiomatic. Out of this principle have grown the maxims, observation before reasoning concrete to abstract, it is better for a child to discover than to be told, empirical to rational, and others. The one large application is multiple sense instruction, or the necessity of appeaUng to as many of the senses as possible. Thus in a lesson the orange, the five senses are used as sources of sensuous impression. 70. The principle of motor reaction. — The meaning of reaction is expressed in the maxims ''no impression without expression" and ''every idea tends to reahze itself in action." Happiness is expressed by laughing; grief, by weeping; and the rhythmic sensation of music, by dancing. So, too, every impression in teaching must have its complementary expression through verbal reproduction, written reproduction or material repro- duction as exemplified in the various forms of manual training. A brief explanation of the process is necessary. An external stimulus of any one of the senses is transmitted by the afferent nerve to the brain; if agreeable, the brain will receive the message and then transfer the message PRINCIPLES OF EDUCATION 43 by an efferent nerve to the motor organs. Thus the brain is said to react upon sensations. It is the teacher's duty to present all subject-matter in such a way that each mind can receive favorable impressions. Then the mind will react, i.e., convert the impressions into action and thereby complete the process of getting ideas. James expresses himself thus: Regular response to stirgulation is reaction. Education as a process con- sists in furnishing proper stimulation and in directing the responses. Sensuous impressions are not properly educative if they fail to beget a correlative motor activ- ity. The physiological process is this: (1) impulse from external centre; (2) the translation in the central pro- cess; (3) the changed impulse is transmitted to the motor organ. — Talks to Teachers, Chapter V. Reaction implies a close relation between the phys- ical and the psychical. This relation shows the neces- sity of observing the physical conditions of the child himself, of the school and of the home. Little progress can be made in mental training if the child is hungry, fatigued, ill, or uncomfortable on account of light, heat, ventilation, or seating. 71. The principles of attention and interest. — Atten- tion and interest are so closely related that one cannot persist without the other. Which comes first? Put your thought into practical ways of securing and retain- ing both and then answer the question by interpreting results. Attention is an attitude of mind and body growing out of and enforcing a feeling called interest. Both attention and interest are habits. 72. The principle of apperception. — See definition in section 53. The educative value of a method is tested by the requirements of apperception. 44 METHODS IN EDUCATION 73. The principle of self-activity. — This principle exacts a distinction between teaching and telling. As the strongest impulse or instinct, it offers the largest field for reactions and stands as a law for both pupil and teacher. It is always a varying but true test of the vahdity of methods. 74. Other principles. — The principles or laws of aim, induction, and deduction, analysis and synthesis, are discussed in the chapter on Methods of Teaching. CHAPTER V METHODS IN SCHOOL ECONOMY 75. Meaning. — The rules, regulations, and laws governing the conduct of schools constitute school economy. The word economy implies a minimum of waste and a maximum of achievement. For details of this subject see Shaw's School Hygiene, Morrison's The Ventilation and Heating of School Buildings, Kotelmann's School Hygiene, and Button's School Management. 76. Space. — At least one hundred twenty cubic feet of space should be allowed for each pupil. The general requirements for recitation purposes, physical exercises, coat halls, etc., vary according to local conditions, but convenience and comfort of pupils and teachers are two essentials in all schools. 77. Light. — The light should come from the left hand side and somewhat above the level of the desk. Light from the right hand side causes the shadow of the hand to fall on the pupils' work; from behind, there is a larger shadow from the head and the trunk; from in front, the light is harmful to the eyes and round shoul- ders are caused by the pupils' bending down to avoid the direct glare. As a rule, light is permitted to enter from many parts of the room and then curtains or bhnds are used to regulate the amount and the inten- sity of the light. 45 46 METHODS IN EDCUATION Ventilation The average temperature desired is 64 to 70 Fahren- heit. The aim of ventilation is to remove impure air and replace it by pure warm air. From thirty to fifty cubic feet of pure air per minute are required for each pupil. Some means of securing ventilation from circulation are given in the following sections: 78. Doors and Windows. — To be opened during marching, games, and recreation periods. *' Boards, five or six inches in width, placed under the windows are a well-known device. Still better are hoods at the top of the windows, closely fitting the sash, so that when the windows are open from the top the air is deflected toward the ceiling, and is gradually diffused throughout the room without falling too directly on the heads of the pupils." 79. Air shafts. — Shafts leading from outside the building up through the floor to a height of six or seven feet. This height is required so that no draught will be felt by the children. 80. Indirect method. — By the indirect method fresh air is carried into the building through large ducts, containing stacks of radiating surface, and directly into the rooms through registers which are usually placed near the ceiling. The impure air is carried out through a register usually placed directly underneath the incom- ing air, by means of separate ducts made somewhat larger than those provided for fresh air. Thus a school- room, heated and ventilated in this way, has a volume of fresh air constantly entering the room and an equal volume of impure air constantly passing out. — Button, School Management, page 62. METHODS IN SCHOOL ECONOMY 47 81. Gravity system. — A gravity system is one where the draught necessary for withdrawing the foul air is caused by a heated chimney or duct. In every large building this method is not adequate or reliable, and ventilating fans are used either as a means of forcing the fresh air into the building, or of drawing out the foul air, or both. — Dutton, page 62. 82. Fireplace. — A fireplace is a good ventilator, but not a uniform heater. Seating 83. Adjustable equipment. — Adjustable seats and desks are the best. The seat should be adjusted at such a height that the pupiFs feet will rest on the floor while the legs from the knee to the thigh are at right angles to the trunk. The best adjustable desk has a slant of about fifteen degrees, but it can be raised to a level when necessary. Seats that are not adjustable are usually arranged according to definite sizes. Decoration 84. Relation to school spirit. — This feature of school equipment has much to do with the spirit of the school. The walls and ceiling should be painted in some color restful to the eye. French gray, pale buff, and light green are approved. A few good pictures should dis- place a meaningless collection of cheap prints. Maps, diagrams, and the superior work of pupils are legitimate kinds of school decoration. Some teachers hold that maps, diagrams, and pupils' papers tend to distract the class by inviting attention away from the lessons, but a sounder view is that such diagrams have a high educative value from visualization during those periods 48 METHODS IN EDUCATION when pupils naturally turn from study to relieve their minds. Compare James on mind-wandering, in Talks to Teachers, page 114. Grounds 85. Suggestions from England. — These three para- graphs are quoted from Garlick's, New Manual of Method, page 6. Physical uses. — A playground is the lung of a school. It is as essential to a proper and efficient education as the schoolroom itself. It is the workshop for the manu- facture of the sound body, as the schoolroom is for the sound mind. It offers relief after mental work, and brings into play the overcramped muscles. It is a healthy agency for the overflow of that abundant spon- taneity of child life, which may become so troublesome to discipline if not regulated. Its moral uses. — It brings brightness to the school life and helps to engender a love for school by making it popular. It is a fine training ground for the emo- tions. Boys learn to discipline themselves in their sport, to submit their wills to the will of others. It is a great leveller and compensating force; for the dul- lard may be a physical adept. He wins in the play- ground the respect which he cannot attain in the school; for muscle is worshipped as much as brain. The bully is checked, the timid and shy get nerve and confidence by means of the playground's supervised play. The teacher^ s work. — Gymnastics should be encour- aged by the teacher, and, in the case of boys, a little instruction might be given. Supervision should always be exercised. The presence of the teacher will often tempt a boy to try something which otherwise might be METHODS IN SCHOOL ECONOMY 49 beyond his inclinations. Games calculated to develop their strength, to give muscular control, to aid the growth of the will, such as our popular games, should be encour- aged, sometimes shared, and sometimes directed by the teacher. Many now form and take an active interest in the cricket, football, and swimming clubs of their scholars, and they do not find it unproductive labor. CHAPTER VI METHODS IN SCHOOL MANAGEMENT 86. Opinions. — The worth of another man's opinion depends upon how much use we can make of it. Our own judgment becomes the court of last resort. Indi- vidualism is praiseworthy in an abstract theory of lib- erty, but there are times when the common welfare demands the acceptance of opinions of those who are competent to stand as authority. For this reason we quote certain passages. 87. Principles. — The three essential principles under- lying school management in New York City are definite responsibility, free discussion, and spontaneity and orig- inality. These essentials were stated by Dr. Maxwell and discussed by him in an address in Brooklyn, Novem- ber 18, 1904. See sections 88, 89, and 90. These same principles may be applied in any other school system. 88. Definite responsibility. — ''The first essential is definite responsibility. There should be a definite field of work, and I believe in looking to the person to whom the work is assigned, to do it, and not bother him in the doing. A principal should give definite work to do in the classroom, and should leave it to the teacher to do it, and not keep nagging her to death." 89. Free discussion. — " The next essential is free discussion. If there is any difference of opinion, I believe the question should be freely discussed among 50 METHODS IN SCHOOL MANAGEMENT 51 all grades of officers in schools. By officers I mean the teachers as well as the officers in the Hall of the Board of Education. I have very little use for teachers who come to me and say, 'Tell me just exactly what you would like to have done and I shall endeavor to do as you hke.' I hke to see a teacher who has the courage of her convictions; who is not afraid to tell me what she likes and what she does not hke in the course of study. We are all laboring toward the same end and should be united in the accomplishment of it." 90. Spontaneity and originality. — " Third, I believe in spontaneity and originahty. Here in Brooklyn the teachers worked out many things with me which have been copied all over the country, and in many cases all over the world. Such was the method of studying Evangeline. We devised a way of correcting compo- sitions which would dispense with that most miserable method of teaching, sitting up nights to mark compo- sitions with red ink. Every one helped, and improve- ment was made possible by spontaneity and originality. The essential thing in carrying out the course of study is to make a wise selection of topics. Throw the non- essentials in the subjects aside and teach the essentials. Do not exact memorization of long lists of names which are in themselves meaningless. Two limits we must place on spontaneity and originality. We must not allow a person to be so original as to wish to try some- thing which in the past has proved a failure. We must never allow a teacher to make experiments which are beyond all reason. The development of the human mind is subject to law, and it is the business of the teachers to know the laws governing the development of the human intellect. Too often we do not know how or 52 METHODS IN EDUCATION why certain things are accompHshed, the reason of the method or the object of the work; but in conies the phi- losophy of education to tell us why, to give us the reason, and to hold up before us that high grade of culture and life which it is the object of every good teacher to attain." 91. Qualification of teachers. — Health, scholarship, character, and professional spirit are requisite qualifi- cations of the good teacher. The importance of each of these is not determined by the order stated, nor do we mean to say that other qualities are excluded. Fidel- ity, sincerity, fairness, sympathy, and other particular characteristics deserve discussion, but our limited treat- ment makes the four general qualifications include all such particular indications of merit. 92. Maxwell on marking teachers. — As an illustra- tion of one detailed plan, we give in four sections an outline of an address delivered by Dr. Maxwell, June 5, 1902. How to Estimate a Teacher's Value Teachers deemed fit and meritorious should be marked A or B; all others, C or D. The A mark should be reserved for teachers of conspicuous ability. 93. Important things in teaching ability. 1. Ability to impart knowledge, or power of exposi- tion. Do not do too much. Talking too much is a common fault. 2. Ability to interest pupils. Without interest, teaching fails to become a part of pupil's make-up. 3. Ability to train pupils to good intellectual and moral habits, i.e., character. 94. Signs of poor teaching ability. 1. Requiring parrot-like repetition of text-book. METHODS IN SCHOOL MANAGEMENT 53 2. Most concert recitation is bad. 3. Neglecting pupils' observing and inventing powers. 4. Weak questioning. 5. Neglect in use of object teaching. 6. Waste of teacher's or pupils' time. 7. Rate teacher's scholarship by her mastery of her subject, daily preparation, and interesting application of current events. Rate effort by her activity in school work and by her efforts to improve by study outside of school. 95. Personality of teacher. 1. Neatness and fitness of dress. No place for old society dresses. 2. Pleasing tone of voice and clear enunciation. 3. Sympathy for children. 4. Decision of character. 96. Control of class. — The only control to be marked meritorious is that obtained by interest in the work. Promise of reward, fear and repression deserve C or D. Repeated presentation of dishonest work by pupils is evidence of unfit control. Your general estimate of a teacher's ability need not be an average of your detailed marks. Bear in mind that the object of these ratings is not to fill columns with marks, but to do something to raise the teaching force of the city to a higher plane than it yet occupies. Program 97. Suggestion. — Each school and every class in a graded school should have a daily program posted in a conspicuous place, and that program should be fol- lowed closely. This matter is so important that we think it necessary to give specific reasons. 54 METHODS IN EDUCATION 98. Teaching by suggestion. — When the teacher makes a program, posts it, and adheres to it for all periods of work and recreation, there is a silent sugges- tion for similar order in the life of every pupil. It is indirect instruction; it is suggestion; it is example. The worth of such systematic procedure is valued by pupils, and teachers will soon see that most of the pupils have made a neat copy of the entire program for individual desk use. By using a rubber pen the class program can be made large enough to be seen from any part of the room. 99. The law of habit. — There is no need of blaming pupils for inability to study so long as teachers do not observe the psychological value of habit in studying. If we eat, drink, sleep, or attend to other physical needs at certain times, habit soon becomes so regular that no clock is needed to guide our wants. It is the same in mental habits. The study of mathematics at a cer- tain time puts the body and mind into favorable condi- tions for mathematics at that time every day, and no great variation in time can be safely made. Likewise for each study and for each recreation exercise on the program. 100. The law of change or variety. — A good pro- gram alternates difficult and easy periods, puts memory processes in the morning, and places the shorter periods in the afternoon. This variety is not theory; it is a physical necessity. The problem of fatigue has demon- strated this. * Opening Exercises 101. Justification. — Some teachers think the regu- lar work is so important that no time should be taken METHODS IN SCHOOL MANAGEMENT 55 for morning exercises. This is a mistaken opinion. Ten or fifteen minutes in the morning will do more in the real work of education than hours in the facts of mathematics or grammar. Why? Look back to the purpose of education. The pupils enter school each day well or ill, happy or angry, industrious or mischiev- ous, as the case may be. There is lack of harmonious thoHght and action, lack of bodily and mental poise, lack of self-control. The one thing to do in education is to furnish the environment that will produce the desired conditions of mind and body. Books aside, com- ' fortable position, reasonable silence, respectful atten- tion, — these are conditions required for the morning exercises. These are the conditions that make the school a harmonious unit for the work of the day. Then fol- lows the reading of Scripture or other exemplary books, singing, current events, recitation, declamation, or brief talks by the teacher. 102. Value of habit. — The value of opening exer- cises in arousing a good school spirit is manifest. A second value is in stimulating punctuality. Habit is here a development; it is always so. Personal experi- ence justifies some of the devices for overcoming tardi- ness. The aim is to get the pupils to school in time once so that the process of habituation may be started. Make the pupil conscious of that one success by commending him. Then try some of the motives and means men- tioned in the following sections. 103. Memory gems. — Have a short, pleasing mem- ory gem on the board. Have pupils read it together, learn it together, and repeat it together. Social stim- ulus in this. Learn one or two each week. 56 METHODS IN EDUCATION 104. Desire. — Read a portion of an interesting story two or three times a week. This arouses desire to hear more. 105. Interest in songs. — Sing the old home songs occasionally. Let pupils select the songs. 106. Expectancy : declamation. — Have a short reci- tation or declamation occasionally. Put title and name of pupil on the board the day before, or simply announce that some one will recite. 107. Monitors. — Appoint tardy pupil a monitor to act before school calls. He will be present. 108. Motives. — Organize for marching, athletics, memory selections, singing, perfect attendance, — some- thing that will arouse class spirit in working under a motive. 109. Anecdotes. — Read or relate an anecdote giv- ing the value of punctuality. Exalt the positive, the good; don't preach about the defects. '' My cook," said Washington, "never asks if the visitors have arrived, but if the hour has arrived." 110. The teacher an example. — Teacher always punctual. Have a program and always follow it. 111. Honor roll. — Roll of honor for good attendance. 112. Fellowship. — The school is a social unity and every person in it owes a duty. Think, feel, and act so that no one can assume the right to be tardy. 113. Our platform. — The selection of memory gems is matter that must be determined by the actual needs of the pupils. The platform given below has satisfied thousands of pupils. The use of the word platform invites a comparison or analogy; use civics and history in discussing party platforms. METHODS IN SCHOOL MANAGEMENT 57 Our Platform 1. The only way to have a friend is to be one. — Emerson. 2. Be not simply good, be good for something. — Thoreau. 3. No one can disgrace us but ourselves. — J. G. Holland. 4. Heaven never helps the man who will not act. — Soyhodes. 5. People do not lack strength; they lack will. — Victor Hugo. 6. It is well to think well; it is divine to act well. — Horace Mann. 7. Whatever is worth doing at all is worth doing well. — Chesterfield. 8. Things don't turn up in this world until somebody turns them up. — Garfield. 9. He that is good at making excuses is seldom good for anything else. — Franklin. 10. I hate to see things done by halves. If it be right, do it boldly; if it be wrong, leave it undone. — Gilpin. 11. The chains of habit are generally too small to be felt till they are too strong to be broken. — Samuel Johnson. 12. Our greatest glory consists not in never falling, but in rising every time we fall. — Goldsmith. 13. He that avoideth not small faults, by Httle and little falleth into greater. — Thomas d Kempis. 14. It requires a good strong man to say: ''I was mistaken, and am sorry." A weak man hesitates and often fails to do the right thing. — Franklin. 58 METHODS IN EDUCATION 15. Labor to keep alive in your breast that little spark of celestial fire called conscience. — Washington. 16. There are two freedoms — the false, where a man is free to do what he likes; the true, where a man is free to do what he ought. — Charles Kingsley. 17. Let us have faith that right makes might, and, in that faith, let us to the end dare to do our duty as we understand it. — Lincoln. 18. Some temptations come to the industrious; but all temptations attack the idle. — C. H. Spurgeon. 19. Look not mournfully into the Past; it comes not back again. Wisely improve the Present; it is thine. Go forth to meet the shadowy Future, without fear, and with a manly heart. — Longfellow. 20. Lord of the Universe, shield us and guide us. Trusting Thee always through shadow and sun! Thou hast united us, who shall divide us? Keep us, oh keep us, the Many in One. — Oliver Wendell Holmes. 114. Grading. — The purpose of grading comprehends the welfare of the school, the teacher, and the pupil. For the school, grading is required as a means of adjust- ing work in the organization or the system. For the teacher, grading establishes a limit for the scope of the teaching. For the pupil, grading is intended as adapta- tion so that a maximum of progress may be guaranteed. The defects to be avoided are too rapid advancement, tardy advancement, and rigid systems not permitting adaptation to the needs of the pupil. 115. Promotion. — Two aims in promotion are to advance pupils as rapidly as their attainments will permit, and to maintain a standard of approximate uniformity of attainment in the grade. Further con- sideration will be found in the next ten sections. METHODS IN SCHOOL MANAGEMENT 59 116. Class teaching. — In our elementary grades there is much discussion about the relative merits of individual and class teaching, the effectiveness of group teaching, the practical apphcation of the Batavia plan and its usefulness in solving the difficulties of promotion, and, lastly, the separation and the special methods of instructing defective children. This section is inserted he^e to direct the attention of teachers to these topics. During any recitation period, is the class taught as one unified grade capable of understanding the teacher's presentation? Or, must each class be divided into groups and each group taught separately? Or, must a certain amount of individual teaching be done? Take individual and class instruction, for instance, and you will find that some educators say that the one cannot exist without the other, and that there are no serious difficulties arising under either if the teacher satisfies the ordinary conditions of teaching. This is a suggestive topic for students and we offer as a point of view that no matter how good the teaching may be, there will be some pupils who will present the necessity of individual instruction, either in or out of class. 117. Group teaching. — Group teaching is not new, although it is so considered by some educators. It means nothing more than dividing the class into groups, according to ability, so that three groups, for example, shall be working on three respective kinds of assignment at the same time during one period. The teacher may be giving oral instruction to one group, while the other two are engaged in written exercises. This plan pro- motes adaptation of matter to the needs of the pupil, and so it becomes only a special illustration of one of 60 METHODS IN EDUCATION the many characteristics of good teaching. Dr. Max- well's arguments in favor of group teaching are given in sections 118 to 125 inclusive. Arguments for Group Teaching 118. General use. — It is now in general use in other cities — a strong presumption in its favor. 119. Adapted to each pupil. — A teacher having, say, only fifteen pupils out of forty-five recite to her at one time is better able to distinguish the individual peculiar- ities of each pupil. 120. Vigorous teaching. — The teacher being com- pelled to divide the recitation for each subject into three periods is constrained to conduct the recitation in a vigorous manner. She is forced to avoid the two most serious errors into which teachers fall in the conduct of a recitation: requiring children to recite verbatim, and talking too much themselves. 121. Study periods. — Each pupil has abundant time in which to study in school. Complaints of overwork and excessive home study have practically disappeared wherever the group system is adopted. 122. Concentrated attention. — The pupil learns not only to study, but to inhibit and concentrate his atten- tion — an invaluable experience for practical life. 123. Promotion facilitated. — A pupil may be pro- moted just as fast or just as slowly as he ought to ad- vance. A pupil may be advanced from one group to another group within a grade; or promoted from one grade to another at any time in the term, without skipping any essential part of the work. 124. No tiresome repetition. — One division should always be composed of pupils advancing more rapidly METHODS IN SCHOOL MANAGEMENT 61 than those m the other, so that the teacher will not be compelled to repeat the same lesson on the same day. 125. Difficulties and advantages. — The difficulty is to find profitable employment for the section or sections not having the oral lessons. Many teachers cannot teach unless every child's eyes are fixed on them. They cannot see that more than a minute of this kind of so-called attention is bad for the child. Some teachers fincl the system hard because they give three-fourths of their attention to the groups not reciting, trying to keep them " in order " and not realizing that more free- dom should be allowed children who are working by themselves as individuals. Some teachers believe that we divide classes only because the children have differ- ent attainments. They do not understand that we divide classes in order that the nervous strain on the children may be lessened, that they may feel that they are individuals, that they must not waste their time waiting for fifty to get a chance to read aloud or to spell or to compute, and. that they may have time to study. 126, Individual teaching. — No matter what devices or methods or novelties may be advocated, the process of true teaching remains a personal relation between the teacher and individual pupils. The most success- ful class or group teaching is that in which the individ- uals in the class or group are able to put their minds into sympathetic communication with the teacher's mind, or vice versa. When the successful pupils have passed along with the satisfaction of a good degree of mastery, slow or defective pupils remain for individual teaching to give them the right of promotion. When any pupil fails to understand the instruction, when 62 METHODS IN EDUCATION disorder interferes with the smooth course of teaching, when illness or other valid excuse causes absence, then there must be a personal meeting of the minds of teacher and pupil to restore conditions to a normal standard of efficiency. So under all circumstances it is safe to argue that individual teaching is the largest factor in the school education. 127. The Batavia plan. — The Batavia plan derives its name from Batavia, N. Y., where it was devised and put into successful operation by Superintendent John Kennedy. This plan of teaching combines the best features of class instruction, group teaching, and indi- vidual teaching. The classes are divided into groups according to ability and two teachers are at work at the same time in the same room. One teacher is carry- ing on the regular work of the grade with the larger part of the class, while the additional teacher is instruct- ing one or more of the backward pupils. As soon as any pupil is capable of doing the next grade work, a promotion is made, no matter what time of the term it may be. This plan of promotion is used all through the elementary schools, and it is found that most of the defects in the ordinary systems of grading and promo- tion have been overcome in the schools of Batavia. Attention is directed to the special value of the individual instruction under the Batavia plan. Examinations 128. For pupils. — This topic relates to the examina- tion of pupils although there is equal interest in the nature of examinations prescribed for teachers. A discussion of examinations for pupils is outlined in the next five sections. METHODS IN SCHOOL MANAGEMENT 63 129. Methods of conducting examinations. 1. By written tests. 2. By oral tests. 3. By combination of 1 and 2. 130. Advantages of written tests. 1. Self-realization, independence. 2. Habits of industry in preparation. 3. Basis of comparative valuation from time to time. 4. Apperception, composition, correlation. 131. Disadvantages of written tests. 1. Not an accurate index of psychical progress. Other conditions — nervousness, lack of facility in ex- pression, etc. — are too strong. 2. Too much time required from pupils and, later, from teachers. 3. Cramming. 4. Mental deceit: word vs. content. 132. Advantages of oral examinations. 1. Time saved. 2. Personality of pupil and teacher united — real teaching. 3. Practical preparation for life. Oral expression, prompt decision, co-ordination of mental powers. Habit. 4. Attention and interest. 5. Adapted to individual needs. 133. Disadvantages of oral examinations. 1. Time lost unless teacher is apt. 2. Effects are transitory. 3. Tends to guessing. 4. Do not sustain class concentration. 134. Reviews. — The lack of systematic and thorough reviews is one of the most serious defects in modern education. In their anxiety to cover the prescribed 64 METHODS IN EDUCATION work, teachers devote most of the time to the presenta- tion of new matter and then pupils are expected to do the extra review and drill work outside of the recita- tion period. A safer plan is to devote at least two-thirds of the school time to drill or review work; the other one- third will be sufficient for presenting the advanced les- sons. The general characteristics of reviews may be considered under the headings in the outlines given in the last section. 135. Home lessons. — It is said that there are five institutional factors in education: the home, the school, the church, the state, and the vocation. The effort to make the home and the school harmonize in relation to lessons assigned in school to be mastered at home is one unsettled problem in elementary and high school work. Many parents object to the assignment of home work on the grounds (a) that it is shifting responsibil- ity from the teacher to the parent, and (6) that overwork is likely to produce fatigue. The teachers, on the other hand, answer (a) that the school hours do not give time to cover the required work, and (h) that the habit of independent work is essential in the education of the pupil. For convenience in presenting a liberal view, both affirmative and negative, an outline is submitted. 136. Advantages of home study. 1. Habits: obedience, industr}^, self-activity. 2. Criterion: honest work is an index of pupil's power. 3. Co-operation: parents become interested. 4. Review: valuable impression and expression of recitation work. 5. Protection: keeps pupils at home. 137. Disadvantages of home study. 1. Habits: incorrect work bad in effect. METHODS IN SCHOOL MANAGEMENT 65 2. Not a criterion: too much dishonesty. 3. Friction: some parents disapprove. 4. Fatigue: due to overpressure. 5. Recreation: pupils need outdoor exercise. Moral Education 138. A contribution from New York City. — These sixteen sections are taken verbatim from The Course of Study, 1905. 139. Moral Aim. — It should be the aim of teachers and principals to make the life of the school, in every activity and relation, count for moral education. This aim should vitally affect not only the teaching of every subject and the treatment of every problem of discipline and training, but also the general atmosphere and spirit of the classroom and of the school. In working toward this aim, the following suggestions will be found useful. 140. Personality of teacher. — The personality of the teacher is at the root of all moral education in the school. The teacher's voice, speech, bearing, and dress; the teacher's poise, self-control, courtesy, kindness; the teacher's sincerity, ideals, and attitude toward life, are invariably reflected in the character of his pupils. 141. Reverence. — Reverence is vital to morality. Whatever quickens in children the feeling of dependence on a Higher Power; whatever leads them devoutly to wonder at the order, beauty, or mystery of the universe; whatever arouses in them the sentiment of worship or fills them with admiration of true greatness, promotes reverence. There is no subject studied in school which, reverently taught, may not yield its contribution to this sentiment. 142. Self-respect. — Self-respect, which is also fund- 66 METHODS IN EDUCATION amental to moral development, is engendered in a child when he does his best at tasks that are worth while and within his power to do well, with proper recognition by teacher and school-fellows of work well done. 143. Principle in character. — The corner-stone of a self-respecting character is principle — the will to be true to the right because it is right, whatever the conse- quences, to act with firmness in the right as God gives us to see the right. The essential difference between principle and mere self-interest should be vividly brought home to each child. 144. Spirit of school. — The spirit of the classroom and of the school — the spirit that makes children say with pride ''my class" and '^ our school" is one of the strongest of moral forces. Where there exists a proper esprit de corps, the problem of discipline is largely solved. Public opinion as a moral force should be moulded and utilized in every school. 145. Social membership. — The child should early gain the idea of social membership. The truth that co- operation and unselfishness are essential to true social living should be made real and vital. This truth is brought home through ''group work" where the work of each is necessary to the work of all; and through the feeling in a school or class that the honor of all is in the keeping of each. The child should also learn that he is a meml^er, not only of the school, but of the family, of the neighborhood, of the city, and of the state and nation. What it means to be a loyal member of these social institutions should be made clear. The naturalness and the necessity of obedi.ence and of helpfulness should be shown. The moral aspect of home tasks, and of working with the METHODS IN SCHOOL MANAGEMENT 67 departments of health, parks, street cleaning, police, and education, and not against them, should be enforced by concrete appUcations. In general, the truth should be impressed that without loyal and effective social membership no individual can lead a complete life. 146. Self-government. — No person has a fully devel- oped moral character until there has been a transfer of the seat of authority from without to within himself; a moral man obeys himself. Each child in every grade should be steadily helped towards self-direction and self- government. Effective means to this end are: appeals to initiative and resourcefulness; the development of such a sense of honor as will preserve order without surveillance; and some form of organization designed to quicken and exercise the sense of responsibility. To trust a child tends to make him trustworthy. A system of pupil self-government, if wisely applied and not en- cumbered with unnecessary machinery, may be found effective. The form, however, of the organization is immaterial. The essential point is that the teacher, himself a member of the community, should make his pupils sharers to a certain extent in the problems arising out of their community life; and that he should intrust to them as members in their own right of the social body the performance of certain functions. Such training in social activity is effective training for citizenship. Under such conditions ''good order" will mean not so much the refraining from disorder as the condition of effective co-operation. 147. Moral values of studies. — Each school study has a specific moral value. Literature and history em- body in concrete form moral facts and principles, show- ing to the child his own self ''writ large," furnishing him 68 METHODS IN EDUCATION with ideals and incentives, and moulding his moral judgment; and they will accomplish these results the more surely as the teacher is himself moved by that which is presented. Every subject involving observation and expression is essentially moral. Every subject, there- fore, should be so taught as to make for truth-telling in word and act, and for training in self-expression. 148. Contemporary civilization. — In connection with the regular studies of the school, such aspects of con- temporary civilization as are of value for developing the social spirit should receive attention. Hospitals, societies for the prevention of cruelty to children and to animals, homes for orphans and for the aged and infirm, fresh air funds, and similar agencies for social service should be brought within the child's compre- hension as opportunity offers. Deeds of heroism and self-sacrifice done by firemen, policemen, soldiers, and other persons, should be presented and commended. The truth that success in life means more than mere money-getting can thus be brought home again and again. The contemplation of deeds of cruelty, dis- honor, and shame has a necessary, though subordinate, place in moulding moral taste. 149. Topics for moral lessons. — The following list of topics affords subjects for many practical lessons in morals and manners: 1. Duties to parents, brothers, sisters, and playmates; to servants and other employees; to employers and all in authority; to the aged, the poor, and the unfortunate. 2. Conduct at home, at the table, at school, on the street, in public assemblies and in public conveyances. 3. The common virtues, such as regularity, punctual- ity, self-control, cheerfulness, neatness, purity, temper- METHODS IN SCHOOL MANAGEMENT 69 ance, honesty, truthfulness, obedience, industry, and patriotism. Principles of Moral Instruction 150. Development. — The course of moral training is a development, in which the child is first led to act rightly and afterward to work from principle; he pro- ceeds from obedience on faith to obedience on principle; frmn regularity to faithfulness. The child also develops from egoism to altruism. His impulse toward self- interest normally develops earlier than his impulse to put himself in another's place. Upon the full develop- ment of the former stage depends the full development of the latter. 151. Cultivation of imagination. — The culture of the imagination is a powerful aid in moral instruction; first, as the power vividly to picture consequences — to put yourself in your own place later on (foresight); secondly, as the power to ''put yourself in his place" (social imagination, sympathy). 152. Employ self -activity. — In using literature and similar material for purposes of moral education, the teacher should not violate the law of self-activity. The child may resent having a moral drawn for him which he can draw for himself. He is the more likely to follow the principle which he himself discovers or formulates because it is his own. 153. Positive vs. negative. — The most effective method in moral education is positive rather than nega- tive. A mind filled with worthy interests, high ideals, and helpful activities has no room for evil. Approba- tion more than censure leads to well doing. Love is a stronger and a better motive than fear. 70 METHODS IN EDUCATION 154. Supremacy of law. — At every stage of school life pupils should be taught that they live under inexor- able laws which they cannot violate with impunity — both physical laws and moral laws. Obedience is not optional: it is compulsory. Penalty follows law-break- ing as surely as night follows day, though the penalty is not always immediate. 155. Discipline. — Discipline in school management has reference to mental, moral, and physical training that tends to secure the self-control of individuals. The general use of the term discipline in regard to human faculties means training that enables a faculty to do more efficient work than it would have been able to accomplish without the discipline. So in a larger sense disciphnary school management aims to develop all the useful characteristics of good citizenship. 156. Authority. — There are writers and teachers who hold that respect for authority is not an American ideal. We do not agree. Constituted authority, wher- ever it may be, deserves constant recognition and respect- ful obedience. Authority is not tyranny; it is a natural and necessary guarantee of order in moral, religious, and civil life. The largest development of individual freedom is impossible Avithout some accepted standard of authority. Pupils should be taught, then, that it is their duty to respect and obey the authority in the school, in the home, and in the community. 157. Co-operation of parents. — In another section of this chapter we have spoken of the five institutional factors in education. One aim of ideal training must always be to get those five factors into harmonious co- operation. It is not always possible to secure such assistance outside of the home, but it is possible to bring METHODS IN SCHOOL MANAGEMENT 71 the parents into close touch with the actual needs of the school. This may be done by correspondence if it is not convenient to have personal consultations in the homes of the pupils. A visit has many advantages over correspondence because it is possible for pupils, teachers, and parents to meet in common and establish a balance of opinions relating to favorable and unfavor- able work in the school. A third means of getting into toiTch with parents is patriotic exercises or other school entertainments. The natural interest in the welfare of the pupils on such occasions is the strongest inducement to parents to present themselves at the place where the entertainment is to be held. Other means of becom- ing acquainted are found in . churches, local societies, and other established means of social intercourse in the community. Punishment 158. Definition. — Punishment is a penalty for the violation of the rules of order. The old idea of punish- ment embodied the necessity of giving the pupils an equivalent for the wrong that had been done. The modern view of punishment looks to the reform of the pupils through the cultivation of desirable habits of activity. The tendency in theory and practice is against cor- poral punishment. What, then, can be substituted? As some penalty is in accordance with the supremacy of law, as expressed in section 154, we shall discuss some approved kinds of punishment. 159. Detention. — The practice of keeping pupils in the schoolroom at recess, during part of the noon or after school, has the approval of many educators 72 METHODS IN EDUCATION although it is severely condemned by others. The loss of pleasure seems to be the basis of the punishment. One serious objection to detention is on the physical side. If the pupils were allowed the privileges of phys- ical exercise during the recess periods, it is probable that some of the sources of disorder would find a natural outlet in the games. The pupil who is detained is not likely to be in a frame of mind suitable for continuing the work of the day after his companions return to the classroom. For these reasons detention cannot be widely approved as a form of punishment. 160. Assignment of extra tasks. — The aim of this kind of punishment seems to be the development of intellectual power through the extra work. It is implied that the mental training will ultimately direct the child into points of view that will cause him to desist from further wrong-doing. On the other hand, the imposi- tion of extra school work is likely to lead the child to dislike that kind of work and also to form habits of care- lessness in performing the assignment. 161. Demerit marks. — This penalty assumes that pupils are ambitious to secure high standings as an indi- cation of proficiency. Some pupils do have such ambi- tions, but their ambitions are easily crushed as soon as one demerit mark appears upon the record. Other pupils care nothing for marks of that kind and so the punishment is wholly external and has little or no effect upon them. 162. Expulsion. — This should be used only as an extreme means of settling the difficulty. Expulsion is justified only when the pupil reaches a state of rebellion which cannot be treated without an injury to the class or to the school. Then it is considered prudent to METHODS IN SCHOOL MANAGEMENT 73 remove the pupil from the presence of his companions. An adverse view of expulsion Hes in the fact that the child expelled is to be at hberty in the community and his idleness is hkely to lead to the development of bad habits. The relation of idleness and crime shows the futility of expulsion as a form of punishment in any community. 163. Incentives. — The ordinary incentives are marks for* scholarship or conduct, prizes, decorations, school privileges, and public commendation. Some of these are forbidden in certain school systems because of the difficulty in doing justice in selecting the best pupils, or because such distinction tends to develop egotism and selfishness in place of altruistic virtues. These incentives are called artificial. In contrast to the artificial incentives are the natural incentives. The latter are respect for teacher, respect of class, school spirit, sharing school privileges, and per- sonal satisfaction in doing one's duty. These are natural because they are human. Each incentive develops a stronger feeling between the pupil and some other mem- ber of the school. The benefit is the consciousness of personal power growing out of self-activity. Notice how the community interest promotes attention, inter- est, and activity. 164. Self-government of pupils. — All education aims at self-government of the pupils. The specific use of the word here relates to the various forms of pupil gov- ernment, in which the pupils themselves participate in the legislative, the executive, and the judicial depart- ments of school organization. In each system of this kind, the government is a republic. The School City and the School State are common forms. 74 METHODS IN EDUCATION 165. Public opinion in school. — Disorder in school is sure to arise if confidence is not established in the motives of the teacher and of the pupils. It is a mis- take for a teacher to think that a large number of pupils hke to do wrong; and it is unfortunate for pupils if they cannot consider their teacher a friend. The establish- ment of mutual confidence, the pleasure of morning exercises, the satisfaction of success in the studies, the interest in rhetorical exercises, and the fellowship of the school grounds and the afternoon walks, — all these will tend to develop a healthy public opinion in school. 166. Evils. — Such school evils as carelessness, lazi- ness, tardiness, truancy, whispering, lying, cheating, stealing, impudence, and rebelUon should be displaced by desirable habits. Repression is only a temporary suspense; substitution is the sound process. 167. Virtues. — The desirable habits to be substi- tuted in section 166 are accuracy, industry, neatness, pohteness, truthfulness, honesty, justice, punctuahty, co-operation, and obedience. The substitution is a matter of gradual habituation. 168. Affiliated interests. — In speaking of natural incentives, in section 163, we referred to the sharing of school privileges. Such privileges are found in the affiliated interest which serve as useful means of educa- tion in addition to the work of the recitation. The vari- ous athletic interests, the debating clubs, the school paper, the musical and dramatic associations and the alumni associations are all helpful in keeping a strong school spirit. 169. Adolescence. — Independence is a mental char- acteristic of adolescence. Management during this period is guidance. Follow these suggestions: METHODS IN SCHOOL MANAGEMENT 75 1. Environment must be adapted to pupil rather than vice versa. 2. Physical health is a predominant consideration. 3. Pupils need direction and inspiration rather than ponderous knowledge. 170. Fatigue. — During adolescence growth is so rapid that strength is not constant. In younger chil- dren, fatigue is produced by other causes. So far as fatigue relates to management, it shows the necessity for finding and removing physical causes of disorder. 171. Devices in management. 1. Use quotations. See Our Platform, section 113. 2. Ask pupil to write an opinion of his own case. Furnish two or three questions to guide him. Assign to be done at home.. This causes introspection. 3. Have pupils write a letter of advice to themselves. They will unconsciously expose their own weaknesses. This aid will show what treatment is best. 4. Ask pupils to write a letter of advice to the pupils in the class one grade below. This work will bring out virtues and vices under the pupils' point of view. 5. Assign a composition on '' My Favorite Teacher." The literary merit may be less interesting than the enu- meration of certain characteristics not admired in the teacher who assigned this theme. But whatever the opinions may be, this device is one more way of helping pupils to the habit of justly measuring themselves in relation to others. CHAPTER VII METHODS OF TEACHING 172. Definition. — By method is to be understood that body of principles drawn chiefly from a sound psychology, which are applicable to all teaching; by methods are to be understood the special plans and de- vices to be used in teaching a particular branch or sub- ject. — Roark, Psychology in Education, page 267. A method of teaching is a series of teaching acts so arranged as to attain a definite end or result. — White, Elements of Pedagogy, page 137. Method is a guidance of the process of adapting cul- ture material to the needs of the child. — Monroe, Text-Book in the History of Education, pages 749-759. Thus we see t^hat in speaking of method or methods in education, we must consider an orderly procedure determined by three factors — the teacher, the nature of the subject-matter, and the needs of the pupils. The procedure is not so changeable as a manner nor so narrow as a device; it is as broad as the nature of child- hood, as fixed as the laws of race development, and yet as flexible as the needs of individuals. Methods should be thought of as a process embodying the blended move- ments of the minds from definite stages of development toward the ultimate possibilities in life. Thus we can set aside the old conception of method as a rigid stand- ard to which all pupils must conform, and in its place 76 METHODS OF TEACHING 77 establish the pedagogical ideal of method as a guiding process that stimulates initiative, enlivens motive, and directs all activities toward desirable habits for life. 173. Classification. — The attempt to classify methods of teaching under twenty headings is a source of con- fusion in theory and practice. The real difficulty hes in the fact that so many teachers think that each classified kind is a distinct method of teaching. While thts misconception may be removed after a few terms in the schoolroom, is it not economy for a young teacher to know at the start that one recitation may include all the known methods? In other words, tact fits the need. If we emphasize six kinds as comprehensive, all the other kinds can be subordinated. The six are analytic, synthetic, inductive, deductive, topical, and Socratic. A better classification, but somewhat in advance, is these four: analytic-synthetic, inductive-deductive, top- ical and Socratic. The full list is given, however, so that students may suit themselves. 174. Conversational method. — This method is a natural intercourse between teachers and pupils. While its use is generally restricted to lower primary grades, it may be used in higher work. Its success depends largely upon the personality of the teacher. Speaking in ordi- nary tones is an indication of natural poise, and pupils will gladly adapt themselves to similar phases of think- ing and doing. It is a method that inspires confidence, invites co-operation, and makes the educative process a matter of personal communication between teacher and pupil. It was the method of Pestalozzi, Froebel, and Colonel Parker. It is frequently called a dialogue method. 175. Development method. — This is another dia- logue method whose use extends over the whole field 78 METHODS IN EDUCATION of education. It is especially adapted to early informa- tion lessons which aim at clear concepts and easy expres- sion. Its aim is to develop right habits of thinking; and by the use of suitable material, the child's interest is aroused so that the matter, the method, and the result have educative value. A further study of methods will show that this method really includes many others, such as, particular to general, known to related un- known inductive-deductive, etc. You will see that these methods shade into one another; they are not so many distinct methods. Caution. — Do not try to develop everything. If pupils give you the answer before you are half way along in your place of development, don't deaden their inter- est or waste your time by completing the developing process on that lesson. 176. Lecture method. — This is useful in intermediate and higher grades, especially where the matter is brought up for discussion and other reproduction in succeeding recitations. A kind of lecture or monologue method is required in all primary classes before text-books are introduced. Narration, description, explanation, and definition are given by the teacher as models for imita- tion and reproduction. But let it be understood that the lecture method, strictly interpreted as a lecture, is suited only to mature minds. Questioning 177. Bases. — The attempt to classify questions under the headings development, drill, review, examina- tion, etc., is putting considerable value upon external form again. There are differences, of course, but the tactful teacher may use all these kinds of questions in METHODS OF TEACHING 79 any one lesson, even though the lesson is strictly a devel- opment lesson. If sound methods of teaching must always depend upon three factors — teacher, lesson, pupil — then sound questioning depends upon these same three factors, and the teacher will adapt the questions to the needs of the children. 178. Consecutive questioning. — This plan follows the order of seating or roll. The advantage is economy of time, and this advantage is potent under a strong teacher. The disadvantages are inattention in class and possible lack of preparation of assigned work, especially by the pupils who can foresee their exemption from obligation to recite. These adverse criticisms presuppose a lack of working spirit in the class and a certain defect in the teacher. 179. Promiscuous questioning. — This method of questioning is that in which the teacher does not follow order in seating or the order of the roll, but calls from different parts of the room as his fancy dictates. The advantage of this method is said to be in the fact that no pupil knows when his turn will come and so all are pre- sumed to be giving attention. The fact that a pupil has recited does not justify him in thinking that he will not be called a second or a third time. The disadvan- tage in the method lies in the loss of time in calling the names, in the exemption of certain lazy pupils, and in the probability that the best ones in class will be called upon more than those who do not show the same amount of eagerness to recite. 180. Simultaneous questioning. — The simultaneous method of questioning is that in which questions are directed to the whole class and pupils are given time to think what the answer will be. Then the whole 80 METHODS IN EDUCATION class or one pupil may answer the question while the others are thinking or answering with him. The advantage of this method is said to be that the atten- tion and the interest of all pupils are held during the time of asking the questions. In those cases where it means concert recitations it is possible that a large number of the pupils are not giving the required thought, attention, and answers as the general tendency seems to indicate. 181. Development questions and review questions distinguished. — Development questions require more time in asking and answering; the order is generally log- ical; the answers are in complete statements. Review questions are rapid; not necessarily in logical order; answers may be brief. 182. Rules. — A few rules for questioning will not be out of place. They may be stated as positive or negative rules. 183. Positive rules. 1. Questions should be adapted to the powers of the pupils. 2. The wording of the question should be simple, clear, specific. This rule is opposed to puzzles, vague questions, double questions, universal questions. 3. The order of the questions should be determined by the law of successive clearness. Questions logically arranged are not always suited to the child's mind. Question to promote progressive clearness in the child's thinking. 4. Make the question as short as clearness will per- mit. 5. Question to impress what the children know, not what they don't know. METHODS OF TEACHING 81 184. Negative rules. 1. Do not end a question with what. 2. Do not ask questions that allow a choice of answers. 3. As a general rule, do not ask questions that can be answered by yes or no. 4. Do not ask a question that suggests the answer. 5. Do not abuse the use of personal pronouns in questions. 185. Weak questioning. — Some questions to be avoided may illustrate the rules under sections 183 and 184. 1. Vague questions. How was the battle of Gettys- burg fought? 2. General questions. What do you think I saw on my way to school? 3. Obscure questions. Cain you comprehend the complexity of civilization? 4. Double questions. Where was Taft born and what service did he render in the Phihppines? 5. Universal questions, similar to general questions. Where is London? 6. Involved questions. Considering the facts in the Missouri Compromise, can you, a student of modern civic problems, trace the results in relation to the prin- cipal causes? 7. Direct questions. Was Burgoyne successful at Saratoga? 8. EUiptical questions. The best kind of questions is—? If any omission in a question causes a pupil to give more energy to the meaning of the question than to the answer, the question is defective. On the other 82 METHODS IN EDUCATION hand, alertness may be stimulated by ellipses in rapid review questions. 186. Socratic method. — This method is a specific kind of questioning. As used by Socrates, it was con- versational in tone. He elicited statements from others by two kinds of questions: one to convince of error; the other to develop truth. Socrates was questioning the Sophists who assumed to be masters of all knowledge and so the first part of the Socratic process was destruc- tive and ironical. Its purpose was to overthrow and ridicule the wrong opinion held by the pupil. The sec- ond part of the process was directing the mind by its own activity toward the truth, and preparing the mind to recognize and accept the truth. 187. Value of the Socratic method. — The Socratic method accepts the pupil's point of view in thought and language; it keeps within the scope of the pupil's comprehension; every movement in thought necessi- tates self-activity of the pupil; it leads into a discovery of the new viewpoint, but it does not tell; it leaves the pupil at the threshold of truth, but does not force him to accept it. It is conviction through directed activity. Sometimes called maieutic, i.e., giving birth to ideas. 188. Irony in Socratic method. — Irony cannot be safely used in teaching. Encouragement, not sarcasm, is what the average pupil needs. 189. Limitations in use of Socratic method. — The Socratic method is adapted to all knowledge in which the pupil's experience is sufficient to enable him to reach the truth. Beyond this Umit it is not useful. 190. Illustration of Socratic questioning in mathe- matics. Meno. Socrates, we come to you feeling strong and METHODS OF TEACHING 83 wise; we leave you feeling helpless and ignorant. Why is this? Socrates. I will show you (calling up a young Greek and making a Une in the sand). Boy, how long is this line? Boy. It is a foot long, sir. Socrates. How long is this Une? Boy. It is two feet long, sir. Socrates. How much larger would be the square constructed on the second Une than on the first line? Boy. It would be twice as large, sir. Under the direction of the boy, Socrates constructs two squares on the sand, thus: Socrates. How much larger than the first did you- say the second square would be? Boy. I said it would be twice as large. Socrates. But how much larger is it? Boy. It is four times as large. Socrates. Thank you, my boy, you may go. Meno, that boy came to me full of confidence, thinking himself wise. I told him nothing. By a few simple questions I led him to see his errors and discover truth. Though really wiser, he goes away feeling humbled. 84 METHODS IN EDUCATION 191. Illustration of Socratic questioning in grammar. — Take a familiar answer in sixth grade grammar, using this sentence: Lincoln was very kind to children. Teacher asks a class to tell part of speech of every word in the sentence. A pupil says very is an adjective. Teacher. You say very is an adjective. Pupil. Yes, very is an adjective. Teacher. Why do you call very an adjective? Pupil. Because very modifies an adjective. Teacher. What adjective does very modify? Pupil. Very modifies the adjective kind. Teacher. You have told me the use of the word very. After finding the use what led you to say adjective? Pupil. I thought of the definition of an adjective. Teacher. Give that definition. Pupil. Anything that modifies a noun or a pronoun is an adjective. Teacher. What noun or pronoun does very modify? Pupil. No noun or pronoun. Kind is an adjective. Teacher. Now, what is your conclusion? Pupil. Very is not an adjective. Teacher. Then what part of speech is it? Pupil. Anything that modifies an adjective must be •an adverb; hence, very is an adverb. 192. Another illustration of Socratic questioning. — Teacher. Define a straight line. Pupil. A line that doesn't slant. Teacher. Draws slanting line on board. Is that a straight line? Pupil. Yes. # Teacher. Does it slant? Pupil. It does slant. Teacher. What is the matter with your definition? METHODS OF TEACHING 85 Pupil. It is not accurate. Teacher. Why not? Pupil. A straight hne may slant and still be straight. Teacher. Correct your definition. Pupil A straight line is the shortest distance between two points. Answers . 193. The kind wanted. — The kind of answers given by pupils will depend largely upon the nature of the questions asked by the teacher. When all the condi- tions are adjusted to insure a fair amount of effort, the answers are an indication of intellectual progress. We shall discuss this topic under four headings. 194. The educational value of answers. — The test can be found in the methods of mind training treated in chapter IV. A good answer is evidence of clear per- cepts, serviceable memory, good concepts, and some application of judgment and reasoning. Furthermore, a good answer is evidence of attention; it may indicate interest; it must utilize apperception; and it requires self-activity. One good answer is the beginning of habituation. Other good answers will, of course, tend to fix desirable habits of mental activity. 195. Characteristics of good answers. — From what has just been said it is evident that a good answer re- quires the child to do some thinking. He must think to get a correct interpretation of the teacher's question and he must think again to furnish material for his own answer. Then follows another quality, namely, the use of good language in clearly expressing the answer. 196. What answers should be received. — First, the good answers just characterized; second, answers which 86 METHODS IN EDUCATION are partially correct providing there can be a division made in the answer required. This view is the one that gives credit for all that the pupil is able to do. The third kind of answer to be accepted is the one that is evidence of fidelity on the part of the pupil. The answer may not be correct, but the effort to make a correct answer deserves some commendation. Strictly speaking, a correct answer is the only one that can re- ceive full credit in the recitation, but as the process of teaching does not expect a satisfactory answer to every question, it is suggested that the other two kinds of answers receive some credit as the means of encouraging the pupils. 197. What answers should be rejected. — Dishonest answers, guesses, and careless answers should not be accepted. They may satisfy certain standards of mark- ing, but they are not educative. Dishonesty may be due to laziness; or it may be a kind of unconscious devel- opment in schools where per cents have been used as the goal of education. In all these cases, require the pupil to work toward the desired answers. This is the only positive cure. A negative treatment may place a zero upon the register, but a zero does Httle or nothing to direct the average pupil into habits of useful effort. 198. From the particular to the general. — This pro- cess was emphasized by Pestalozzi in these words: '^It is a chief business of education to pass from dis- tinctly perceived individual notions to clear general notions." Individual notions are notions or ideas of individual things. Each of the five senses furnishes sensations which the mind may or may not accept. As soon as the mind considers sensation by examining the object that caused the sensation, the mind gains a METHODS OF TEACHING 87 percept of that object. This percept may be considered a particular or individual notion. Then the memory and the imagination work on these percepts, until the mind combines the percepts into a concept or general notion. In all early education the teacher strives to train the senses to see things, to observe things, so that the mind may get clear, accurate percepts as the foundation of knowledge. Concrete material in teaching is useful because the pupils can use more than one sense in observation. Illustration To teach the definition of a noun, write sentences on the board. Longfellow was a poet. Pupils like poems. Lincoln loved children. Do you know nouns? The presentation will lead pupils to see that each name word in these sentences is a noun; and so from seeing particular name words are nouns, they infer that in general name words are nouns. So this inductive lesson proceeds from the particular to the general. The same process is found in all elementary develop- ment lessons. 199. Simple to complex. — The meaning of these words varies as individuals vary. We must take each child's point of view. What is simple for the teacher may be complex for the pupil. 1. In language work, the simple things are the things the child knows. Talk about toys, pets, experience. Use short, simple, familiar words. 88 METHODS IN EDUCATION 2. In learning numbers, the process of scoring is a simple way of indicating a knowledge of the number concept, thus: 11 for 2 or two; 111 for 3 or three. 3. The simple sentence is mastered before the com- pound or the complex. 4. In music the natural scale is taught first. 5. In nature study the plant as a whole is studied as one single, simple, living thing. Later the child will become familiar with the complex structure of the plant and the functions of its various parts. 200. Concrete to abstract. — The abstract concepts cannot be formed without first having a concrete con- cept. Thus, an abstract concept of whiteness comes after associating whiteness with a number of white objects. Another reason for using objective or concrete teaching is the demand for multiple sense instruction. Seeing, hearing, feeling, and even tasting and smelling may be employed. 1. Alphabet blocks as play in education. 2. Warlike toys for Spartan children. 3. Foot-rule and yard-stick in linear measure; gill, pint, quart, and gallon measures in liquid measure; ratio and proportion by handling blocks in Speer method. 4. Moulding-board, putty maps, relief forms, and pictures in geography. 5. The study of a model to get form, style, and rules in composition. 201. From the known to the related unknown. — A child is master of considerable knowledge when he enters school. This knowledge in possession must be used as apperceiving groups as a basis for new knowledge. The adaptation of the old and the new will utiUze interest and attention. METHODS OF TEACHING 89 1. The schoolroom, the playground or the city may each or all be used in early lessons in geography. This plan illustrates from the particular to the general. 2. From knowing the agreement of subject and pred- icate, the child passes to concord of adjectives and nouns, pronouns, and antecedent, etc. - 3. Unity in a sentence is a foundation for unity in paragraph and essay. 4. Definition of a verb is necessary for an under- standing of the participle, and the nature of nouns and adjectives leads to the secondary nature of participle. 5. The common denominator for addition of frac- tions opens a way to subtraction and division of frac- tions; and common fractions in general are a basis for decimals and percentage. 202. Observation before reasoning; processes before rules; facts before definitions or principles. — The'se axioms are a demand for inductive processes in teaching. They are justified by psychology because percepts precede concepts, and definitions require related classes. Discovery aids activity. 1. Window gardens are means of causing the child to discover the relation of hght, heat, and moisture to plant life. 2. Five or more examples worked in multipUcation of decimals will lead to the rule. 3. Actual experiments with levers will quickly im- press the rules regarding fulcrum, weight, and power. 4. See also inductive method. 203. From the empirical to the rational. — Science is organized knowledge; and before knowledge can be or- ganized, some of it must be possessed. Every study therefore, should have a purely experimental introduc- 90 METHODS IN EDUCATION tion; and' only after an ample fund of observations has been accumulated, should reasoning begin. — Spencer, Education, Chapter II, page 93 of Kellogg's edition. So this rule means that knowledge must be gained wholly by personal experience. It embodies all of the other preceding axioms. We admit that pupils should learn much by their own efforts, but all subject-matter cannot be mastered in this way. Some must be taken on the authority of the teacher, as the deductions in history, economics, and advanced mathematics and science. Our criticism is that the rule should not be absolute because all subjects do not admit personal experimentation. 204. Heuristic method. — This name is derived from a Greek word meaning to find; and so it is a method of directing instead of telling. By questions, directions, problems, and suggestions the child is encouraged to find out everything for himself by discovery. It is a constructive method which aims to promote self- realization. It is the method of discovery under sympathetic and intelligent guidance. Illustration A class is beginning the study of Asia. Without any lecturing by teacher or reading by pupils, turn to the map of Asia. Each pupil has a geography. Take a general view of surface; location, direction, and name of mountains. Next take drainage; rivers, running north, east, and south; hence, three great slopes; highlands and lowlands contrasted and located. Coast line, peninsulas, harbors noted. Conditions affecting climate and the probable modifying elements. Probable occupations, productions, and consequent states of civilization. METHODS OF TEACHING 91 The second process is verification. Observation and inference in the first process beget hvely interest and active thinking, and then the verification by consulting the printed pages completes the first period of study. Contrast the old memory exercise in studying Asia. See last two sections in chapter on geography. 205. Prussian method. — Hinsdale says that " teach- ing is bringing knowledge into due relation with the mind." In the effort to induce pupils to share willingly in all the activities of the school, the Prussian method puts the pupils and teacher under a feeling of equality in a kind of social participation. For instance, a les- son covers eight problems in arithmetic. All pupils are equipped for written work at desks. The teacher calls for the interpretation of the first problem, and several pupils in turn contribute their opinions. This arouses the social stimulus or the general feeling in favor of individual and class success. All begin the written solution; one is called to explain a step, another explains a second step, and so on. After reciting, each one con- tinues his written work. So every step is explained in interpretation, solution, and analysis; every pupil has shared in oral and written work; every problem has been solved and all the difficulties have been Cleared away. The tone is conversational, the manner is nat- ural, the work is interesting in process and results, and the spirit of a civic community has been experienced by all. This kind of education is living, and not a mere preparation for living. 206. Inductive method. — A process of reasoning which estabhshes a general rule, definition, principle, or proposition based upon the knowledge of particular cases. In chapter IV we explained briefly that the nat- 92 METHODS IN EDUCATION ural order in acquiring knowledge is percepts, concepts, judgments. This order is said to be the order of race development. Primitive man learned, through con- crete and individual experiences, certain facts which he later formed into general conclusions. For example, flint is good material for arrow-heads. Such knowledge became a general possession and each generation added to the general fund of knowledge. Illustrations Solving several examples in division of fractions and then deriving the rule for inversion of the divisor; study- ing sentences containing relative pronoun and ante- cedent, and then constructing a rule showing that the pronoun and antecedent need not agree in case; begin- ning the study of history at seven o'clock every school day for two weeks, and then noticing that the mind has formed a habit or rule of thinking about history daily at that hour. 207. Deductive method. — A process of reasoning that starts with general rule, definition, principle, or propo- sition and shows its respective appUcation to particular cases. Thus in teaching grammar, have pupils learn definitions first and then apply them; in arithmetic, learn rule and then work examples; in geography learn defi- nitions of land forms and later look for illustrations. 208. The inductive-deductive method. — Neither in- duction nor deduction can alone constitute a suitable method in a complete act of instruction. The two must be combined. On account of this necessity, some writers mean inductive-deductive when they use the term induc- tive method. Let the student remember, then, to com- bine these two processes in every development lesson. METHODS OF TEACHING 93 A second point to be remembered is that these two methods are justified by psychology; they satisfy the working of the mind. Teachers hear much about the action of the mind in passing from particular to general and then from general back to particular. In develop- ing the definition of an adverb, the teaching emphasizes several adverbs in sentences. A knowledge of each adverb is a particular notion. Then the mind general- izes these particular notions and expresses the general nofion in a definition of an adverb. But this does not complete the process; the impression is not deep enough. In other words, this definition must be applied to other adverbs in sentences, and pupils must construct sen- tences containing adverbs. This application or drill completes the educative process by passing from the general to other particulars. Thus the inductive- deductive method makes a complete mental act in every development lesson. 209. Analytic method. — This method proceeds from wholes to parts. In grammar, begin with sentence and proceed to parts of sentence. In literature, study the whole selection before considering paragraphs, sentences, and words. In primary reading, begin with sentence and go to words, letters, and phonics. In nature study, observe the plant or other material as a whole before studying its parts. 210. Synthetic method. — The synthetic method pro- ceeds from parts to wholes. In grammar, begin with words and build sentences. In primary reading, the building of phonic elements into words is synthesis. In primary geography begin with the schoolroom, having the children make a map of it and understand how a map represents an object; thence proceed to the 94 METHODS IN EDUCATION schoolyard, the street, the city and show upon the city and state maps all the children have themselves observed, including rivers, hills, mountains, etc. 211. Comparison of analysis and synthesis. — Both relate to the action of the mind in dealing with individual things and the parts of those things. Analysis seeks to show the relation between the parts; synthesis empha- sizes the parts themselves and later shows their relation in construction. Both processes are required in every complete mental act. Important Distinction 212. Individual things vs. classes. — There is a com- mon misconception about the difference between the inductive-deductive method and the analytic-synthetic method. Analytic teaching is considered identical with deductive teaching, and synthetic teaching with induc- tive teaching. This is an erroneous idea. Analysis and synthesis are employed in dealing with single things, and their parts — a word and its letters, a sentence and its elements, a method in reading and its steps, a subject like arithmetic and its constituent processes; induction and deduction are employed in dealing with more than one thing in working to or from classes or generalization. The inductive method does begin with one thing, not so much to ascertain the nature of the thing itself as to find the larger class in which the one thing belongs; and while the inductive comparison of one thing with another may seem to be a synthetic process, let it be noted that synthesis seeks to put the constituent parts of one whole into proper relations, but induction seeks to put several wholes into a proper classification. Like- wise analysis is confined to the relations between one METHODS OF TEACHING 95 whole and its parts, while deduction passes from the large classification of many wholes down to the appli- cation to one thing. In other words, analysis and syn- thesis deal with individual notions, individuals or single things; induction and deduction deal with general notions, or classes. 213. Topical method. — Subject-matter may be divided so that each heading will include material for a unit of discussion. The ordinary division into chap- ters does not always suit the requirements for class assignment or for individual discussion. A topic should be complete in itself and yet be one of the related parts in a larger division. The advantages of the topical method are convenience in assigning lessons, definite responsibility in recitation, and independence of pupil in thought and expression. The disadvantage comes only from abuse in which facts are disconnected and class stimulus is sacrificed to indi- vidual achievement. 214. Discussion in class. — The topical method sug- gests the important topic in this section. As it is frequently an examination question, an outline is sug- gested in the next four sections. 215. Advantages of discussion in class: 1. Aids in retaining attention. 2. Pupils learn to express thoughts without direct question. 3. Teacher can get a broader insight into pupils' method of thought and general knowledge and associa- tions. 4. Pupils may have a keener feeling of responsibihty concerning the success of the lesson. 5. Fear of error is at a minimum. 96 METHODS IN EDUCATION 6. It is an inducement to thorough and comprehen- sive study, volunteered information, etc. 7. Is not so restricted as a direct answer to a question. 216. Dangers in discussions in class. 1. The bright and precocious will monopolize the time. 2. The lazy, careless, and indifferent take a vacation. 3. Wandering from subject. 4. Loss of logical sequence of thought. 5. Disproportionate emphasis of minor points. 6. Confusion of ideas due to lack of clear and defi- nite statements and the variety of answers. 7. Encourages guessing. 217. Directions for creating and profitably conduct- ing a discussion. 1. Arouse interest in the question by association with previous ideas or by a healthy spirit of emulation, etc. 2. Get various opinions even if an excellent answer has been given. 3. Put the children on their mettle by speaking of the excellence of certain remarks. 4. Encourage independent ideas by catching those who answer by following sheep fashion. 5. When there is danger of guessing put a pointed why? or how? 218. Characteristics of effective discussion: 1. Interesting subjects. 2. Unity of idea. 3. Alertness. 4. Subject alive with associations, concepts. 5. Calls for thought. 219. Text-book method. — This name was formerly given as a kind of reproach to teachers who followed METHODS OF TEACHING 97 the matter and method of text-books. A reaction went to the other extreme of oral teaching. Now educators are trying to secure a reasonable average. The abuse of the text-book method required verbal memory of the contents. The extreme oral teaching has made pupils dependent upon the teacher. Pupils have become passive on account of not knowing what to study, where to find it, and how to study. Text-books should be used, and the prudence of teachers is a safe guide in avoiding extremes. CHAPTER VIII GENERAL METHOD 220. Device, method, general method. — In the dis- cussion of methods of teaching, there is not enough distinction between a mere device and a method. A device is simply a tactful presentation of some part of the lesson. It is generally personal, particular; it may or may not work well with another teacher under dif- ferent circumstances. For instance, in teaching about a lock in a canal an ingenious teacher may have a wooden model made by himself or a pupil. This is strictly a device, and a commendable one, but not properly a method although it is entitled to classification under objective or concrete methods of teaching. Again, a teacher makes a chart of figures covering the ordinary combinations for rapid drill. It is a good device, but it is not a method. We have described some of the methods which are useful in regular teaching. Now we come to consider whether there is one general method that is applicable in all teaching. V If there is such a general method, it must be that there are general psychological laws which apply to the development of all human beings. We think there are such universal principles or laws and there is one general method. Right here we may empha- size a thought suggested in the preceding chapter in regard to the desirability of eliminating several kinds of 98 GENERAL METHOD 99 methods by making a better classification. Strictly speaking, method in education is one composite process embodying all of the methods described in chapter VII. This view is upheld in a book recently pubHshed, Col- grove's The Teacher and the School, page 319: " In spite of all the diversity of subject-matter, text-books, school surroundings, and teaching devices, in spite of all the differences *in age, acquirement, and individuahty of pupils, there is a truly typical method of teaching which is, 'in the main, constant and capable of being adapted to nearly all subjects and classes. And this is so because the major movements of the mind are so common to all learners and because the fundamental laws of teaching, based as they are on the nature of the mind, are valid for all subjects and find application in every recitation." 221. Herbartian view of the order of the mind. — " No matter what the study may be, whether Latin, mathematics, science, or some other, the mind follows a certain order. Through the old related experiences (first step, preparation) new individual notions are reached (second step, presentation); these are compared and their essential characteristics abstracted (third step, comparison), and the resulting general truth is worded (fourth step, generalization); this generalization finally receives application (fifth step, application.)" These five steps are known as the formal steps of instruction. These names are the ones used by Amer- ican writers in place of the four used by Herbart, namely, Clearness, Association, System, Method. A modified form is commonly used in making plans for development lessons and examination answers, as follows: I. Aim TIL Presentation 11. Preparation IV. Application or drill 100 METHODS IN EDUCATION 222. Justification of the formal steps. — Prior to Herbart's time (1776-1841), the old faculty theory of Aristotle was the prevailing psychology. That theory held that the soul was endowed with higher and lower faculties which were entirely distinct. The general divisions — knowledge, feeling, will — were subdivided into capacities or faculties, each subdivision having a distinct individual function. In place of this faculty theory, Herbart put the conception of unified mental life and development. He argued that the soul is a blank at birth, not endowed with intuitive faculties, but having capacity for adaptation to environment through sense-perception. Mental development is the result of these perceptions of presentations. The inter- action of presentations passes through generalization to concepts, and then in turn to judgment and reasoning. In this development of a unified mind, the concept is the ideal; the process is apperception; and the result is a habit of thinking. Thus this formal method in a development lesson adjusts mind and matter for ap- perception and at the same time habituates the pupils to a desirable way of studying. Justification is claimed, therefore, since the process secures clear concepts, thorough apperception, and effectual habits of study. 223. Preparation. — This step is an effort to make the pupils' minds ready to apperceive the new knowledge. It does not mean the teacher's preparation or the pupils' prior study although both are necessary and useful. It uses acquired knowledge as an apperceiving group by which the new knowledge may be assimilated. So the purpose of this preparation is to put the body and the mind into a receptive attitude, and to relate the new and the old so that attention and interest will be active. GENERAL METHOD 101 In brief, it is putting mental, moral, and physical powers into harmonious co-operation with the teacher's efforts. How should such preparation be made? Agreeable opening exercises are the first contribution. In the reci- tation, it may be an anecdote, a description, a brief review of related work, or simply a statement of the aim of the lesson. During the day, brief physical exercises, the singing of a song, or even a two-minute visiting priv- ilege may dispel fatigue and adjust the minds to the required condition. Tact is the best guide. The one danger is in making the preparation too long, — a scat- tering of attention and energy. Sometimes it is best to go straight to the presentation. In this, let the minds of your pupils be the criterion. 224. Presentation. — In this part of general method the teacher utilizes some of the specific methods dis- cussed in the last chapter, as the inductive-deductive method. The minds prepared in the first step are now getting needed individual notions. Watch the process of passing to general notions. 225. Comparison or association. — The mind con- tinues the process of apperception by associating, com- paring, and contrasting the facts of the new lesson with the facts previously acquired. The mind here abstracts the essential characteristics of each notion presented. 226. Generalization. — Now the notions so clearly distinguished in the previous step are classified in the form of rules, principles, definitions, laws, maxims, or tables. The mind has formed general notions, 227. Application or drill. — We have seen that the purpose of instruction is the formation of general no- tions or ideas. But general ideas will not remain a possession without thorough drill. So this step requires 102 METHODS IN EDUCATION impressive drill and application to practical life. It is the completion of each educative act, namely, the return from general notions to particular notions. Modification of Formal Steps 228. Aims. — In writing lesson plans, it is always advisable to state the aim of the lesson first, although this law of aim is not one of the Herbartian steps. A few years ago teachers in training were told not to express the aim of the lesson for fear pupils would lose inter- est in the development. It was supposed that the anticipation of results would guarantee co-operative interest and that thereby the pupils would discover the essential purpose of the lesson. That view is not sound today; it exalts the process of the presentation too much. Better state the aim as a focal point for all lines of energy during that recitation period. 229. Rein on aim. — Professor Rein, of the Univer- sity of Jena, was a follower of Herbart, but the Her- bartian doctrines were modified in many particulars by him. This opinion on the law of aim agrees with the current American view: " The pupil should know beforehand what is coming, if he is to bring all his powers to bear upon the work of learning; and it is easier to call out all his effort if he knows beforehand what is to be gained. To conduct a child along an unknown road, toward an unknown ob- ject by means of questions and hints, the purpose of which he does not see, to lead him on imperceptibly to an unknown goal, has the disadvantage that it develops neither a spontaneous mental activity nor a clear insight into the subject. Having reached the end of such a fine of thought the pupil looks about himself GENERAL METHOD 103 bewildered. He stands at the goal, but does not see the relation that the result bears to the labor performed. He does not rise to that satisfactory mental activity and favorable disposition of mind which are stimulated by the pursuit of a clearly set purpose." 230. Dr. Hervey on formal steps of instruction. — Dr. W. L. Hervey, a member of the New York City Board of Examiners, gave his opinion of these formal steps in the New York Teachers' Monographs, Decem- ber, 1900. The article is conservative and practical. He admits the validity of the opinion regarding general method and the movement of the mind, but he dis- approves a rigid observance of the formal steps. He emphasizes the point that the five steps need not come in the order in which they are mentioned, but they all should come somewhere in every complete act of instruction. He cautions teachers against making the preparation too long because he has observed that pupils' minds have wonderful powers of adjustment to a straightforward and even blunt approach. He thinks that preparation instead of standing alone at the beginning of the recitation occurs at each step in teaching; each step should prepare for the next. Good teaching from start to finish is steeped in preparation. Preparation is no more an antecedent of the first step than it is of the third; hence preparation may involve the presentation, thought, or application or all of them; and second, that each of these involves preparation. There are an infinite number of preparations within each method-whole, and there should be infinite vari- ety in the method of handling them. Nor is it neces- sary that comparison and generalization should hold rigidly to the order in which they are named, for 104 METHODS IN EDUCATION we frequently ask children to think and afterwards to imagine. 231. Dr. Hervey's conclusion. — " The human mind, (generally speaking) is not a blunderbuss. Yet from the direction for making lesson plans which I have known to be given to advanced classes by teachers of the form- alist type, it would appear that teaching the mind is precisely analogous to loading a brass cannon. Swab- bing, taking aim, loading with powder and shot, ram- ming home, setting off the fuse, all must come in a certain order not to be deviated from. Such a figure limps on both feet. In more senses than one it smacks of militarism. One who is appealed to by it belongs in a factory where things are made, or on the firing line where people are shot at, not in a school where minds grow and are fed. " Therefore, the best way, in my judgment, to profit by the doctrine is not to think chiefly of steps, or of sequence, or of separateness, or of junctions at which one must change cars for the next step — the best teachers when at their best are, I trow, not thinking about the formal steps — but to think chiefly of the ideal end of instruction, as being that happy state of pupils' minds in which, for warmth and resource, there are abundant stores of concrete imagery, and, for economy and serviceableness, there is organization-pigeon-holes, and tags, card catalogues and indexes, or if you will, generals, lieutenants, and privates, each knowing his duty, and each on the qui vive to do it. The formal steps are, then, so many ideals which the teacher must attain before his work is done." 232. Colegrove on formal steps of instruction. — '/These so-called 'formal steps' do not form a strait- GENERAL METHOD 105 jacket to fetter the individuality of the teacher, as some critics seem to think; nor, on the other hand, are they a Procrustean bed on which every recitation is to be stretched, for lessons consisting of arbitrary facts or unrelated ideas cannot be taught in this way. Like all general principles they admit of great variety in their application to details. They do not solve all the problems of method, but they do serve as a standard by which the teacher can measure the correctness of his daily practice, and, once mastered, they contribute very much to the teachers' skill, power, and success in instruction. It is a misnomer to speak of the 'five steps in the recitation,' for very often the whole recitation must consist of one or two steps only. Many consecutive lessons may consist of the fifth step alone." — The Teacher and the School, page 324. Illustration of General Method 233. Illustrative lesson on attribute complement. — Attribute complement or attribute is known as predicate noun, predicate pronoun, and predicate adjective. I. Aim. To teach attribute complement. II. Preparation. Review definition of sentence, subject, predicate, noun, verb, pronoun, adjective. III. Presentation. Have these sentences on board: 1. Birds sing. 2. Happy children sing. 3. The children are happy. 4. Pupils become students. 5. Lincoln was a good man. 6. Longfellow was kind. 7. Longfellow was a poet. 8. It is he. 106 METHODS IN EDUCATION 9. This is an attribute. 10. Who is it? It is I. Sentences 1 and 2 will impress some of the points covered in the preparation. Sentence 2 is an easy approach to the adjective happy in 3. All read the third sentence. Then individual answers on subject children and predicate are happy. Next get subject noun children and predicate verb are. Note that are alone is not the predicate; are happy is the predicate. Teacher. Covering word happy, asks one to read. Pupil. The children are. Teacher. Is what you have read complete or incom- plete? Pupil. It is incomplete. Teacher. Uncovers happy. Now is the expression complete or incomplete? Pupil. The sentence is complete. Teacher. What word makes it complete? Pupil. Happy makes it complete. Teacher. Happy is a complement. Write word on board; analyze it: complete + nient; ment — that which. Now define. Pupil. Complement means that which completes. Teacher. What part of the sentence is completed by happy? Pupil. Happy completes the predicate. Teacher. What part of speech is happy in sentence 2? Pupil. Happy modifies the noun children; hence happy is an adjective. ^ Teacher. What part of speech is happy in sentence 3? Pupil. The same; it is an adjective. Teacher. Yes; an adjective completing the predicate. GENERAL METHOD 107 It is a predicate adjective. Another name is some- times given. If the children are happy, you can say that happiness is an attribute of the children. Thus for good children, goodness is an attribute; industrious pupils, industry is an attribute. So we may call happy a predicate adjective or an attribute complement. Teacher. Find another adjective used as an attri- bute. Pupil. Sentence 6, kind is an attribute. Teacher. Then, as far as you have observed, what part of speech may be used as an attribute? Pupil. An adjective may be used as an attribute. Teacher. All read sentence 4. Then proceed as be- fore to teach that students completes the predicate and refers to the subject. It is a noun used as attribute complement; or it is a predicate noun. Likewise for predicate pronouns, eliciting for each complement (a) that it completes the predicate, and (6) that it describes the subject or means the same as the subject. IV. Comparison. Pupils distinguish attribute from object. V. Generalization. Call for definition of attribute and, when suitable wording is secured, write definition on board. All read; individuals read. All define; individuals define. VI. Application or drill. Direct apphcation in such sentences as these. 1. This definition is easy. 2. Grammar is a useful subject. 3. Easy is a predicate adjective. 4. Emerson was a scholar. 5. The wind feels cool. 6. Who called? It was she. 108 METHODS IN ^ EDUCATION Then apply by requiring contrast; thus: 1. This is our school. 2. We have a new school. 3. Whom did you ask? 4. Who was it? 5. This work seems pleasant. For further drill, have pupils construct sentences containing attributes. It may be helpful to learn this hst of verbs which are generally followed by an attri- bute complement. be seem become feel appear look 234. Method-whole. — The use of the general method requires a special classification of subject-matter. In order that we may apply the formal steps of instruction the subject-matter has to be grouped and classified into definite unities. Each unit of instruction is considered a method-whole. Thus in studying New York State all of the drainage could be put under an outline or clas- sification; and then this general outline could be divided for particular lessons each week or each day. So it is that each division may be treated as a method-whole. Gordy defines method-whole as a group of particular facts involving a universal. In other words, any topic or portion of a subject that constitutes a unity such that the process of teaching follows the inductive- deductive method is a method-whole. It should be noted in connection with this explanation of method- whole that the matter of general method, formal steps of instruction, particular notion to general notion, inductive-deductive method, and complete act of GENERAL METHOD 109 instruction are all different names for one general prin- ciple underlying the Herbartian general method. The lesson on the attribute complement is an illustration of a method-whole. 235. A definition of method- whole. — Each group of particular facts involving a universal is a method-whole. — Gordy, A Broader Elementary Education, page 197. CHAPTER IX SPELLING 236. Accuracy a worthy aim. — As long as accuracy remains a requisite of success in life, correct spelling should be considered a vital aim in education. A theo- retical search for the causes of poor spelling may place the blame upon the pupil, the words studied, or the methods of teaching; but the practical accomplishment of spelling correctly will never come until teachers agree that spelling deserves to be taught as an individual sub- ject and not merely as an incidental study. Errors are too often excused on the ground that it is impossible for certain pupils to learn to spell, or that misspelling is a mark of genius. Better strive for accuracy as an ideal than to justify errors by excuses. 237. Value of spelling. — It is not a culture study like history and literature, but it is a necessary art which is to be acquired in the most positive way and which is to become automatic as soon as possible. It is no particular credit to be a good speller, but it is a disgrace to be a poor one. Spelling, therefore, has a conventional value which may not be despised with impunity. — Taylor, Word Study in the Elementary School, pages 27 and 28. 238. Psychology of Spelling. — It is a mistake to say that spelling depends upon the eye alone or upon any other single sense; spelling demands multiple sense 110 SPELLING 111 instruction. In learning to spell, as in all other educa- tive efforts, the child should be taught to use as many senses as possible. One sense may do more than an- other, but one sense cannot accomplish the best results without the co-operation of the other healthy senses. This opinion is upheld by Dr. Shaw in his little book on Three Studies in Education. After discussing experi- ments with more than two thousand children, he ex- presses this conclusion on page 10: '' Spelling is largely a matter of association, and the eye, the ear, and the motor must be appealed to so as to produce the strongest complication of sensory elements. Care then in the right kind of oral preparation, with considerable oral test before writing, training pupils to build up words by using small unities into which words can be divided, is a method of teaching spelling productive of the best all-round results." 239. The problem. — Poor spellers are found in every class. This is a fact, not a supposition. Our duty is to find the causes of the trouble, and then try to apply specific remedies. Pedagogy is not a panacea, nor is wholesale criticism a helpful aid to efficiency. There are difficulties in subject-matter, in pupils, and in teachers. Difficulties in Suhject-M alter 240. Composite language. — The English language is a composite one, derived from a large number of other languages, and so there are many irregularities. For illustration, note the origin: depot, French; coffee, Ara- bic; banana, Spanish; waltz, German; sloop, Dutch; drink, Anglo-Saxon; gale, Scandinavian; manual, Latin; epistle, Greek. The principal difficulties are the fol- lowing : 112 METHODS IN EDUCATION 1. Silent letters. 2. Language not phonetic, i.e., spelling different from sound; as, eight, phonic, praise. 3. Different pronunciations for same combinations of letters; as, ou in ought, soul, bough, etc. 4. The numerous sounds of the vowels. One edu- cator puts ninety-five per cent of all errors in spelUng under this head. Difficulties in Pupils 241. Not knowing how to study. — In every lesson there are certain words which the pupils already know. In spelling, as in all other subjects, the process should be one of separating the known from the unknown so that the child may direct his energy toward what he does not already know. Habituate pupils to this pro- cess of selection so that they may devote their energy to the mastery of the new words in the list. Notice, too, the specific difficulty in each word. Can the word be spelled phonetically? If not, why? The answer will direct attention to the difl[icult3^ Homonyms illus- trate this difficulty. Where is the accent? Pupils rarely misspell any accented syllables because the em- phasis has impressed those syllables upon sight and hearing. Hence, observe the unaccented syllables for visualization. 242. Failure in observation. — Take the pupil apart from the class for personal instruction. Test him on a few words to find his difficulty, and it is probable that the difficulty is in not seeing the word exactly as it is. Take two or three words apart from the printed or writ- ten exercise and encourage him by having him master these few words by oral and written effort, and then give SPELLING 113 him credit for every indication of progress. This is a special effort in the formation of right habits of study, and every progress made by a defective pupil will be an encouragement that will work its own reward. A persistence in right habits will overcome the defect in failing to see the word exactly as it is printed or written. 243. Carelessness. — Try visuahzation. Write five words on the board. Have pupils look intently at them, then cover or erase the words and let pupils try to write the list in order. A few exercises of this kind will direct attention to the difficulties in each word, the order of the words and their particular relation to one another. An entire lesson can be learned by a whole class in a short time in this way. It is another means of pro- moting the social stimulus advocated by Dewey. Difficulties in Teachers 244. Defective teaching. — The third cause for poor spelling can be found in the teachers themselves. In- stead of making an adverse criticism in general, let us consider ten specific waj^s in which a teacher may fail to make a pupil get a complete, accurate grasp of the words in spelling. 245. Using eye alone. — This plan has produced some excellent results, especially under the process called visualization. Pupils have acquired habits of silence, intensive apphcation, interest, obedience, and mastery. Such pupils are called eye-minded, a rather vague classification for children who are endowed with capacity for intelligent observation. When failures have to be explained, we are told that some pupils are ear-minded. This is another instance of juggling with terms, a practice that has associated pedagogy with 114 METHODS IN EDUCATION nonsense. An elementary knowledge of mind is enough to make us understand that the mind of any normal child retains and reproduces an idea more easily if the impression of that idea has been enforced by as many senses as possible. For this reason, the good teachers encourage the use of eye, ear, tongue, and hand. The child is denied none of his natural rights, and, in most cases, the results are satisfactory because the using of all of those powers together produces an effect much stronger than the total effect of appealing to those powers one by one. 246. Rote work. — The memory is overtaxed by learning lists of unrelated words. The remedy is in turning to words used in conversation or in the daily lessons. 247. Neglect of spelling as a subject. — Spelling can never be satisfactorily taught as an occasional exercise in connection with other subjects. It can be correlated in this way, of course, but it deserves a place as an individual subject in the regular program. 248. Abuse of dictation. — It is an abuse of dicta- tion to use it for purposes of drill or review before pupils have mastered the spelling of new words. The term dictation as used here has reference to the teacher's reading of certain sentences to be written by the pupils for the purpose of testing the pupils' knowledge of the spelling and the use of the words in the assigned lesson. Premature use of dictation leads to confusion instead of clearness. The evident remedy is to make effectual study of the lesson prepare for effectual application. Then the habit of learning spelling will require dictation as a process supplementary to the intensive study of the words, — a process that will prove to be effectual SPELLING 115 because it brings into use all of the available powers of the child. 249. Indistinct concepts. — The meanings of words are given as dictionary definitions. Encourage pupils to give their own expressions and applications. This is a suggestion for the use, not the abuse, of the dic- tionary. 250. Lapses. — Infrequent recitation periods and lack of varied and thorough drill. This failure to give adequate drill is one of the serious defects in modern education. Is not repetition a fundamental law of habit? 251. Unscientific classification. — Classification of words according to the number of syllables. This is unscientific and uninteresting. Use grouping under comparison and contrast. 252. Interruption. — Trying to teach spelling when the child's mind is unprepared. Do not interrupt connected thinking in other subjects to correct a mis- spelled word. Keep the word for a special list. 253. Lack of variety. — Failure to use a variety of interesting drills involving competition such as spelling down or choosing sides. See section 33. Remember the necessity of satisfying instincts or impulses if we wish to secure reactions. 254. Excuses for failure. — Permitting pupils to form the habit of thinking that correct spelhng is impos- sible. The will is weakened every time we permit pupils to substitute excuses for effort. 255. What words shall pupils spell? — Some favor a list of words selected from the pupils' vocabulary and from the lessons of the grade, while others advocate the use of a spelling book. In either case, the present 116 METHODS IN EDUCATION tendency of opinion seems to be this : It is sufficient for a child to be able to spell the words he can use. This view is in accordance with the principles of adaptation, utihty, and interest. Arguments for Text- Book 256. Convenience. — Time saved for pupil and teacher. 257. System. — Modern books are not miscellaneous lists of words; grouping and scope are determined by the needs of pupils. 258. Breadth and utility. — Adequate provision is made for future demands as well as for actual present use. 259. Accuracy. — Spelling, syllabication, accent, and even pronunciation are accurately given. Errors are frequently made in copying lists. 260. Stimulus. — Ownership is an instinct, and happy is the child who is made to feel the worth of such an incentive. The average pupil can go far beyond the limited list of words in his grade, and a simple appeal to personal ambition will encourage him to do so. The book is an invitation to self-activity; it is a means to helpful rivalry; and it offers individual guidance to the future of the child who must leave school to earn a living. Arguments for Lists of Selected Words 261. Specific utility. — The words become a part of definite knowledge through the child's thinking, feeling, and acting. Opposed to vague concepts because the child knows and uses every word; development through activity and apperception. SPELLING 117 262. Interest. — The child's interest is limited to the present; hence, Hmit words to present use. 263. Adaptation. — Books adapted to average groups may not satisfy individual needs. 264. Economy of effort. — Lists are conducive to concentrated, productive effort; books present many words that are useless on account of being too easy or too difficult. 265. Correlation. — Lists selected from all the sub- jecfs in the grades tend to produce unity and accuracy in each child's circle of thought. 266. Summary of arguments. Text-Book List of Words General utility Specific utility Economy of time Economy of effort Provision for future Satisfaction of present needs Accuracy of spelling Clearness of concepts Adaptation to average Adaptation to individual pupils pupils Breadth through individual Concentration upon essen- effort tials 267. Combination of book and lists. — Use the best text-books available, and then meet the deficiencies of the text-book by a list of selected words applicable to the individual needs of the class. Combine all useful devices. 268. Three ways of conducting recitations. — Oral, spelling, written spelling, and a combination of oral and written spelling are usually classified as three methods. Numerous devices are often discussed as methods. The three methods mentioned should be combined or alternated frequently so that pupils may profit by all of the advantages in each method. 118 METHODS IN EDUCATION 269. Advantages of oral spelling. 1. It teaches enunciation, syllabication, pronuncia- tion. 2. Interest stimulated through honest rivalry. 3. Economy of time by avoiding the necessity of correcting papers. 270. Disadvantages of oral spelling. 1. It does not insure correct written spelling. 2. Every pupil does not have to spell all the words of the lesson. 3. Inattention may be fostered in a large class. 271. Advantages of written spelling. 1. Practical because it prepares for accurate written work. 2. Every pupil has to spell all the words. 3. Co-ordination of many senses. 4. Correlation of many subjects. 272. Disadvantages of written spelling. 1. The pupil must use his sense of hearing to obtain proper enunciation and pronunciation. 2. Social stimulus is lacking until the report of the exercises is made. 3. Dishonest work by copying and also in correcting the work when papers are interchanged. Directions for Studying Spelling Lessons 273. Physical conditions. — See that the environment is satisfactory: hght, heat, ventilation, seats, books, and other material. 274. Responsibility a stimulus. — Prepare the minds by telling the children that the purpose of this exercise is to master a definite amount of work in a specified time. This kind of approach is a compliment to the SPELLING 119 intelligence of the children. There is no harm in using the word work since the average healthy child welcomes any assignment that carries the possibility of quick mas- tery. There is a stimulus in the certainty of success. The acceptance of responsibility under hope of success is the first victory for the child as the teacher tries to help him acquire the habit of vigorous and persistent work. 275. Concentration. — Have pupils look carefully at the word. See sections 241 to 243 inclusive. 276. Reproduction. — Close book, think of the word, write it. Do not permit pupils to try this frequently for the purpose of testing themselves. Teach them the value of intensive study mentioned in the preceding section; then the supplementary use of this reproduc- tion will be evident. Observe how this reproduction utilizes co-ordination of powers. 277. Comparison. — Compare the written word with the printed word. This is called verification, checking. or proving. It is habituation in self-correction, an edu- cative effort which Spencer calls empirical. 278. Repetition. — Repeat the process when mistakes have been made. But here is a place to distinguish useless repetition and legitimate repetition required in fixing habits. While perfection is not expected, every pupil should be made to feel the serious waste in repeating processes that were first passed over in a thoughtless way. The habit of consciously using one's powers effectually is the paramount value here as else- where. 279. Rowe quoted. — In support of these suggestions, a quotation from Rowe's new book is inserted: ''Four habits have usually been formed by the pupil before he spells accurately: (1) the habit of critically observing 120 METHODS IN EDUCATION the spelling of new words as he comes upon them in reading; (2) the allied habit of noticing where words differ slightly from his image or expectation of them; (3) the habit of hesitating to write a word whenever its spelling may be in doubt; and (4) the habit of taking a final glance at the word just written to see that it conforms to the intention of the writer and seems cor- rect. — Habit-Formation, page 112. 280. Difficulties. — Meaning of words, use of diction- ary, and other pertinent topics relating to the study of a spelling lesson are discussed in other parts of this chapter. 281. The old way. — When spelling held equal rank with arithmetic and other studies, it was customary for the teacher to assign an exercise for study in school or at home, and then the pupils considered it a part of their duty to learn to spell every word in the exercise. This plan of assignment and study is criticised in the new education on the ground that the learning of such words in that manner is a mere exercise of the memory without the use of correlation or multiple sense in the process of learning. What, then, shall be substituted? Let us interpret some investigations. Experiments in Studying Spelling 282. In Germany. — A German educator, Herman Schiller, has made a practical investigation of oral and visual modes of learning spelling. His conclusions are quoted in Principal W. B. Wait's Annual Report for the New York Institution for the Blind, 1903. They are in the order of merit, from highest to lowest. The quotation marks indicate Mr. Wait's report; the comments are ours. SPELLING 121 1. '^Copying with speaking (naming the letters softly)." This plan employs the eye, the ear, the tongue, and the hand; it requires attention, observation, and physical poise; it presupposes good control of the class and favorable environment. 2. '^ Copying with speaking aloud." This plan is criticised because the noise made by a large number of the pupils may be a source of disturbance to several pupils in the class. 3. '^Seeing with writing movements." Lender this plan a word is written on the blackboard or on a card so that every pupil in the class can see it. Pupils vis- ualize the word. In making the writing movements in the air, their effort to learn combines the sense of sight and the motor activity. 4. ''Spelling (hearing the letters named)." This plan is criticised because it deals with letters as the units of our language instead of considering words as symbols of ideas. 5. "Seeing with speaking aloud." 6. "Seeing with speaking softly." 7. "Seeing alone." 8. "Hearing with writing movements." 9. "Hearing and speaking aloud." 10. "Hearing with speaking softly." 11. "Hearing alone (word pronounced only)." "In all these methods, except hearing the letters named, and hearing the word pronounced, but not spelled, the work is done by the pupil alone. Spelling based upon words pronounced but not spelled to the pupil takes the lowest place, but spelling based on words both pronounced and spelled to the ear takes fourth place. Here it should be noticed that there is a long 122 METHODS IN EDUCATION period in the child's hfe before it has learned to read or write, when hearing and speech are the only available means of learning language." ''It will be seen that Schiller gives first place to a composite method, copying and speaking softly; the complete act involving the four memories, namely, a visual form of memory, a manual motor memory, vocal motor memory, and the aural memory." 283. Suggestions to the teacher. 1. Pronounce the word only once. 2. Give only one trial in oral spelling. 3. Work for natural tones in spelling. 4. Do not mispronounce unusual words for the sake of aiding the child in spelhng such words. 5. Vary the order from that given in the spelhng book. 6. Have pupils pronounce the word before and after spelling it. 7. Have children pause at the end of each syllable, but do not have them pronounce each syllable separately. 8. Teach phonic spelling whenever that will be an aid in mastering the words. 284. Rules for spelling. — A few simple rules may be helpful to pupils who find difficulty in ordinary spelling, but such memorizing should be limited to actual useful- ness. The limitations are evident as soon as a child finds more difficulty in learning and applying the rules than in memorizing the words themselves. The substance of the rules is the same in all texts, but simplicity and clearness in wording is found in the following from Reed and Kellogg's Higher Lessons in English, page 258. Rule I. — Final e is dropped before a suffix beginning with a vowel; as, fine, finer, love, loving. SPELLING 123 Exceptions. — The e is retained (1) after c and g when the suffix begins with a or o; as, peaceable, change- able; (2) after o; as, hoeing; and (3) when it is needed to preserve the identity of the word; as, singeing, dyeing. Rule II. — Y after a consonant becomes i before a suffix not beginning with i; as, witty, wittier, dry, drier. Exceptions. — Y does not change before 's, nor in forming the plural of proper nouns; as, lady's, the Marys, the Henrys. fiule III. — In monosyllables and words accented on the last syllable, a final consonant after a single vowel doubles before a suffix beginning with a vowel; as, hot, hotter; begin, beginning. Exception. — X, k, and v are never doubled, and gas has gases in the plural. 285. Classification of words. 1. Primitive. A word in its simplest form is a prim- itive or prime word; as, by, in, man, short, go. 2. Derivative. A word formed from a primitive word by joining prefixes or suffixes is a derivative word; as, going, unmanly, recall. 3. Compound. Two or more words united into one word form a compound word; as, today, watchman, subject-matter, text-book. 4. Synonyms. Words having the same or similar meaning are synonyms; as, hope and expect; certain and sure; devout and pious. 5. Antonyms. Words having opposite meaning are antonyms; as, good and evil; lazy and industrious. 6. Homophones. Words having the same sound but different spelling and meaning are homophones; as, sell and cell; beer and bier; write, rite, and right. Some- times called paronyms or homonyms. 124 METHODS IN EDUCATION 7. Homonyms. Words having the same sound and spelling but different meaning are homonyms; as the verb bear and the noun bear; the verb receipt and the noun receipt. Sometimes called homographs. 286. How to teach synonyms. — The first attention to synonyms will be directed by the teacher. During the class criticism of compositions, favorable occasions will arise. The teacher's explanation must be the source of information until pupils are able to under- stand the dictionary distinctions. Pupils enjoy the liberty of expression that seems to be granted by the choice of words. Following are suggestions: 1. Let oral and written language show the need of synonyms. 2. The early use of synonyms is larger power of expression; a later use is precision in language. 3. Observe the choice of words in quotations, dicta- tion, and other literary material. This is using a model. 4. Have pupils use their own language in making distinctions; verify answers by dictionary or other authority; use the synonyms in sentences. Illustrations 1. Ability, capacity. Ability is active power; capac- ity is receptive power. You have shown ability in algebra and capacity in literature. 2. Between, among. Between is a preposition show- ing relation of two things; among, more than two. Rachel stood between first and third among forty pupils. 3. Character, reputation. Character is what you are; reputation is what people think you are. ''Char- acter is injured by temptations and by wrongdoing; reputation by slanders and libels." SPELLING 125 4. Compare, contrast. Compare is to find resem- blances; contrast, to find differences. Compare Labra- dor and England in latitude and contrast them in climate. Habit, custom, usage. Habit relates to acts of an individual; custom implies the consent of many; usage is established custom. If you wish to conform to the usage of literary men, observe the custom of our best writers and then try to form habits accordingly. A Lesson on Synonyms Aim. To teach the synonyms habit, custom, usage. Preparation. The teacher has directed the atten- tion of the pupils to synonyms in the correction of com- positions. Models in Hterature have been studied for the purpose of observing choice and distinction of words. Synonyms in reading lessons have been explained and discussed. Now the pupils are prepared to note the differences in meaning in these synonyms: habit, cus- tom, usage. Three sets of sentences are written on the board: Set I 1. John has the habit of arising at six every morning. 2. Mary's habit is to practice every afternoon. 3. Rover has the habit of watching for his young master every afternoon. 4. Lincoln formed the habit of collecting and telling amusing stories. Set II 1. It is the custom of factories to close at five o'clock. 2. The custom of our school is to have assembly every morning. 126 METHODS IN EDUCATION 3. It is the custom of the boys to subscribe to Current Events every term. 4. The Chinese customs do not differ from those of their ancestors. 5. It is the custom of the American people to honor the anniversary of Lincoln's birthday. Set III 1. Usage demands that February 12th be celebrated with appropriate pubHc exercises. 2. The usage of the best writers calls for simple, direct English. 3. The usage of the Chinese has prevented the intro- duction of western ideas. 4. Usage demands that men remove their hats on entering church. Presentation. The sentences containing the word habit are read by several pupils. Then the teacher conducts the lesson by questioning. Brief answers are suggested here, but answers in complete statements may be required in the lesson with the class. Teacher. How many people are spoken of in the first sentence? Pupil. One. Teacher. What habit has he? Pupil. The habit of arising at six. Teacher. How often has he arisen at six? Pupil. Every morning. Teacher. Does this action require effort and think- ing? Pupil. No. Teacher. Why? Pupil. He has done it so often it is easy now. SPELLING 127 Teacher. What have we called Mary's act of prac- ticing, in sentence two? Pupil. A habit. Teacher. In each sentence we have spoken of how many people? Pupil. One. Teacher. What have we called the action of each? Pupil. A habit. Teacher. Habit is used, then, in relation to how many people? Pupil. One. Many pupils are called upon to state: Habit is used in relation to the acts of one person. Set II. On Custom Teacher. Does the fifth sentence refer to one or more than one? Pupil. To more than one. Teacher. What does that sentence say the people do? . Pupil. Honor the anniversary of Lincoln's birthday. Teacher. What is the action called? Pupil. A custom. Teacher. Why did the United States form the cus- tom of honoring Lincoln's birthday? Pupil. Because the people loved him and wished to show their gratitude to him. Teacher. They all agreed, then, to the act of honor- ing his birthday. That agreement of many people made the honoring of Lincoln a custom. Similar procedure with the other sentences in Set II. Teacher. Look at the sentences in Set II again. Do you think a few people can make a custom? 128 METHODS IN EDUCATION Pupil. No; custom requires the agreement of a large number of people. Teacher. Custom implies the consent of many, as you have said. This conclusion is expressed by several pupils. ^ ^ Set III. On Usage Teacher. What demands that February 12th be celebrated with appropriate pubhc exercises? Pupil. Usage. Similar procedure with other sentences in Set III. Teacher. How was Lincoln regarded by his country? Pupil. He was regarded as a hero whom all loved. Teacher. According to the first sentence, how may we honor our heroes? Pupil. By celebrating their birthdays. Teacher. How long has this custom been observed? Pupil. A very long time. The people of the olden times did likewise. ' Teacher. A custom that has lived very long becomes usage. It is accepted and followed by the best thinkers. Teacher. What does usage or long established cus- tom ask of good writers of English? Pupil. Simple, direct language. Comparison. One sentence in each group is consid- ered. All three are compared and the differences in meaning brought out. Children state in their own words the distinction. Pupils are sent to dictionaries to verify the distinction in use. Application. The teacher requires the children to give sentences employing the synonyms. Sentences with blanks are written on the boards. The pupils fill in the blanks with the proper synonyms, always stating why they have used the synonyms chosen. SPELLING 129 Teacher encourages the use of the synonyms learned in oral and written work. 287. How to teach homophones. — As these words are ahke in sound, the sense of hearing alone will lead to error. Observe the difference in spelling and the difference in meaning. With younger pupils, the words should be mastered one at a time; with older pupils, the whole group furnishes a basis for contrast and a stimulus for mastery. A few groups will suffice. It is under- sfbod, of course, that use in good sentences is one final test of a knowledge of the spelling and the meaning of homophones. The Rational Spelling Book, by Dr. J. M. Rice, calls such words as these homonyms : bad, wicked rite, a ceremony bade, did bid right, correct write, to record letters dying, expiring wright, a workman, dyeing, coloring air, atmosphere rain, water from clouds ere, before reign, to rule e'er, ever rein, part of harness heir, one who inherits Ayr, a town in Scotland 288. How to teach homonyms. — Since homonyms differ in meaning only, this one difference is the point to attack in teaching and learning. Recall all that has been approved as efficient teaching of spelling and apply as much of it as possible in teaching homonyms. Here are a few specific directions: 1. Teach only such homonyms as young children need to know. 2. Teach one homonym at a time. 130 METHODS IN EDUCATION 3. Teach by conversation and explanation ; have pupils converse, explain, and use the word; write sentences. 4. Teach the corresponding homonym in a similar manner. 5. Use both in sentences; drill on meaning and spell- ing; pupils construct sentences. 6. Illustrations of homonyms. bear, an animal bear, to carry cheer, good feeling cheer, to encourage saw, a carpenter's tool saw, did see How to Teach the Meaning of Words 289. Associative or objective process. — The object is shown and the name applied. If object cannot be used, show picture or other representation such as a drawing. Moulding board is a familiar means. Thus in teaching the noun divide, a word used for watershed in geography. Observe a divide in the school yard after a rain; compare roof; make an excursion to a hill and see that it is a divide; use pictures, drawings, and sand table. 290. By imitation. — Buzzing, flying, swimming, row- ing, and similar words are represented by action; likewise for words like mew, bark, purr, neigh, and bleat. This activity appeals to the dramatic instinct in children. Compare kindergarten activity. 291. By the context. — Most words being under- stood, focus attention upon what is not understood and then try to supply or substitute the meaning needed SPELLING 131 to complete the thought in the sentence. Take a quo- tation from Hawthorne: ''Happiness in this world, when it comes, comes incidentally. Make it an object of pursuit, and it leads us a wild-goose chase, and is never attained." The itahcized words can be defined from the context. 292. By etymology. — Take autograph: graph, write; auto, self; a signature written by the person himself. Compare telegraphy, phonograph, geography, stenog- raphy. Consult Anderson's ''A Study of English Words," American Book Company, 1897; Trench's " On the Study of Words"; Greenough and Kittredge's ''Words and their Ways in Enghsh Speech," Macmillan, 1901; Kennedy's "What Words Say." In analysis and synthesis pupils should use the tech- nical names of parts of words. Root, stem, base, ad- junct, prefix, and suffix are used by different authors, but base, prefix, and suffix are enough. The primitive form of a word is the root. It is the name used by philologists to denote the original form and meaning of the word. That part of a word to which the inflectional endings are added is the stem. The stem may be the same as the root, or it may be a modified form of the root. Thus in abduct, due is the root; duct is the stem. The word or stem to which other parts are joined is the base. The base may be a word, as in man + hood; or it may be a stem, as in auto + graph. A form or word joined to the base is an adjunct; as, rest + ful, steam + boat. A form placed before the base is a prefix; after the base a suffix. 132 METHODS IN EDUCATION ILLUSTRATIONS PREFIX ad, to bene, well or good contra, . against super, above ob, against BASE SUFFIX DERIVATIVES MEANING join, add adjoin to join to factor, doer benefactor one who does good diet, speak contradict to speak against script. ion, that super- that which is written written which scription above vi, way ous, being obvious being directly in the way, against or in front of us ject, ive, in- adjective inclined to be thrown thrown clined to to another word ad, to 293. By the history of words. — This is another kind of etymology. Thus dahha is derived from the name of the botanist Dahl. Dunce is from Duns Scotus, a famous scholar, whose theories were later ridiculed so much that his name became a synonym for stupidity. Trivial is from tres viae, the junction of three roads in Rome where gossipers spent their time in idle talk. Sincere is sine, without, and cera, wax; a guaranty applied to perfect vases sold in Italy. 294. By finding synonyms. — Comparison and con- trast impresses the meaning and at the same time enlarges the vocabulary. For example, take excite and incite. Excite, to rouse feelings for action; incite, to urge the excited feehngs to accomphsh something. A teacher excites her pupils for the consideration of social duty and then incites them to do their duty. SPELLING 133 295. How pupils may show their knowledge of the meaning of words. 1. By the use of the words in conversation. 2. By interpretation of the words in reading. 3. By constructing illustrative sentences. Inflam- mable means burning with a flame, while combustible means burning without a flame. 4. By forming definitions. 5. By using synonyms. d. By giving etymology. 7. By drawings and models. 296. Means of learning pronunciation. 1. By imitation of teacher. 2. By phonic drill. 3. By practice under 295. 297. Uses of the dictionary. — The dictionary is intended as a means of verification and also as a source of general information. Facility of use of the diction- ary implies the following: 1. How to find the word. 2. How to understand the sounds of the letters as indicated by the diacritical marks. 3. Mastery of syllabication. 4. Observation of accent. 5. Pronunciation. 6. In the higher grades, discrimination in the use of words, etymology, etc. 298. Devices in word-building. — This synthetic drill supplements the exercises in analysis of words, and also serves as generalization and appHcation of all phases of knowledge in spelling. 1. Write on the board a dozen prefixes with meanings, root-words, and sufl&xes. Help the pupils memorize 134 METHODS IN EDUCATION these three lists, and encourage pupils to add other pre- fixes, roots, and suffixes. Copy lists in books for perma- nent use at home or in school. This material can be used in a lively competition to form the largest number of words. Pupils should consult dictionary to prove the accuracy of their own work. For helpful reference books, see section 292. 2. Each pupil gives a word having the suffix er, and then defines the word. 3. One pupil gives a word and another pupil names synonym or homonym. 4. Teacher suggests a word like graphic; pupils give other words having the same root. 5. Suggest phonogram such as ail; conduct phonic drill on b, f, h, j, m, n, p, qu, r, s, t, w; combine; spell phonetically; use in sentences. Proceed in a similar manner with other phonograms like ate, at, et, air, ow. All the letters of the alphabet will thus receive phonic drill. 6. Form words from letters. Grant right to use the whole alphabet, but put a time limit upon the work. This exercise is a test in the constructive ability of the pupil. It is the synthetic process of testing analysis. Every effort to form a word from the given letters makes an exercise in recalling the roots, the prefixes, and the suffixes in familiar words. At the same time it may be a review of phonics as employed in homonyms and anto- nyms. 299. Grouping words by comparison. — We have already said that grouping words according to the number of syllables is unscientific. Some authors group accord- ing to meaning; others according to subjects or occupa- tions. Comparison in spelling looks for similarities. SPELLING out ought rough hour thought enough drought sought tough pout bought slough stout brought southern dough through should soul wound would source tour could shoulder you although 135 300. Grouping by contrast. hour bow nought too power sew naught through rough wood dough ruff should low 301. Correlation through dictation. — The dictation exercises made by the teacher or the pupils will use the related parts of the grade work. If the pupils are fol- lowing a selected list of words instead of a spelling book, it is likely that every word is studied in its related sense rather than as an isolated word. The summarizing value of adapted dictation exercises includes the correct use of the assigned words, the words misspelled from time to time, the words considered essential in the assign- ment of other lessons, and, in general, whatever words are needed in making the transition to a new grade by promotion. If this summary seems too comprehensive, it is justified by the requirements of the pupils' daily experience. The habit of accuracy in written work and the breadth of content secured by correlation make dictation exercises a direct preparation for life. 136 METHODS IN EDUCATION 302. "Make every lesson a spelling lesson." — Not approved pedagogy. The custom of directing atten- tion to misspelled words in every recitation is likely to distract the pupils l>y taking their attention from con- nected thinking in some other line of work. Such dis- traction cannot be justified for the sake of correcting misspelled words. As already suggested, there should be a special spelling list in every class. It is better for the teacher to make note of any errors in the other lessons and then reserve those misspelled words for the regular exercise during the spelling period. 303. Pronunciation of each syllable. — This practice is not generally approved. It is better to indicate a syllable by a pause, since the pronunciation of each syl- lable tends to separate the word into too many elements and thus to destroy its function as a symbol of one idea. 304. Repetition in writing misspelled words. — Do you approve writing misspelled words fifty times or more? No, not even ten times. Such an exercise is harmful as a means of correction. After a number of repetitions, the writing becomes a formal exercise with- out thought. Variety in the Recitations 305. Combination plan. — Teacher pronounces words, pupils write on paper; teacher spells words, each pupil marks his own paper and rewrites misspelled words. Oral spelling of all the misspelled words. This plan maintains order, institutes the habit of systematic pro- cedure and requires the use of self-activity and individ- ual responsibility. It is a preparation for future pupil government in the spelling period. 306. Self-correction. — Teacher pronounces words, SPELLING 137 pupils write; self-correction, pupils consulting books; papers submitted to teacher. This plan is an effort toward self-correction and a test of observation, indus- try, and honesty. The pupil does the work. 307. Interchange. — Teacher pronounces words, pupils write; papers exchanged, marked, and returned; critics consult each other if necessary and refer to books to settle disputes. Such mutual criticism exalts the function of criticism, habituates the critic in accuracy, ha's justification by authority, and gives the conscious- ness of social responsibility. Each pupil begins to feel his twofold duty to the class and to himself. 308. Monitor. — Teacher pronounces words, pupils write; one pupil stands, faces class, pronounces and spells while the others mark their own papers. Replace the spelling monitor if he misspells a word. This device tests enunciation, syllabication, and pronunciation; stimulates the desire of recognized leadership; promotes an active class spirit, and sustains a healthy interest in the work of the recitation period. 309. Group criticism. — Divide the class into two groups; all pass to the board; one group writes, the other group criticises; teacher or pupil pronounces words. Alternate the groups. In this way the teacher sees all the work and readily estimates its accuracy while the pupils are actually doing the work. 310. Individual responsibility. — One group at board, one group writing at desks. Teacher pronounces words, notices errors at the board, and pronounces a second time the misspelled words. Pupils at seats aid as critics. This exercise is an economy of time for teacher and pupil as it serves to approximate the work of a regular exam- ination. 138 METHODS IN EDUCATION 311. Class responsibility. — Appoint a committee of five pupils to prepare words for one week. Let this committee put words on board, conduct spelling reci- tation, mark papers,^ tabulate reports, and suggest remedies for faults. This plan has so many merits that none but a weak teacher will reject it. 312. Alertness. — All stand, spell in order, teacher not mentioning the misspelled words. The pupil who detects and corrects a misspelled word passes to a place of honor. This utilizes the competitive instinct in chil- dren and promotes the habit of thoughtful alertness. 313. Choosing sides. — Group instinct, loyalty, deter- mination to win. 314. Spelling down. — Individual satisfaction in vic- tory after honest rivalry. Co-operation through Responsibility 315. Pupils as examiners. — Ask the pupils to prepare twenty-five words for spelling examination. Suggest that this work be done at home so that the individual element may be sure to be felt. 316. Pupils as reviewers. — Invite pupils to make dictation exercises covering the work of a week or a month. Insist upon the standard of accuracy in spell- ing, capitalization, and the proper use of the words. Invite the use of sentences taken from literature or some other subject in the grade rather than the construction of sentences dealing with meaningless thoughts of the child. 317. Pupils as critics. — Assign one pupil as leader with the privilege of choosing four others to serve with him as critics in marking the class exercises for a certain day. Have the work done at home and have each critic SPELLING 139 sign his name to the paper marked by him. Return papers the following morning and distribute them to their owners. Give each pupil the right of appeal to his critic and finally to the teacher. This exercise emphasizes the responsibility of the critic while it teaches the child the real meaning of criticism as distinguished from fault-finding. 318. Pupils as friends. — Suggest the desirability of trying to attain the teacher's ideal of neatness and accu- racy. This appeal from a true teacher will secure the desired response. CHAPTER X COMPOSITION 319. Utility and culture. — To him who looks for the practical value of education, oral and written composi- tion has recognized usefulness as a means of business intercourse. No argument is needed to justify the prominence given to composition in the course of study; the only appeal is for some kind of teaching that shall assure rapidity and accuracy in the approved forms of commercial expression. There is another value in composition, aside from that which helps to earn a living. It is the culture value. Literature is composition; and out of the treasures of literature many a mind has drawn a compensation that is not measured by dollars and cents. It is a compensa- tion that serves as a satisfactory substitute for much that is lacking in life. This joy of literary appreciation is a direct stimulus to imitative construction in composi- tion. Here is one reason why pupils are required to study literary masterpieces as models. In studying a type of composition, the pupils are getting proper habits of interpretation and appreciation; the appreciation arouses a desire to imitate; and the desire to imitate is carried into execution through the voluntary act of the will. Thus we have an educational process in which the fruitage of culture is both a cause and an effect. 320. General aims. 1. To educate by stimulating thought. 140 COMPOSITION 141 2. To develop the habit of fluent, easy, and correct expression. 3. To help impression through expression. 321. The pupils' motives; pleasure, spontaneity, in- terest. — To relieve the writing of compositions from all feelings of drudgery, teachers are urged to make the desire of giving pleasure the predominating motive of the child. As soon as a pupil aims to write something that will please his teacher or his classmates, or any other friends, his production will be characterized by spontaneity; in reading it or having it read, his interest will be sustained or increased; and after receiving favor- able criticisms, which should always be given, he has a powerful stimulus for more and better work in this line. Note that the intellect, the feelings, and the will are all strengthened as the pupil habituates himself to writing under these conditions. 322. Principles determining selection of matter for compositions. 1. Within scope of child's knowledge. 2. Within scope of child's interest. 3. Limited to prevent wandering. If we assume that grading satisfies the welfare of the pupils, we may conclude that these principles apply whenever a theme for composition is selected within the prescribed limits of the grade work. In the fourth grade, for instance, is the theme Columbus a satisfac- tory theme? Under principle one, it should be satis- factory; under principle two, it is satisfactory; but under the third principle, it must be rejected. But limit the thought to The Boyhood of Columbus, and we have a theme that satisfies the three principles. Test in the same way for the seventh grade. The theme Columbus 142 METHODS IN EDUCATION presents even more danger of scattering thoughts; but choose The Discovery of Land for a descriptive com- position, and there will be no need of depending upon text-book theory for the valid application of the three principles mentioned. As another illustration, take The Panama Canal. Is it, as a subject, topic, or theme for elementary grades, justifiable? It is or can be within the realm of interest of every child above the third grade, but has the average pupil enough definite knowledge for serviceable exposi- tion? Probably not; and, for this reason, the third principle is not satisfied. But it is possible to limit the scope of this subject, get the desired information, and then write a composition in accordance with the prin- ciples stated, or any other principles accepted for the guidance of the work in composition. The experienced teacher passes quickly from abstract principles to test the results of classroom work. Theo- retical tests must yield to practical tests. The good teacher makes the subject conform to accepted prin- ciples because she knows the interrelation of knowledge and interest. Having these two, she makes the writ- ing of the composition a pleasurable reaction. Thus the three principles are exemphfied in one teaching act. 323. Suggestions for the teacher. — Much help can be found in Carpenter, Baker, and Scott's The Teaching of English. See page 134, in support of these sugges- tions on the preparation of the teacher: 1. Choose a subject that has possibilities; keep in mind the principles given in section 337. 2. Present it in such a way as to make the pupils see its possibilities. COMPOSITION 143 3. Stimulate oral discussion, but so direct it as to prevent wandering. 324. Kinds of composition exercises. — The two gen- eral divisions of composition work are oral and written. Under each of these there are various subordinate kinds which will be discussed in this chapter. One mistake in teaching is to separate oral and written exercises. Each aids the other and both should be used in every development exercise. ' 325. Oral composition. — This form of composition naturally precedes written composition, but pupils do not realize that talking is composing. While oral com- position is a specific kind in itself, it should always be used as a preliminary preparation for every written composition. It makes the transition easier because the pupil feels that the writing is only another way of express- ing what has already been expressed orally. ■ 326. In primary grades. — In the lower primary grades, the oral work may be divided into conversation and reproduction, the aim of the latter being to have the child give the exact words as nearly as he can. Simple and interesting conversation topics may include nature study, pictures, experiences of childhood, facts impressing kindness, good conduct, cleanhness, and courtesy; and a little later the use of myths, fables, and historical narratives may be introduced. 327. Dr. Maxwell on oral composition. — The phases of oral composition are here presented in seven headings, as originally printed in School Work, Volume I, page 1. In regard to the use of sentences to explain the meaning, some recent writers do not agree with Dr. Maxwell's opinion in number 7 below. They hold that correct use in a sentence is a serviceable way to teach the meaning of words. Compare section 295, 144 METHODS IN EDUCATION Kinds of Oral Composition 1. All answers to questions should be given in com- plete statements. 2. Discussion of the contents of the reading lesson. 3. Reproduction of stories told or read by the teacher. 4. Description of processes in arithmetic and manual training. 5. Separation of sentences into their complete sub- jects and predicates. 6. Recitation of prose and poetry. 7. Explanation of the meaning of words. Putting words into sentences is not a method of teaching the meaning of words, but a method of determining whether the meaning of a word is known. Kinds of Written Exercises 328. Optional classification. — Some kinds of written work are suggested here, but other classifications are accepted. Teachers will see the necessity of using oral work in connection with transcription, dictation, forms of correct expression, reproduction, paraphrase, abstract, and elaboration. 329. Transcription or copying. — Much importance is placed upon the habit of copying correctly from the board, paper, or books. Very few advanced pupils are able to copy accurately, because they never formed the habit of doing so in the primary grades. This exercise may be directed so as to teach or review capitalization, punctuation, unity of the sentence, sequence of thought, and paragraphing. Select material that is interesting and intelligible, and then require absolute accuracy. Do not make these exercises too long or too frequent. COMPOSITION 145 330. Dictation. — Exercises in dictation have a wide use in applying the principles of composition, and espe- cially in forceful drilling to correct errors. Dictation exercises teach the child to put on paper what is in his mind, thus helping to make the transition from spoken to written language. Use exercises having ethical or literary content. If the exercises for dictation are taken from the books used by the pupils, self-criticism is made easy and practical. ' 331. Forms of expression. — Exercises on correct forms of expression will habituate the pupils to the proper use of words before the technical reasons are understood. It is a good plan to devote at least five minutes a day to oral exercises of this nature. Repeat the essential exercises day after day until the form sounds right to the children. Remember that it is the ear that gives us most of our habits of speech. Only oral repeti- tion will fix the correct habits. Keep a list of the errors frequently made, and then arrange the dictation exer- cises accordingly. These exercises include such words as is and are, have and had, doesnH and donH, shall and will, may and can, double negatives, and other common errors. 332. Reproduction. — This form of composition exer- cise means the recalling of the exact words of the author. This restricted meaning of reproduction may not be accepted outside of New York City. Here and else- where the selections for reproduction should be models in thought and style. 333. Paraphrase. — This exercise means the expres- sion of another's thought in one's own language. It is helpful in causing a pupil to get the thought expressed in a given passage; but many educators consider it a 146 METHODS IN EDUCATION harmful exercise because it degrades the author's beauty of style and thought. Better to memorize the selec- tions for reproduction. 334. Abstract. — A condensed statement of the sub- stance of another's thought in one's own language is an abstract. 335. Elaboration. — This term is the converse of abstract writing. Brevity characterizes the abstract; en- largement and elucidation are characteristic of elabora- tion. It is an exercise conducive to freedom of thought and expression in narration, description, and exposition. 336. Kinds of written composition. — Description, narration, and exposition are three kinds used in ele- mentary classes. Description presents the appearance of things; narration presents a series of actions or hap- penings; while exposition seeks to explain the meaning of things. For a satisfactory treatment of how to teach these and other kinds of elementary composition, see Maxwell and Johnston's School Composition, or any other good text. 337. Problems. — The difficulties or problems in teaching composition may be summarized as follows: 1. The selection of subjects, topics, or themes. 2. How to conduct the recitation preparatory to writing. 3. Criticism and correction. 4. The use of models in 1, 2, 3. 338. Selection of subjects. — Three considerations are sufficient. 1. Principles. Same as in section 322. 2. Correlation. Select subjects from history, geog- raphy, and other grade work. This kind of selection comes under the principles in 1. COMPOSITION 147 3. Avoid such abstract subjects as Vanity, Ambition, The Growth of Pessimism. This suggestion is also under the principles in 1. Teachers are frequently asked for a positive suggestion on the selection of subjects, and so 2 is given; for negative suggestion, use 3. 339. Some suitable subjects. FOURTH YEAR Science. Coal and Its Uses. ' Geography. The Harbor of New York.\ History. Henry Hudson. Biography. Longfellow. Personal experience. A Visit to the Museum. FIFTH YEAR Subjects similar to those in Fourth Year. Narrative. The Boyhood of Lincoln. Descriptive. The Making of a Base Ball. SIXTH YEAR Advantages of the Panama Canal. The Aunt in Snow Bound. Why I Like Whittier. The Necessity of Bathing. What I Should Do with a Thousand Dollars. The History of Our Flag. SEVENTH YEAR Narration. My Progress in Four Years. Description of a picture. The Signing of the Declara- tion of Independence. Exposition. The Uses of Our Forests. 148 METHODS IN EDUCATION Argumentation. Virginia vs. Massachusetts in Amer- ican Progress. Science. Wireless Telegraphy. History. The Decisive Effect of the Battle of Sara- toga. Geography, History, and Literature in Evangeline. EIGHTH YEAR My Favorite Character in the Deserted Village. The Kinds of Levers. My Opinion of Webster as an Orator. The Power of Simple Words in the Gettysburg Speech. The Causes of the Mexican War. 340. The model as a preparation for writing. — See specific directions in School Composition. We shall pre- pare the class for writing by studying, analyzing, and imitating a model. Another exercise will deal with the preparation of original material. 341. The selection of a model. 1. Select a model from some book in the class. Every pupil should have a copy in his hand. Why? See last two sections in geography. 2. Select a model that the class will appreciate. There can be no culture value in interpretation that lacks appreciation. 3. Select a model having some rhetorical excellence, such as clearness, choice of words, or good outline. 342. The study of the model. — Suppose the model selected is The American Indians, a prose selection in the class reading books. 1. Pupils read selection to get the general nature of the selection. 2. Second reading for the more careful treatment of COMPOSITION 149 important parts, the aim being to bring about an appre- ciation of the beauty of the selection rather than to accumulate a fund of information concerning words or allusions. But there is special attention given to what words are used and how they are used; to structure, capitalization, and punctuation of sentences; to unity, continuity, and topic sentence in each paragraph. This analytic study reveals the structure of the parts and the whole, and also enables the class to make an outline skowing the thought or plan of the author. 3. A third reading will give increased appreciation and leave the selection as a unit in the pupils' minds. 343. Imitation of the model. — The study of the model gave as an outUne. It shows the thought in the author's mind and the arrangement or plan in the selec- tion. It follows: THE AMERICAN INDIANS I. Introduction. Probable origin of the Indian race. 11. Body. 1. Physical appearance and dress. 2. Manner of living; occupations, pleasures. 3. Relation to the white people, as friend and as enemy. 4. Future of the Indians. III. Conclusion. A peculiar type of man in Ameri- can life. Now have the pupils give the substance of the selec- tion, using their own oral wording. Observe outhne again. Take The Eskimo for a sub- ject and write a composition according to this same outline. A kindred subject is considered better than 150 METHODS IN EDUCATION the same subject, as the latter invites too much use of verbal memory. 344. The model in criticism. — Now the compositions on The Eskimo are ready for criticism, supposing that a day or more has elapsed since the compositions were WTitten. Comparison with the model is the process; and the points to be observed are the ones observed in the study of the model. This first criticism by com- parison should be done by teacher and pupils working together. 345. Outlines. — The study of the paragraph leads to the use of outlines. In the fourth grade the teacher should co-operate with pupils in making outlines and then have pupils compose orally on these outlines before writing. Some hold that this making of outlines pro- duces mechanical, uninteresting, and unimaginative writing; but, on the other hand, the weight of opinion favors the plan as a means of securing unity and con- tinuity of thought. 346. Purposes of outlines. 1. To aid in the gathering of material. 2. To secure its proper organization and condensation. 3. To secure the logical order of topics. 4. To leave the mind of the writer free for the expres- sion of his ideas. 5. To prevent wandering. 6. To fix the habit of clear, logical thinking. 347. Composition without model. — The time will come, of course, when pupils will write compositions without using a model as a preliminary preparation. The model is only a type, and so the model is not re- quired after the type has become familiar. In such cases, a regular order of procedure may be used. COMPOSITION 151 1. Assignment of theme. 2. Books should be read, lessons reviewed, subjects investigated; in short, information gathered from all convenient sources. 3. Oral discussion for summarizing, condensing, and organizing material. 4. Write outline. 5. Oral composition following outline. This may be omitted in the higher grades. -6. Write composition. 348. Criticism of compositions. 1. By pupil acting under general direction of teacher. Have first reading for paragraph structure; second read- ing for sentence structure covering concord of subject and predicate, adjective and noun, pronoun and ante- cedent, etc.; third reading for spelling of every word. 2. By use of the model. Typical composition read or written on board, and then each pupil corrects his own. 3. Interchange of compositions. 4. By the teacher. This is necessary once a month as a means of estimating the work of the class, but it is not approved for regular weekly criticism. It mort- gages teacher's time which should be reserved for rest or change of work; it violates the principle of self-activity of the pupil; it is practically useless unless the composi- tions be returned and the pupils be led to avoid similar errors in the next composition. 349. Suggestions on criticisms. 1. Teach pupils to consult grammar, dictionary, book of synonyms, and any other helpful references. This will aid self-criticism and at the same time teach pupils how to study. 152 METHODS IN EDUCATION 2. Reject all slovenly work and, if due to careless- ness, have the composition rewritten. 3. Do not try to read all compositions. Select a representative group and then make these the subject of criticism. 4. Establish a standard of excellence and adhere to it. 5. Treat individual difficulties in brief, personal interviews. 6. Give maximum praise for every indication of improvement. 7. Use constructive criticism. The child must think as a child and write as a child. 8. Assist pupils to clear thinking. The outhne aids clearness. 9. Use a simple code of marking. One is given in Maxwell and Johnston's School Composition, page 223. Place code on a chart in the front of the room. 10. Give oral drill on errors found to be general. Structural Errors 350. Too many rules. — We do not expect pupils to acquire a finished literary style during eight years in the elementary grades, but we do expect to find fewer structural errors from year to year. One cause for dis- appointment is the number of rules given for guidance. Nearly all the points can be grouped under the sentence and the paragraph; and the only safe remedy for recur- ring errors is to return to a review as suggested in the next two paragraphs. 351. The sentence. — It is a matter of discussion whether the sentence or the paragraph should be con- sidered the unit in composition. Reserving the decision, COMPOSITION 153 the teacher must teach the individual sentence before pupils can become proficient in composition. SpeUing, capitahzation, punctuation should be observed in all grades; recognition of subject and predicate in primary grades; simple, compound, and complex sentences with word, phrase, or clause modifiers in grammar grades. Neither subsequent construction nor criticism can be intelligently done if pupils fail to master a working knowledge of the sentence. . 352. The paragraph. — If we view composition work as a whole, the paragraph is the unit of thought Lower primary pupils may be able to think only in sentences, but pupils in grades four to six can understand the use of the paragraph. The concept of the paragraph is most easily secured by the analytic study of a model. Such a study will reveal the writer's plan made up of beginning, middle, and end; or, as the parts are called later, introduction, body, and conclusion. An oral dis- cussion of the plan or outline will lead to an inter- pretation of this framework of the paragraph; and then, following that outline, the pupils may write a paragraph; the last process is comparison and criticism. This exercise embodies analysis and synthesis. Pertinent Questions Answered 353. Rewriting compositions. — Should pupils he com- pelled to rewrite all compositions for the purpose of approx- imating perfection f No. Such expenditure of time in the correction of errors does not seem prudent. Better write another composition and thus apply principles of correction. 354. Occasional rewriting. — Should compositions ever be rewritten f 154 METHODS IN EDUCATION Yes, if carelessly done. Have the work done as extra work. If pupils write thirty compositions a term, it is thought useful to have four or five perfect compositions in the set. 355. Original drafts. — Are original drafts kept for reference as an indication of progress f Yes. Many teachers prefer to have a separate book for composition, so that the pupil may have a guide to his own progress. 356. Ink or pencil. — Are first comes written in ink or pencil? Pencil in lower grades; ink in upper grades. 357. Envelopes. — When letters are written, does the addressing of the envelope {or rectangle representing same) form part of the exercise f Yes. 358. Consulting references. — Do teachers allow pupils to consult dictionaries and other such aids during the composition lesson? Yes. Teach pupils to use all helpful material. 359. Choice of model. — Should a model be constructed by the teacher ? No; make a selection from good literature. 360. Cause of errors. — Are errors due to carelessness or ignorance? Most of the errors are due to carelessness. The pupils rely upon the teachers to find and mark the errors. 361. Time before criticism. — How long a time usually elapses between the writing of a composition and its cor- rection by pupils? If possible, allow at least two days to elapse. Au- thority is against correction during the same period, since pupils should not be expected to change their COMPOSITION 155 mental attitude within a period of forty minutes or an hour. 362. Effect of criticism. — Does criticism tend to check spontaneity and originality? With conscientious pupils, yes; with indifferent pupils, no. The tendency toward sympathetic, constructive criticism is no likely to produce unsatisfactory results. 363. No criticism. — Do you ever have compositions on which no criticism is made? -Yes, to encourage individuality. Let it be known in advance that the productions are to be read by the writer without oral or written criticism. 364. Signature of critic. — When pupils correct the compositions of others, do you require the critics to sign their names? Always. This allows the right of appeal to the critic or the teacher. It fosters criticism rather than fault-finding. 365. Colored pencil used. — Should teachers use colored pencil or black pen or pencil when they correct compositions personally ? Colored pencil. Economy of time for teacher and pupil in reviewing marking. 366. Errors indicated. — Do teachers indicate errors, or actually correct them? Indicate the errors. 367. Self -correction. — In what grade may self -correc- tion he advantageously introduced? As soon as pupils are capable of writing a sentence, they should begin self-criticism. Their knowledge of self-criticism should increase with their general knowl- edge. It is a part of self-realization. Hence, self- criticism can be justified in all grades above the third. 368. Time limits. — 7s a time limit assigned ? 156 METHODS IN EDUCATION Yes, in school; on original composition at home, no. But it is advisable to habituate pupils to approximate time limits at home as well as in school. They must meet such requirements in business. 369. Pupils choose subjects. — Do you ever allow pupils to choose their subjects? Yes, within specified hmits. Unlimited choice leads to vacillation and consequent loss of time. 370. Reading best work. — Should the best composi- tions be read at morning exercises f Yes; this establishes an honor standard. 371. Writing poetry. — Are your pupils encouraged to write poetry? Yes, occasionally. Every class can produce some meritorious poems. 372. General progress. — Is the habit acquired in composition work strong enough to be effective in the written exercises in other subjects ? Yes, if there is a good spirit among the teachers. When a school exacts a certain standard of excellence, the pupils respond. An Examination Question Answered 373. The question. — (l) What is the relative value of composition in school work? (2) How should outlines be used ? (3) Give an effectual method of criticism. (4) Dis- cuss the scope and method of correction. (1) Composition is one of the most important exer- cises in school work. It is a means of expression in all the other studies, and it can be made an efficient test of general intellectual progress. (2) Outlines should be used as guides in the selection and arrangement of important points. Pupils should be COMPOSITION 157 taught to make their own outhnes by study and analysis of model compositions. Take interesting selections from such writers as Hale, Irving, Alcott, Thoreau, or any others hked by the pupils; read the selections and make a list of the topics. Have children reconstruct stories from given outlines and then compare their compositions with the model. (3) Have compositions read in class and criticised favorably by teacher and pupils. Try to arouse the interest of the pupils by encouraging them to do their best to merit the approbation of their associates. (4) Teachers should not pass valuable time in cor- recting compositions. Make the pupils critics of their own work. In this way the pupils will learn to find their own errors, amend them as well as they can, and try to avoid similar errors in the future. Following are some rules to train pupils to criticise and correct their own compositions: " (l) Give the pupil all needful books of reference, and teach him how to find what he wants. (2) Have the pupil look for only one class of errors at one time. He should examine (a) his outhne; (6) his sentence structure; (c) his capitahzation, punctuation, and spelling. This would necessitate three careful read- ings of his composition." See Maxwell and Johnston's School Composition. Primary Language Attention is directed to Plans and Details of Pri- mary Language Work, by Catherine L. O'Brien; pub- lished by the author of Methods in Education ; 50 cents postpaid. This is a comprehensive treatment of all phases of language work in the first four years of the elementary 158 METHODS IN EDUCATION school. The schedule of lessons for daily, weekly, and monthly assignment satisfies all the requirements of the Elehientary Course of Study in New York City, and yet the scheme is flexible enough to suit the needs of primary schools in other localities. To give greater efficiency in using references. Miss O'Brien has cited references by pages for every topic treated in the four years of language study. No other one publication on elementary language work gives so much specific guidance to teachers, principals, and superintendents. CHAPTER XI GRAMMAR 374. Value of technical grammar. — A third phase of language study in the elementary school is formal gram- mar. The works of literary art in the readers, re-enforced as they ought to be by supplementary reading at home of the whole works from which the selections for the school readers are made, will educate the child in the use of a higher and better English style. Technical grammar never can do this. Only familiarity with fine Enghsh works will insure one a good and correct style. But grammar is the science of language, and as the first of the seven liberal arts it has long held sway in school as the disciplinary study par excellence. A survey of its educational value, subjective and objective, usually produces the conviction that it is to retain the first place in the future. Its chief objective advantage is that it shows the structure of language, and the logical forms of subject, predicate, and modifier, thus revealing the essential nature of thought itself, the most important of all objects because it is self-object. On the subjective or psychological side, grammar demonstrates its title to the first place by its use as a discipline in subtle analysis, in logical division and classification, in the art of ques- tioning, and in the mental accomplishment of making exact definitions. Nor is this an empty, formal dis- cipline, for its subject-matter, language, is a product 159 160 METHODS IN EDUCATION of the reason of a people not as individuals but as a social whole, and the vocabulary holds in its store of words the generahzed experience of that people, includ- ing sensuous observation and reflection, feehng and emotion, instinct and volition. — Report of Committee of Fifteen, page 48. 375. Scope of this chapter. — In this chapter it is not necessary to try to cover every point in grammar. Approved text-books suggest suitable methods of pres- entation in accordance with the characteristic plan of development of such texts. It is necessary, however, to present some of the most important and most difficult parts; and so we have selected what may serve as types in the matter presented and in all related matter. Thus the plan of teaching the noun clause is a distinct type of mental procedure which may be followed in teaching adjective clauses and adverb clauses. 376. A habit of thinking. — One specific value of grammar is the habit of mental activity acquired by an orderly way of attacking each sentence. Teach chil- dren to read the sentence, to find the principal parts, to select and classify the modifiers, and then to dispose of the independent elements. Teach the fundamental facts; and make all pupils feel that a mastery of the simple sentence means a mastery of nearly all gram- matical relation. In this way, grammar will not remain a synonym for what is difficult or impossible. 377. Facts before conclusions. — In regard to mental processes, teachers are urged to habituate pupils to observe the facts first and then draw the conclusions. We may illustrate this by taking one sentence, GRAMMAR 161 Pupils work faithfully Teacher. What part of speech is work? Pupil. Work asserts action; hence, work is a verb. Or this answer: Work is a verb because it asserts action. These two answers illustrate two mental processes, each tending toward a habit. Which process is preferred? The former requires attention, thought, judgment. It is the empirical, scientific method: observation, facts, conclusion. The second process is conducive to guessing and inactivity. Answers are given quickly, but the responsibility of testing the answer is shifted to the teacher. Cross-examination follows and frequently induces the pupil to change his opinion. Deliberate reasoning in the first instance is a clear gain for the pupil even though time is precious. One clear concept in the beginning of any process in grammar will obviate hours of drill in subsequent work. 378. The syllogism. — A closer analysis of the mental process just mentioned shows that pupils are constantly using the syllogism. Thus in the sentence given, what part of speech is faithfully? The child observes the word and then his thought follows this form: Whatever modifies a verb is an adverb. Major premise. Faithfully modifies the verb work. Minor premise. Therefore faithfully is an adverb. Conclusion. 379. Fundamental facts in grammar. — In treating the subject of errors in composition, we reached the decision in favor of going back to a simple classification under sentences and paragraphs. Some teachers make a chart of essentials under words, sentences, and para- graphs, and keep that chart in sight for daily use until 162 METHODS IN EDUCATION those essentials become a part of every pupil's mental equipment. This is ideal instruction. As technical grammar is not usually studied until the fifth or the sixth year, any normal child comes to the study of grammar with an apperceiving mass which embodies two or three years of systematic language work on words and sentences and, to a certain extent, on the paragraph. The first lessons in technical grammar are, therefore, simply an interpretation of EngUsh which the child is able to construct or comprehend. The transi- tion requires the use of new terms, but the interpretation of the sentence is not a new process. Difficulty arises because teachers do not hold to the mastery of basal facts. Three thoughts deserve consideration: the sen- tence, parts of the sentence, parts of speech. Nearly all of the relations comprehended in these three are simply classified in the following five statements: 1. The typical English sentence has two principal parts, subject and predicate. The subject may be noun or pronoun; the predicate must be a verb. 2. All modifiers of the subject have the nature of adjectives. 3. All modifiers of the predicate have the nature of adverbs. 4. A sentence may have a third principal part, namely, a complement. An object complement may be noun or pronoun; attribute complement may be noun, pronoun, or adjective. All of these parts of speech are known from drill on the first three fundamental facts. 5. Simple sentences may be combined into compound or complex sentences by the use of connectives. 380. Development based upon fundamental facts. — It is not supposed that the foregoing classification can GRAMMAR 163 be mastered in one term, but every step in grammatical study will be made secure if the child is taught to use that criterion during the first term. The syllogism is unconsciously used every time a child goes back to test himself by one of those five statements. In brief, the purpose of such a guide is to teach pupils how to study. An elaborate treatise on teaching how to study may be more welcome to the disciples of theory, but every successful teacher knows that the best results cannot b^ secured unless the guiding process is simple enough for children to understand and interesting enough to follow. This plan has met these two requirements. The following procedure suggests the general develop- ment under this plan. 1. Flowers bloom. All is new: sentence, subject, pred- icate, noun, verb. 2. Pretty flowers bloom early. Known, same as 1; unknown, adjective and adverb. 3. The pretty flowers of spring bloom early in our fleld. Here we have added another adjective, a pronoun, a preposition, and phrases. The adjective and the ad- verbial uses of these phrases are known from 2. The phrase is simply a new form. 4. The pretty flowers of spring bloom early and late in our fields. Conjunction is new. 5. Children like daisies. The daisy has petals. Chil- dren pluck them. The daisy is the day's eye. The daisy is pretty. Who brought the daisies f It was she. Here we have the purpose to present third principal part of sentence; new, names object and attribute; related old, nouns and pronouns and adjectives in third part of sentence. 6. Flowers bloom. Simple. Summer comes. Simple. 164 METHODS IN EDUCATION Flowers bloom and summer comes. Compound. Flowers bloom when summer comes. Complex. Notes on Plan of Development 381. Types. — These suggestions embody a basis or type of procedure in studying all the related parts of a sentence. This matter is merely an outline; more material is required for a full presentation. 382. Independent elements. — The interjection may be studied with nominative absolute and other inde- pendent elements. 383. Simple sentence first. — Too much emphasis cannot be placed upon a thorough knowledge of the simple sentence. Master the declarative sentence first, and then the other kinds from form of expression appear as easy modifications of the declarative form. All the parts of speech, too, may be studied in the simple sen- tence. A knowledge of nouns, adjectives, and verbs is a direct approach to participles and infinitives; and adding the adverb, you have the foundation for all kinds of phrases and clauses. See development lessons fol- lowing. 384. Maxims applied. — The process of development mentioned employs the maxims known to related un- known, simple to complex, from whole to parts. Interest is stimulated and apperception is assured. Teachers understand, of course, that the study of the simple sentence means more than analysis. Synthesis of given parts, original construction, reconstruction, filling blanks, and the various composition exercises will all be used to satisfy the needs of the pupils. 385. Content of illustrative sentences. — While it is advisable to use material that is familiar and interest- GRAMMAR 165 ing, there is no reason for using sentences that do not express a valuable thought. The following sentences are suitable: 1. Birds sing. 2. Respect the flag. 3. Bees gather honey. 4. The whale is an animal. 5. Plants need air and moisture. 6. Fawns are graceful. 7. The Mohawk valley is fertile. 8. The Mayflower sailed from Plymouth. 9. Icebergs from the Arctic Ocean melt in the Gulf Stream. 10. Magellan's ship sailed around the globe. 11. The territory claimed by the Dutch was called New Netherlands. 12. Staten Island has an area of nearly sixty square miles. 386. Oral analysis. — This process does not receive sufficient attention. When used according to an orderly plan, it requires close, accurate thinking; it is a means to mental and physical poise; and it has the twofold value of developing the power of oral and written expres- sion at the same time it is interpreting the oral or written expression of others. The diagram becomes more useful when it is supplemented by oral analysis. 387. Diagrams. — A diagram is a graphic representa- tion of the grammatical relations in the sentence. Some systems are too elaborate for practical use, but a simple and reasonable system of diagrams means economy of time, interested self-activity of pupils, and co-ordinated multiple sense instruction. The rule of limitation of use may be put this way: Use diagrams whenever they 166 METHODS IN EDUCATION satisfy the purpose of instruction in grammar. It is an abuse of diagrams to make them displace all oral analysis and parsing. 388. Drill. — The schools fail to give adequate drill. In the effort to cover the assigned limit of work, teachers present new matter day after day and then wonder why pupils have not retained the matter which was so care- fully presented. The average pupil will not give him- self the drill alone; drill is essentially the work of the recitation period. It should be simple, specific, frequent; and instead of repeating in all the lessons in this chapter, we offer the following suggestions for kinds of drill: 1. Use sentences that clearly illustrate the point of the lesson. Unnecessary elements in the sentence are likely to draw the attention away from the one point under consideration. This is specific, deductive applica- tion to complete the inductive process. It is the passing from the general notion to the particular notion. 2. Application in sentences found in the grammar. Habituate pupils to use the text-book as authority in grammar. 3. Use sentences in history, geography, reader, etc. This is another attempt to show pupils where to find suitable material. It tends toward independent study, as every pupil has a book; it permits physical adapta- bility, according to sight, comfortable position, etc.; it is correlation of studies. 4. Synthesis of sentences from given lists of words, phrases, or other elements. This appeals to the con- structive instinct of children. It may also be used as a stimulus in competitive effort. 5. Pupils find sentences in books or construct original sentences. GRAMMAR 167 6. Memorize mottoes, maxims, or other quotations that will serve as typical illustrations. 7. Apply grammatical knowledge in writing and in criticising compositions. 8. Pupils prepare questions for oral or written review or examinations. A good question requires a knowledge of subject-matter, and experience proves that the average class makes such requisite mastery if the teacher uses the questions prepared by the class. -9. Correlation as a preliminary drill in primary grades before beginning the study of formal grammar. 389. Parsing literary masterpieces. — The value of parsing as an educative process should be approved as only one of the useful exercises in grammar. The sen- tences used in parsing must satisfy interest and culture. The question arises, then, whether we should use literary masterpieces for this purpose. Does the dissection by analysis and parsing destroy the literary value of the selection? We quote from the Report of the Committee of Fifteen, page 49. *'A training for four or five years in parsing and grammatical analysis practiced on literary works of art (Milton, Shakspere, Tennyson, Scott) is a training of the pupil into habits of indifference toward and neglect of the genius displayed in the literary work of art, and into habits of impertinent and trifling attention to elements employed as material or texture, and a corre- sponding neglect of the structural form which alone is the work of the artist. A parallel to this would be the mason's habit of noticing only the brick and mortar, or the stone and cement, in his inspection of the archi- tecture, say of Sir Christopher Wren. A child over- trained to analyze and classify shades of color — 168 METHODS IN EDUCATION examples of this one finds occasionally in a primary school whose specialty is 'objective teaching' — might in later life visit an art gallery and make an inventory of colors without getting even a glimpse of a painting as a work of art. Such overstudy and misuse of grammar as one finds in the elementary school, it is feared, exists to some extent in secondary schools and even in col- leges, in the work of mastering the classic authors." 390. False syntax. — There is some difference of opinion about the advisability of using faulty sentences for correction. The objection is supported by the argument that the child is more likely to remember the incorrect form than the correct form. He will image the incorrect form by visualization instead of remember- ing the correct form which he reaches through abstract reasoning. But this argument is not convincing. The writing of the correct form gives the pupils the same opportunities for visualization; and, besides, comparison and contrast will intensify the impression of the correct form. Another consideration in favor of using false syntax is the fact that nearly all the leading text-books in grammar contain such exercises. See the last section in this chapter. '' The author is utterly at a loss to conceive on what principle the introduction of faulty sentences for cor- rection can be objected to. Specimens of bad spelling for correction are injurious, because, in English, speUing is not reducible to fixed rules, but is for the most part a matter of simple recollection, and if the eye gets accus- tomed to the look of ill-spelt words, it is often difficult to recollect the correct mode of spelling them. Syn- tactical errors are of a totally different kind. They admit of being corrected on fixed principles; and as the GRAMMAR 169 learner is pretty sure to meet with numerous examples of faulty sentences, both in conversation and in reading, it seems desirable that he should have some practice in the correction of those mistakes .which are of most frequent occurrence.. Those who object to exercises of this kind should, to be consistent, exclude from books on logic all specimens of fallacies given for the purpose of correction. Yet those who have studied and taught logic are aware that few exercises are more beneficial." -V Mason's English Grammar, Ed. 1861, p. 173. 391. Types of lessons. — The material furnished in these lessons is intended to give one sound method of presenting each topic, but teachers are not supposed to think that there is no other material or no other way that can be considered acceptable. No matter what the topic for presentation may be, a tactful teacher will find other ways of adapting the work to individuals and to classes. 392. Parts of speech. — The one fundamental fact to be impressed in teaching the parts of speech is that words are classified according to their use in the sen- tence. Pupils who work upon this basis find it neces- sary to observe the use of a word in every instance rather than to rely upon mere memory in giving definitions. Another point which needs emphasis is that the words must be used in sentences. No word can be classified as a part of speech in grammar until that word is given a correct use in a sentence. Under this interpretation the teaching of nouns, pronouns, or other parts of speech from miscellaneous lists of words cannot be justified. The old way of teaching the parts of speech required pupils to memorize definitions and then apply those definitions. It was the deductive method. Modern 170 METHODS IN EDUCATION investigation of the process of learning requires the inductive method, as we have already shown. The same general plan of teaching all the parts of speech is, therefore, a combination of inductive and deductive. Let us take a lesson on the noun. 393. Development lesson on the noun. I. Preparation. The preparation in this lesson illus- trates an instance where the teacher should not pass much time in reviewing the work already covered in grammar. It is possible that pupils know the sentence, the subject, and the predicate, but it is doubtful if much time passed upon reviewing these three terms would serve as a useful preparation for a lesson on the defini- tion of the noun. Perhaps the best preparation in a lesson of this kind is to go directly to the presentation after telling the pupils that we are beginning to make an effort to tell the names of all the kinds of words used in speaking and writing. II. Presentation. 1. Mt. Vernon is in Virginia. 2. Mt. Vernon was Washington's home. 3. Mt. Vernon is near the Potomac River. 4. The house has a large porch. 5. High columns support the roof. 6. Martha Washington had a pet cat. 7. A hole was cut in the door for the cat to enter Martha's bedroom. 8. An old negro watches Washington's tomb. 9. The tomb is locked. 10. The keys were thrown into the Potomac River. This series of sentences gives enough name words to be used in developing the definitions. The series of sentences forms one general thought which may be a GRAMMAR 171 source of interest to young children if the teacher will fill out some of the details suggested. It is not necessary to ask and answer questions here; teachers can use their own ways. III. Application. Similar sentences may be used in applying the definition that a word used as a name is a noun. The use of simple sentences will give drill enough for one lesson. Succeeding lessons should employ sen- tences made from lists of words furnished and also OMginal sentences constructed entirely by the pupils. 394. Development lesson on attribute complement. — See section 233. 395. Predicate adjective and adverb modifiers dis- tinguished. I. Aim. To determine the correct use of the predi- cate adjective and the adverb modifier. II. Preparation. Define and illustrate subject, predicate, noun, verb, adjective, adverb, and adverb of manner. III. Presentation.' 1. That boy appears prompt. 2. That boy appears promptly. 3. The sun shines bright in my old Kentucky home. 4. The sun shines brightly on Kentucky homes. 5. The horses are running wild on the prairies. 6. The horses are running wildly from the prairie fire. 7. The ship returned safe. 8. The ship returned safely through the rocky channel. 9. The pupils are faithful. 10. The pupils worked faithfully. The presentation is simply an application or drill upon the definitions called for in the preparation. The 172 METHODS IN EDUCATION adjectives in sentences 1, 3, 5, 7, and 9 denote a con- dition of the subject; the adverbs in sentences 2, 4, 6, 8, and 10 express manner of performing an act. This distinction suggests the rule. Use the predicate adjec- tive to denote a condition of the subject; use the adverb modifier to express manner. IV. Drill. Recall the verbs generally followed by an attribute complement, namely, be, become, appear, seem, feel, look. 1. Be kind. 2. Try to become courteous. 3. You appear well. 4. You work well. 5. This distinction seems easy. 6. Do you feel good? 7. Stand and sit erect. 8. The door stands open. 9. You will grow taller. 10. You will grow rapidly. For further drill use the device allowing a choice and have each choice justified. 1. awkward, awkwardly. The blind musician felt for a place to rest. 2. good, well. The child worked on his lessons. 3. glad, gladly. The children appeared when they were promoted. 4. strong, strongly. The cable is made enough to support a ton. 5. kind, kindly. The teacher spoke to the class. Correct these errors and give reasons: 1. How are you? I am nicely. 2. She looks beautifully. 3. The team played good. GRAMMAR 173 4. The food tastes very nicely. 5. Start quick and walk slow. 396. Personal pronoun and relative pronoun. — This exercise is put under one treatment to show the value of pronouns in the economy of expression. There is material enough here for two lessons. I. Aim. To show that personal and relative pro- nouns are sources of economy and euphony in expression. II. Presentation. SECTION I 1. Lincoln was President. Lincoln delivered the Gettysburg Speech. 2. This is Frank. Frank's declamation won first honors. 3. Mason was an active boy. Mr. Loring liked Mason. 4. See that bicycle. Harry Ransom made that bicycle. 5. The pocketbook was the prize. The pocketbook was given to the best speller. SECTION II 1. Lincoln was President. He delivered the Gettys- burg Speech. 2. This is Frank. His declamation won first honors. 3. Mason was an active boy. Mr. Loring liked him. 4. See that bicycle. Harry Ransom made it. 5. The pocketbook was the prize. It was given to the best speller. SECTION III By the use of the relative pronoun each pair of sentences can be combined into one sentence. 174 METHODS IN EDUCATION 1. Lincoln was the President who delivered the Gettysburg Speech. 2. This is Frank whose declamation won first honors. 3. Mason was the active boy whom Mr. Loring liked. 4. See that bicycle which Harry Ransom made. 5. The pocketbook was the prize that was given to the best speller. The sentences given in the three sections are closely related in wording and meaning so that pupils may employ their energies upon the differences in wording. Section II illustrates how a personal pronoun may avoid the repetition of nouns; the last five sentences illustrate how relative pronouns avoid the repetition of nouns and also improve the expression by uniting the two parts into one good sentence. Test the three sections by the sense of hearing and notice the pleasing effect in the last five expressions. Shall and Will 397. Meaning and use. — In early English shall was the past tense of a verb meaning to owe or to he under obligation to do. In its present use with other verbs to form the future tenses, shall has lost nearly all of its early sense of obhgation excepting in the second and third persons. Shall in the first person denotes simply future time; in the second and third persons, shall denotes promise, command, or threat. Will is from another old verb meaning to choose, to desire, or to he willing to do. It used to show that the subject had the power to determine the action. Will in the first person still retains the original meaning, but not so in second and third persons. In these two will denotes simply future time. gr.a:m:mar 175 Statements and Commands 398. Rule. — In the first person, shall expresses simply future time; in second and third persons, shall expresses promise, command, or threat. Will in the first person expresses promise, command, or threat ; in second and third persons, will expresses simply future time. 1. I shall go to Europe this summer. 2. You shall remain here to study. .3. He shall study this lesson in grammar. 4. I will help you. 0. You will be read}^ for me. 6. He will work with us. 399. Rule. — Shall may be used in the second and the third persons for prophecies and promises 1. You shall have your reward. 2. Thy future shall lead to flowery paths. In Questions 400. Rule. — In the first person, use shall; in second and third persons, use whichever auxiliary is expected in the answer. 1. Shall I recite? 2. Will you read our answers? 3. Will your father insist on punctuaHty? He will. 4. Shall your son be punctual? He shall Should and Would Should is the past tense of shall. Should has the same general uses as shall, but should, in all persons, retains its original meaning of duty or obligation. Would, the past tense of will, is governed by the general rules appljdng to ivill. 176 METHODS IN EDUCATION 401. Applications. — Give reasons for shall, will, should, and would. 1. Truth, crushed to earth, shall rise again. 2. We shall study. 3. We will study. 4. If I can't pray, I will not make-beheve. — Long- fellow. 5. She could not think, but would not cease to speak. — Crabbe. 6. There is no if in the case. That we shall succeed is certain. — Nelson. 7. The union must and shall be preserved. — Jackson. 8. Heaven never helps the man who will not act. — Sophocles. 9. I would rather be right than be president. — Clay. 10. Herodotus wrote as it was natural he should write. — Macaulay. 402. Modes. — The study of all English presupposes the desire to interpret good English and to acquire facility in writing and speaking good English. Gram- marians differ so much about the number of modes and about the distinctions between modes that it is not necessary to take a young class into these mooted ques- tions. Our general plan of development is one of com- parison and contrast. So it is in getting the different kinds of sentences from form of expression, in distin- guishing attribute complement and adverb modifier, in developing the function of participles and infinitives. So it should be in teaching modes. The declarative form of the simple sentence furnishes an illustration of the indicative mode. The same thought expressed in the interrogative form is another illustration of the indicative mode. A thought involving doubt must be GRAMMAR 177 expressed in the subjunctive form; while the imperative sentence gives the verb in the imperative mode. The following sentences will serve in this development: 1. The pupils study grammar. 2. The pupils are studying grammar. 3. Do primarj^ pupils study grammar? 4. If you study well, you will understand grammar. 5. Study diligently one hour each day. In helping pupils to discriminate the modes it is useful tu impress upon them that the indicative mode expresses a fact; the subjunctive mode a doubt; the imperative mode a command. The doubt is the only point that is really new in this process of discrimination. The pupils are familiar with the expressions in the declarative form and the imperative form from their study of sentences from form of expression. Hence, as an aid in recogniz- ing the expression of doubt, direct attention to the use of the connectives if, though, except, unless. Note that they simply aid in introducing a clause that is likely to contain a verb in the subjunctive mode, but the con- nectives alone do not make the subjunctive mode. Mode is a modification of the verb, not a modification of the conjunction. 403. Drill on modes. 1. I hate to see things done by halves. If it be right, do it boldly; if it be wrong, leave it undone. — Gilpin. 2. If you know the quotation, you can recite it. 3. Learn this definition well, and then you can apply it easily. 4. Do you understand the indicative mode? 5. If you can distinguish the expression of a fact from the expression of a supposition, you can distinguish the indicative mode from the subjunctive mode. 178 METHODS IN EDUCATION 6. The subject of a verb in the imperative mode is seldom expressed. 7. If you are here, you will understand these defini- tions. (Fact; we know that you are here.) 8. If you are present tomorrow, we shall drill upon modes in grammar. (Doubt; we are not certain about your attendance tomorrow.) Participles and Infinitives 404. The meaning of terms used. — Much confusion arises from the different classifications of participles and infinitives. This lack of agreement does not produce serious consequences in a school where any good text- book is followed as an authority, but it is a matter of inconvenience to students who have to pass various examinations. We meet the terms verbals, adjectival verbals, verbal nouns, participles, and infinitives. Any word derived from a verb may be called a verbal. Some grammarians adopt verbals as the general heading and then classify infinitives, gerunds, and participles as the three subordinate kinds. So it is done in Longmans' Enghsh Grammar, edited by George J. Smith of the New York City Board of Examiners. Maxwell treats infinitives as a mode of the verb and then puts the gerund and the participle under the verbals. Milne considers the gerund a form of the infinitive. Reed and Kellogg's grammar favors an explicit wording, such as, a participle used as an adjective and a participle used as a noun. For the purpose of clearness, we summarize : Verbals 1. Participle used as an adjective; verbal adjective; or simply the participle. 2. Participle used as a noun; verbal noun; or gerund. GRAMMAR 179 References Longmans' English Grammar, 144. Maxwell's Advanced Lessons in English Grammar, 144, 155. Milne's An Enghsh Grammar, 189. Reed and Kellogg's Higher Lessons in Enghsh, 65. Partici'ples 405. Lesson on participle used as an adjective. — There are three points to be used as a basis in this les- son: verb, adjective, noun. In this lesson we present the adjective participle. I. Aim. To teach the participle combining the nature of a verb and the nature of an adjective. II. Preparation. Review definitions and illustra- tions of verbs and adjectives. III. Presentation. 1. The sun rises. 2. The sun dispels the mists. 3. The sun rising dispels the mists. 4. Evangeline wandered from place to place. 5. Evangehne, wandering from place to place, sought her lover. 6. Wandering from place to place, she patiently waited her lover. 7. You recited well. 8. I heard you reciting well. 9. We, being weary, rested ourselves in the shade. Rapid drill upon subject and predicate in each of the first three sentences. Emphatic mention of predicate verb in each of the three sentences. Then direct atten- tion to rising in sentence 3. 180 METHODS IN EDUCATION Teacher. What part of speech is rising? Pupil. Rising is a verb. Teacher. What is the predicate verb in this sentence? Pupil. Dispels is the predicate verb. Teacher. Then are there two predicate verbs here? If pupils say yes, contrast predicate verb rises in sen- tence 1 and rising. If pupils answer no, go at once to the question to bring out the adjective use. Is the subject sun modified or unmodified? Pupil. Sun is modified by rising. Teacher. What part of speech, then, is rising? Pupil. Rising modifies the noun sun; hence, it is an adjective. Teacher. Rising is used as two parts of speech, a verb and an adjective. We say it participates or par- takes of two natures, and so it is a participle. Silent reading of sentences 4, 5, 6. Give time for thought. The development already done should sug- gest to all pupils what they are to find in these three sentences. They have before them what, where, and how to study. Teacher. Who has found another participle? If all fail, repeat process of passing from predicate verb in 4 to adjective participle in 5. Teacher. Find the adjective participle in 6. Pupil. Wandering is an adjective participle. Another Pupil. Wandering is a form of the verb modifying the subject pronoun she; hence, wandering is an adjective participle. If any pupils have failed to discover that the participle modifies a pronoun, this last answer should impress that fact. It is information from a classmate, not from the teacher nor from circuitous development. GRAMMAR 181 Proceed in similar manner with the other sentences. Then have definition formed. A form of a verb, not a predicate, having the nature of an adjective and a verb, is an adjective participle. IV. Drill. 1. The pupils studying grammar are attentive. 2. Do you know the definition taught yesterday? 3. See the pupils writing the lesson. 4. Having finished the lesson, the class marched to the gymnasium. 5. I, knowing your ambition, offered you an oppor- tunity for promotion. Constructive drill follows this analytic drill. 406. Uses of participles. 1. As a noun. (a) Subject and attribute. Begging a courtesy is selling liberty. (6) Object of verb. Pupils enjoy studying history. (c) Object of preposition. We receive good by doing good. (d) Apposition. Invention, applying old ideas to new uses, benefits mankind. (e) Independent. Generally speaking, interest sus- tains attention. 2. As an adjective. (a) Modifying noun. Lessons learned from experience are costly. (h) Modifying pronoun. Hearing your voice, I re- turned. 407. Distinctions required. — The student must dis- tinguish the mere adjective from the participle used as an adjective, and the mere noun from the participle used as a noun. The mere adjective does not have the nature 182 METHODS IN EDUCATION of adjective and verb. It is simply an adjective and it usually precedes the word it modifies. 1. Concealed resentment is dangerous. 2. Coming events cast their shadows before. 3. His soul was the 'pleasing companion of his body. 4. Beauty is only a doubting good and shining glass. 5. The growing plant needs light, heat, and moisture. The participle used as an adjective has the double nature of verb and adjective, usually follows the word it modifies, and may have the same complements and modifiers that verbs have. 1. Keep the pupils working. 2. Start the ball rolling. 3. The complement is the part completing the sentence. 4. Participles, or the words partaking of the nature of two parts of speech, have many uses. 5. Here is a paper neatly written, properly punctuated, carefully thought out, and placed on the teacher's desk at the appointed time. The mere noun has a single nature. It is often pre- ceded by the and followed by a phrase introduced by of. 1. The handling of money pleases some people. 2. Angry feeling is betrayed by the countenance. 3. The mastery of grammar is a difficult undertaking. 4. The groaning of the prisoners and the clanking of chains were heard. 5. Our pupils study drawing, sewing, and physical training. It is argued by some that when drawing, sewing, etc., are simply the names of subject-matter in the recitation they are nouns. Other authorities hold that as long as such words possess anything of the nature of verbs they are still to be classed as verbals. Thus Maxwell in his GRAMMAR 183 Advanced Grammar, page 155, classes drawing as a gerund. John learns drawing. Walking is healthy exercise. To avoid mooted points on examinations, the student is advised to use an object after drawing, singing, etc., if he wishes to classify those words under gerunds. 1. The pupils practice drawing natural objects. 2. The children enjoy singing songs. - 3. Do you enjoy reading English history? 4. Writing good English is a pleasing exercise. 5. Spelling ordinary words is not too difficult a task. The gerund, or participle used as a noun, has the twofold nature of noun and verb, implies or assumes action without asserting it, and may take modifiers and complements like those of a predicate verb. 1. We should encourage reading good books. 2. My going will depend upon your coming. 3. Persuading by kindness is sometimes the making of hard tasks for one's self. 4. Your studying now will prevent your worrying at the close of the term. 5. In carefully preparing every assigned lesson, one is doing one's duty to the class and to the school. 408. Drill on participle used as adjective; verbal, or verbal adjective. 1. Children come rejoicing. 2. He fell at his master's feet, weeping. 3. Wounds made by words are hard to heal. 4. Your credit being good, I will trust you. 5. I, being your guardian, expected to have my way. 6. Rising to reply, Washington stood blushing and stammering. 184 METHODS IN EDUCATION 7. The treaty having been signed, trade was resumed with Spain. 8. Pronouns denoting the person speaking are of the first person. 9. The region drained by a river system is called the river basin. 10. Columbus, seeking the back door of Asia, found himself knocking at the front door of America. — /. R. Lowell. 409. Drill on participles used as nouns; gerunds, or verbal nouns. 1. Let us beware of losing our enthusiasm. 2. Doing well depends upon doing completely. 3. What do you think of his writing that letter? 4. By writing slowly you may learn to write legibly. 5. Forsaking evil companions is often the first step in reform. 6. All students should form the habit of reading poetry. 7. The object in saihng west was to find a shorter route to India. 8. He that is good at making excuses is seldom good for anything else. — Franklin. 9. Being in a ship is like being in a jail with a chance of being drowned. — Johnson. 10. Talking is like playing a harp; there is as much in laying the hands on the strings to stop their vibrations as in twanging them to bring out their music. — Holmes. 410. Drill on participle used as a mere adjective. — Here the twofold nature is not considered; the verbal forms should be parsed as adjectives. 1. The breaking waves dashed high. 2. The creeping night stole up the hills. GRAMMAR 185 3. Education is the moulding force of life. 4. Here sailing ships delight the wandering eye. 5. Now toward the early dawning east We speed our course away, With eager minds and joyful hearts, To meet the rising day. There, as we turn our wondering eyes. We view one constant show, — Above, around, the circling skies, * The rolling seas below. — Cape Cod Song. 411. Drill on participle used as a mere noun. — Notice that these forms are used to name an act rather than to express an act. 1. Slow traveling is tiresome. 2. The cackling of geese saved Rome. 3. The visitors joined in the singing. 4. Giving is more blessed than receiving. 5. A little learning is a dangerous thing. 6. The shearing of the sheep in Austraha is done by machinery. 7. The setting of a great hope is like the setting of the sun. — Longfellow. 8. The treatment of drowning is simply to perform artificial respiration. — Overton. 9. Drawing, reading, writing, spelling, physical train- ing, and declamation come in the afternoon. 10. The firing of signal guns was telegraphing by sound. It used only the hearing. But there were other ways of telegraphing that used the sight. — E. Eggleston. 186 METHODS IN EDUCATION Infinitives 412. Uses of infinitives. 1. As a noun. (a) Subject. To see is to believe. (5) Attribute. To see is to believe. (c) Object of verb. Pupils like to sing. (d) Object of preposition. We are about to sing. (e) Appositive. It is easy to find fault. (/) Independent. Every object has its face, so to speak. 2. As an adjective. (a) Modifying a noun. I have a lesson to teach, (h) Modifying a pronoun. Teach them to think. 3. As an adverb. (a) Modifying a verb. They came to study. (5) Modifying an adjective. They are eager to study. (c) Modifying an adverb. The fruit is ripe enough to eat. 413. Drill on infinitives used as nouns. 1. Never fear to do right. 2. Learn to govern yourself. 3. Your aim should be to govern yourself. 4. It is not impossible to govern yourself. 5. To govern yourself is a duty in citizenship. 6. It is never too late to mend. 7. It is not all of hfe to live. 8. To bear our fate is to conquer it. 9. To dispute about trifles is foolish. 10. It was proposed to tax the colonies. 11. To be just is easier than to be generous. 12. To be plain with you, you have not tried. 13. It is helpful to study the life of Lincoln. GRAMMAR 187 14. To submit to insult is to give occasion for it. 15. To cultivate kindness is a valuable part of the business of life. — Johnson. 16. In great crises, it is a woman's special lot to soften our misfortune. — Napoleon Bonaparte. 414. Drill on infinitives used as adjectives. 1. Have you time to study grammar? 2. Alger's stories seem to suit boys. 3. Ask them to sing patriotic songs. , 4. Pupils have a desire to appear well. 5, Columbus did much to calm the sailors' fears. 415. Drill on infinitives used as adverbs. 1. There is work enough to do. 2. Are you anxious to govern yourself? 3. She is too sensible to be flattered. 4. You should strive to govern yourself. 5. You are old enough to govern yourself. 6. I paused to observe the bird's proceedings. 7. Call to see me if you happen to pass this way. 8 Irving's writings were the first to make American literature popular in England. 9. Every morning the Persian wife used to kneel at the feet of her husband and ask nine times, " What do you wish that I should do?" 416. The infinitive without to. — The verbs hid, dare, feel, hear, let, make, need, see, behold, and a few others, are generally followed by the infinitive without to. 1. The teacher bade the pupils come at one o'clock. 2. Would you dare swim in the ocean? 3. Can you feel yourself grow? 4. Did you hear your mother call you? 5. Let music swell the breeze. 6. Make yourself speak distinctly. 188 METHODS IN EDUCATION 7. The first division need not do this home work. 8. Can you see the flag wave? 9. Behold the soldiers march in solid ranks. 10. Watch me diagram this sentence. A Development Series 417. Words, phrases, clauses. — This development shows how to proceed from the known to the related unknown. This lesson aims to secure different forms of expression for the same thought; an exercise in ampli- fication. I. Aim. To increase knowledge of phrases and clauses. II. Preparation. Review definitions of phrase and clause. III. Presentation. Recall the simple sentence of tw^o words, subject and predicate; then the added adjective modifier and the adverb modifier. Have following sen- tences on board: 1. .The athlete is a strong man. 2. The athlete is a man of great strength. 3. The athlete is a man who has great strength. 4. Study here. 5. Study in this school. 6. Study while you are in school. 7. Tell us an historical story „ 8. Tell us a story about history. 9. Tell us a story which relates to history. 10. The guide proceeded cautiously. 11. The guide proceeded in a cautious manner. 12. The guide proceeded as a cautious man proceeds. Pupils know definitions of parts of sentences, parts of speech, phrase, and clause. Now impress word, phrase, GRAMMAR 189 and clause as the three kinds of grammatical elements frovi form. All read sentence 1. Individuals name parts of sen- tence and parts of speech. Teacher underlines strong, Visuahze strong. Suggest the purpose of making or finding other expressions for the same meaning. The direct statement of the purpose of this recitation will be enough to encourage a class to select, discuss, and define the phrase elements and the clause elements. These twelve sentences will furnish the analytic drill. For synthetic drill the following italicized words are suitable for expansion: 1. We respect an honorable pupil. 2. Washington arrived punctually. ^ 3. An honest effort will be rewarded. 4. Diligent men are usually happy. 5. Franklin arose early. Note. — The presentation in this lesson is essentially a drill. This shows that the five formal steps need not be rigidly followed in all lessons. 418. Drill on adjective clauses. 1. I that speak unto thee am he. 2. The evil that men do lives after them. 3. He is well paid that is well satisfied. 4. Men must reap the things they sow. — Shelley. 5. Words are the only things that live forever. 6. Put your trust in those whom you have tested. 7. He serves all who dares to be true. — Emerson. 8. Blessed is he who has found his work. — Carlyle. 9. He that plants trees loves others besides himself. 10. Choose carefully those with whom you will associate. 190 METHODS IN EDUCATION 11. Time, which deadens hatred, secretly strengthens love. 12. Sunday is the golden clasp that binds the volume of the week. 13. That that that that boy used should have been a which. 14. We never tell our secrets to people who pump for them. 15. California is the state whose mines became known in 1849. 16. Self-respect is the noblest garment with which a man may clothe himself. 17. The power which brings a pin to the ground holds the earth in its orbit. 18. He who has resolved to conquer or die is seldom conquered. — Corneille. 19. Memory is the holy paradise out of which we cannot be driven away. — Richter. . 20. It is a behef in the Bible which has served me as the guide of my moral and literary life. — Goethe. 419. Development: Concord of relative pronoun and antecedent. I. Aim. To show that the relative pronoun need not agree in case with the antecedent. II. Preparation. Define pronoun, relative pro- noun; name the properties of nouns and pronouns. III. Presentation. 1. You are the pupils who make the school. 2. You are the pupils whose records give this school its reputation. 3. You are the pupils whom the teachers trust. 4. I dislike an eye that never twinkles. — Longfellow. 5. Life is a bubble which any breath may dissolve. — Greeley. GRAMMAR 191 6. He is a free man whom truth makes free. — Dry den. 7. No man is born into the world whose work is not born with him. — Lowell. 8. Construct a sentence which will have a relative pronoun in the nominative case. This lesson is an opportunity for real self-activity. It is application rather than the presentation of new matter. There are four inquiries for each sentence. What is the relative pronoun? What case is the relative pronoun? What is the antecedent? What case is the antecedent? Thus in the first sentence who is the relative pronoun, nominative case; pupils is the antecedent, nominative case. Here the pronoun and antecedent do agree in case. Take the second sentence. The relative pro- noun whose is possessive case; the antecedent pupils is nominative case. The pronoun and the antecedent do not agree in case. Likewise in 3, 6, 7, and 8. IV. Drill. For further effective drill have pupils recall, find, or construct sentences to prove that the relative pronoun need not always agree in case with the antecedent. 420. Development: The noun clause. I. Aim. To outline a plan of teaching the noun clause. This plan is a simple way of passing from the known uses of nouns by substituting a clause for each specific use of the noun. II. Preparation. Review uses of nouns as illus- trated in the sentences. Say that this lesson in grammar will use material taken from a discussion in astronomy. Some astronomers say that every star is like the sun in 192 METHODS IN EDUCATION brilliancy, but the stars appear like small lights simply because they are so far from us. The statement spoken of in these sentences is the statement that stars are suns. 1. Subject. The statement is beheved. 2. Object. Some people believe that statement. 3. Attribute. It is an interesting statement. 4. Object of preposition. Have you any doubt about the statement? 5. Appositive. This belief or statement is fascinat- ing. III. Presentation. The preparation has gone di- rectly to the points to be emphasized, namely, the principal uses of nouns in sentences. The pupils know the definitions of phrases and clauses. Now their efforts will be directed toward substituting the clause for each use of the noun in the sentences given. 1. That stars are suns is believed. 2. Some people believe that stars are suns. 3. The statement is that stars are suns. 4. Have you any doubt about whether stars are suns? 5. The statement that stars are suns is fascinating. IV. Drill. Two kinds of drill are suggested here, namely, interpretation of sentences given, and expan- sion. The constructive experience in making sentences to illustrate all the uses of noun clause is also advised. 1. Let us see how the earth revolves. 2. My desire is that you may become useful men and women. 3. The opinion that children are naturally bad is not favored by me. 4. Have grammarians any proof of what they say? 5. Nature teaches that there is order in her ways. 6. That you are ambitious is proved by your record. GRAMMAR 193 7. The question is whether I ought to do it. 8. Can you understand that a noun clause is used hke a noun? 9. Frankhn learned that self-help is one way to success. 10. Trouble teaches how much there is in manhood. — Beecher. Further drill by substituting and expansion is valuable in teaching the specific uses of noun clauses. Such a process in teaching is both natural and logical. It is sug- gested that pupils expand the itahcized parts into clauses. 1. The teacher asked the pupils to study. 2. We believe in the heroism of Nathan Hale. 3. Have you read of Arnold's sad death f 4. The beauty of Mi. Vernon is fascinating. 5. Grant proved his ability. 421. Drill on noun clauses. 1. I saw that you were faithful. 2. Galileo taught that the earth moves. 3. We believe that the soul is immortal. 4. Many men advocate whatever seems popular. 5. Can he hold the position? is the question. 6. Where Warren fell is not precisely known. 7. That he is rich does not mean that he is happy. 8. The charge is that you have neglected your duty. 9. Who wrote the Book of Job is not positively known. 10. Much will depend upon how you write your answers. 11. It is not work that kills men; it is worry. — Beecher. 12. The good is always the road to what is true. — Hamilton. 194 METHODS IN EDUCATION 13. I regret that I have but one Hfe to give to my country. — Hale. 14. " Beautiful creature," said the fox, '* you sing like a nightingale." 15. One would think that the fate of our country depends upon who will be our next president. 16. Have you any explanation of why you say that noun clauses are used as nouns? 17. The world will little note nor long remember what we say here, but it can never forget what they did here. — Lincoln at Gettysburg. 18. If ever it is a question whether you or the flag must perish, you will instantly choose that it shall not be the flag. — W. T. Sherman. 19. • Have we not learned that not stocks nor bonds nor stately houses nor lands nor the product of the mill is our country? It is a spiritual thought that is in our minds. — Benjamin Harrison. 20. That the daring barques of the Northmen had long before found their way from Greenland to the coast of North America is likely, though not certain. What is certain is that nothing more came of their first visit. — Goldwin Smith. 422. Connectives : Explanation and drill. — Pupils have already had some uses of the conjunction, the rela- tive pronoun and possibly the conjunctive adverb. The aim of this lesson is to give breadth to their knowledge of connectives. This aim may be attained by analysis to find illustrative uses and then by synthesis to impress those uses. I. Conjunctions 1. Words. Boys and girls study connectives. 2. Phrases. Pupils study at home and in school. GRAMMAR 195 3. Independent clauses. Some pupils study at home and then they recite well in school. 4. Noun clause. Teachers know that pupils need drill on connectives. 5. Noun clause. Can you tell whether you understand this or not. 6. Adverb clause of time. Careless people speak before they think. 7. Adverb clause of cause. Napoleon was sad because he was in exile. - 8. Adverb clause of condition. If you understand, let us proceed. 9. Adverb clause of purpose. We study that we may prepare for successful living. Correlative conjunctions mutually relate to each other. They should be placed before similar parts of speech or before corresponding groups of words. 10. Flattery corrupts both the receiver and the giver. — Burke. 11. There is nothing either good or bad, but thinking makes it so. — Shakespeare. 12. Try to observe whether to speak or to be silent. 13. Man is neither the vile nor the excellent being which he sometimes imagines himself to be. — Beacons- field. Relative pronouns. Used in adjective clauses Who, which, what, and that are the common forms. See sec- tion 418 for illustrations. The pronoun is often omitted, as in the following sentences. 1. This is the lesson you will learn. 2. Cicero is the orator you mentioned. 3. Connectives is the topic the teacher assigned. 196 METHODS IN EDUCATION II. Conjunctive Adverbs The name is derived from the double function of conjunction and adverb. First illustrations are in adverb clauses. 1. Time. You learn easily when you are interested. 2. Place. Cattle will graze where the grass is best. 3. Manner. The Indians live as their forefathers lived. 4. Comparison. New York has a better harbor than Baltimore has. 5. Degree. The greater a man is, the less he is dis- posed to show his greatness. — Channing. (Here the first the is an adverb modifying greater; the second the is a conjunctive adverb modifying the adverb less and connecting the two clauses. The principal clause is, The greater a man is.) Conjunctive adverb in adjective clauses. Why, when, and where are the common forms, and they are fre- quently associated in this way; reason why, time when, place where. 1. Give a reason why you study grammar. 2. This is the time when you study grammar. 3. This is the place where you study grammar. 4. The child trusts because it finds no reason in itself why it should not. — Holland. 5. Some schools are places where laziness becomes habitual. 6. The place whereto he came was an abandoned mine. 7. This great world is the mirror wherein we are to behold ourselves. — Montaigne. 8. The play is the thing Wherein I'll catch the conscience of the king.. — Shakespeare. GRAMMAR 197 9. Not a soldier discharged his farewell shot O'er the grave where our hero was buried. 10. Is patriotism a narrow affection for the spot where a man was born? — Fisher Ames. III. Relative Pronoun See illustrative uses in sections 418 and 419. 423. Distinctive uses of connectives illustrated. — Use in the sentence determines the specific classification of connectives. Take as for illustration. - 1. Strong men wept as the procession passed. Con- junctive adverb of time. 2. Grammar is as easy as arithmetic is. The first as is an adverb of degree modifying the adjective easy; the second as is a conjunctive adverb of degree. 3. Your place has been filled, as you came too late. Conjunction. 4. There are such pupils as one could desire. Rela- tive pronoun. 424. Synthetic drill on connectives. — Construct sen- tences to illustrate the following: I. Conjunctions 1. Co-ordinate: and, but, or. 2. Expressing cause: as, since, because. 3. Condition: if, unless, except. 4. Concession: though, although. 5. Purpose: that, in order that. II. Conjunctive Adverbs 1. Time: when, before, after. 2. Place: where, whence, whereto. 3. Degree: as-as, the-the. 198 METHODS IN EDUCATION 4. Comparison: than, as. 5. Why, where, when, introducing adjective clauses. III. Relative Pronouns 1. Who, whose, whom, which, that. 425. Fill blanks, tell kind of connective, and classify dependent clauses: 1. you have nothing to say, say nothing. 2. I admire his courage, I consider him cruel. 3. Do not go the sun has set. 4. Holmes wrote he amused others. 5. I am proud I am an American. 6. any one attempts to haul down the flag, shoot him on the spot. — John A. Dix. 7. We join ourselves to no party does not carry the flag and keep step to the music of the Union. — Rufus Choate. 8. There is no language or speech their voices are not heard. 9. He will neither come in go out. 10. I see no reason you should not succeed. 11. You cannot succeed you work. 12. The moon rose the sun had set. 13. he fails to repay me, I will trust him. 14. These are the pupils future will determine civic questions. 426. Exercises in false sjmtax. — These sentences illustrate many of the common errors in speaking and writing. Have pupils read a sentence, tell specifically what the incorrect use is, give reason, and then give the correct form. ^ 1. It is me. 2. I done that. GRAMMAR 199 3. I seen him. 4. This here one. 5. Do like I do. 6. I have got back. 7. Not as I know of. 8. I have saw him. 9. Who do you see? 10. I had ought to go. 11. See that there bird. 12. Can you learn me? 13. I had rather write. 14. He had laid down. 15. Set down and rest. 16. What are the news? 17. He was to Henry's. 18. Don't never do that. 19. They returned back. 20. It was her who called. 21. He must stay to home. 22. Did you see them men? 23. Either of the men are rich. 24. Henry and John is coming. 25. You hadn't ought to go. 26. Continue on in this way. 27. Who does this belong to? 28. He had near ten dollars. 29. I have a couple of dollars. 30. He died with consumption. 31. I guess I can do this work. 32. I only want five dollars. 33. This is the best of the two. 34. Many words they darken speech. 35. We had an awful nice time. 200 METHODS IN EDUCATION 36. I expected to have seen him. 37. He had four brother-in-laws. 38. There is lots of them in school. 39. The two first men are strongest. 40. Let you and I study together. 41. He dropped down into the water. 42. They differ between one another. 43. Some one has broke my pencil. 44. It is funny how long he stays sick. 45. You are better than me in arithmetic. 46. I don't like these kind of sentences. 47. Wanted a room by a man ten feet by fifteen feet. 48. You are not as careful as you should be. 49. The general, as well as his soldiers, were taken. 50. There seems to be no good reasons for tardiness. 51. At the North and South Poles the latitude is ninety degrees. 52. He spoke his piece clear and distinct. 53. A lady wants to sell her piano as she is going abroad in a strong iron frame. 54. I went to New York, you know, and when I came back, you see, I entered school. 55. With a few simple words he proved the previous speaker to have been mistaken. 56. He denied but that he was opposed to the law. 57. San Francisco is the largest city of any city west of the Rocky Mountains. 58. The company which she had taken so much trouble to select were not pleased with each other. 59. The elephant and beaver's instinct approaches close to reason. 60. If any pupil does not understand, let them say so now. CHAPTER XII GEOGRAPHY 427. The old and the new. — In the widespread criticism of old ways of teaching, geography has received its full share of censure. Slavish following of the text- book, memorizing long lists of names, and the study of unrelated facts are among the faults mentioned. The new presentation of geography makes man the centre of interest by relating all the facts to the welfare of man- kind. This is what is meant by saying that " geography should be invested with human interest"; and that ''the aim in teaching geography should be to give the pupil knowledge of the earth as it ministers to human life." Illustrations 428. The old way. — The old way of studying the rivers of the United States required a description of each river under the form "rises, flows, and empties." Today those three items are subordinate facts in the larger effort of finding what each river does to aid agri- culture, manufactures, commerce, and the pleasures of life. Aside from the use of drainage, the student studies the correlated facts of science, literature, history, and geography until every important geographical fact be- comes a related cause in the past, the present, and the future progress of humanity. 201 202 METHODS IN EDUCATION 429. The new way. — " Once there was no geography of the Rocky Mountains, for example, except a study of their location and elevation and their representation on colored maps. Today the student studies its Yellow- stone, its Salt Lake, its palisades, parks, and canons, but he soon runs aground in the legitimate fields of geography, and finds himself encroaching upon the territory of geology or botany, zoology, chemistry, physics, or mineralogy. Even in an elementary dis- cussion of the influences of these mountains upon the climate of the continent, many facts must go unexplained without the principles of natural philosophy. That geography of the Rocky Mountains is incomplete which does not include a typical and detailed study of its industries, of its mining, smelting, lumbering, herding, and its method of agriculture and irrigation. A study of the various peoples of the mountains may take the direction of sociology, economics, ethnology, and govern- ment. The geography of the Rocky Mountains thus approached, and only thus, may give a true insight into, and an ability to interpret, that part of the world." — Heeter, Commercial and Industrial Geography, N. E. A. Report, 1907, page 509. 430. Definitions of geography. — 1. Description of earth's surface. 2. Study of concrete environment. — Bagley, Educa- tive Process, page 37. 3. Biological investigations of living matter; political and industrial. — Harris. 4. Science of present appearance of earth^s surface; physical. — Parker, Talks, page 27. 5. Study of earth as home of occupations of man. — Dewey, School and Society. GEOGRAPHY 203 6. Study of earth as home of man. — McMurry, Special Method in Geography, 431. Broader educational use. — This modern con- ception of the industrial value of geographical knowledge is proof enough that the study of geography is more than a mere memory process. Present methods of teaching employ observation, memory, imagination, reason, and judgment in every complete study of a topic. An Eclectic View 432. The courses of study. — Several American cities have recently adopted courses of study which exemplify a kind of common agreement on matter and method. No other subject in the elementary schools is so near uniformity under our national ideal. One illustration of this excellence is seen in New York City. The general course of study for New York City was adopted by the Board of Education May 27, 1903; revised June 21, 1905, and June 11, 1907; and the syllabus in geography was adopted by the Board of Superintendents in Octo- ber, 1905, and revised in July, 1907. This last revision embodies the consensus of opinion of the best thinkers on this subject, and so some parts of the suggestions on geography are taken verbatim, as in sections 433 to 436 inclusive. 433. Introductory note. — Geography has been defined as '^the study of the earth as the home of man." How this phj^sical environment aids or hinders the develop- ment of man, and what man has done to modify, adapt, and utilize his physical environment, constitute the subject-matter of geography. The human feature — man's achievements in industry, commerce, and political organization — should predominate in the 204 METHODS IN EDUCATION study. As Dr. Harris has stated the proposition, the pupil ^'must begin with the natural differences of climate and lands and waters and obstacles that separate peoples, and study the methods by which man strives to equalize or overcome these differences by industry and commerce, to unite all places and all people, and make it possible for each to share in the production of all." The objects of teaching geography may be classified as practical, intellectual, and ethical. 434. Practical purposes. 1. There are many geographical facts, such, for example, as the location and characteristics of important cities, mountain systems, and large rivers, which it is a disgrace and a misfortune not to know. Every public school child must be made to know such matters so thoroughly that he will never forget them. 2. Maps and plans are now constantly used in news- papers and in business. The child must, therefore, be made to understand their conventional symbols and to become expert in referring to them and interpreting them. 3. The child, as a member of a great manufacturing and commercial community, should be familiar with the resources and productions, raw and manufactured, of his own country, and of all countries with which we have dealings; he should know the chief markets, home and foreign, for our goods; he should learn the quickest, safest, and cheapest trade routes; he should be able to form conceptions of the kind of goods which home and foreign customers require from New York. While it cannot be expected that a child's judgment on such mat- ters will be highly trained, he should know how and where to find such information when he needs it. GEOGRAPHY 205 4. Our current literature, magazines, and news- papers assume an intimate knowledge of geography on the part of the reader. School training in the sub- ject should, therefore, result in the ability to determine quickly, by the use of an atlas, gazetteer, or other work of reference, the location and characteristics of places, the names of which are met with in reading or required in business. Special training along this hne is required during the last three years of the course, under the head- ing, ''Location of places associated with important current events." 435. Intellectual purposes. 1. Geography may be made to train the observing powers. As far as possible everything taught should be illustrated from what the child may see in this city. This statement holds good not merely of the introductory lessons in home geography, but of the lessons throughout the course. Representatives of the chief races of men, every conceivable product of man's skill and industry, every modern means of transportation and communica- tion, may be observed in this city, while our parks and museums are full of objects of historic and contemporary interest. It is suggested that each pupil be furnished with a small blank book in which to record out of school the results of his observation. ' 2. It may be made to train the imagination. At every step the pupil is called upon to build up conceptions of objects unseen and places un visited through images derived from things seen, from pictures, and from verbal descriptions. 3. Rightly taught, geography trains the memory. The great vice, however, of geography instruction is the learning by rote of hsts of names, (rivers, cities, etc.), 206 METHODS IN EDUCATION or the descriptive matter in the text-book. To avoid this barren and wasteful process, the facts of geography should be linked by natural associations. ''What association so strong," asks Professor Laurie, ''as the association of all our knowledge of a subject with the famiUar objects of our daily hves, out of which we have made the teaching of geography spring? What associa- tion so strong as the organic connection which this mode of teaching estabUshes in the mind? " Names of places, whenever possible, should be associated with important historical events and with literary allusions. 4. Geography should also be made, particularly during the last three years of the course, to train the reasoning powers. When you ask a child to classify the natural features of a country, rivers, for example, according to some common property, as navigabihty; or the products of a country, as necessaries and luxuries; and still more when you ask him to generalize after he has classified, as, for instance, to determine the status of a people after a classification of their products, you are training him to reason. 436. Ethical purposes. — The ethical purposes of the teaching of geography are to lead to the moral lesson that all men must work and that each man should so work that his labor will benefit not only himself but the whole community, and that what is true of individuals is equally true of nations. "There is probably," says Professor Laurie, "no one subject so prolific of matter for independent thought and judgment on the affairs of life, and the destiny and duty of man. By means of it, too, we not merely furnish moral material, so to speak, but we extend the sympathies of the pupil, and lay the foundation of that sentiment of humanity which is the GEOGRAPHY 207 necessary counterpoise to narrow and parochial preju- dices." In order that these matters may be more fully under- stood, the pupils must also be led to consider the earth in relation to the sun, its forms, its motions, and such resultant phenomena as the seasons, air and ocean currents, and rains. 437. Col. Parker quoted. — The first steps in geogra- phy should give the child the means to imagine that which he cannot see. Begin with the forms around you; the close and careful study of the chains or ranges of hills, valleys, plains, coast-lines, springs, brooks, rivers, ponds, lakes, islands, and peninsulas. Study them as you do objects in botany or zoology. Take the chil- dren out into the fields and valleys; return to the school- room; let them describe orally what they have seen; then mould and draw it; and, finally, have them describe the objects they have seen by writing. Teach them distance by actual measurement; boundaries by fences, and other limitations; drainage by gutters, and the flow of water after a rain. Let them find a spring, and dis- cover how the water comes out of the ground. Have them bring in different kinds of earth — gravel, sand, clay, and loam. I have not time to give you any regular order of subjects — if there be one. Begin with one object, study it carefully, then take another and combine the two, and so on. I wish to call your attention espe- cially to the three great means of thought expression: first, the concrete expression; second, drawing; third, language. The first may be done by mouldings and obtained from an iron-foundry. Have pupils tell you what they have seen by moulding the form. Second, have them draw everything they see in relief and hori- 208 METHODS IN EDUCATION zontally. Third, describe what they have seen orally, and then in writing. Use these means continually in teaching geography. — Talks on Pedagogics, page 125. 438. Home geography. — No matter where the school may be located, the first lesson in geography should be an observation of the facts at hand. Schoolroom, school yard, district, town, country, etc., make a series in going from the known to the related unknown. But what facts should a child know as a basis for geography? 439. Fundamental facts. — A knowledge of geography implies a knowledge of location, direction, form, size, and distance. A further analysis might require space, time, proportion, and other elements, but our purpose is to ascertain useful essentials rather than to try to make a complete category. 440. Early lessons. — Nature study and object les- sons are a preliminary preparation for geography. In this way pupils acquire the elementary knowledge of soil, climate, productions; animal, vegetable and mineral life; and the general needs of mank:nd. This concrete approach to technical geography invites the use of approved methods and devices, and so it is probable that the plan is made familiar as a means of getting a concept of forms. The woid plan in this use means a representation of anything drawn on a plane. Thus the point of the pencil is represented by a dot; the pointer, by a straight line; the pane of glass, by a rect- angle; the face of a cube, by a square; the sphere, by a circle. The top of the child's desk furnishes an easy plan. Drawn full size, the plan requires actual measure- ment; a smaller size calls for the use of proportion and scale. Other plans may include the room, one floor of the building, the yard, and a part of the district or the GEOGRAPHY 209 city. Right here in this early work distinguish picture and plan or map. Show picture and plan side by side. 441. Points of compass. — The exercises 438 and 440 may be used in teaching the points of the compass. North, east, south, and west can be fixed in mind by positions of objects on each desk. Enlarge the applica- tion by indicating directions in room, yard, or district. Use sunrise and sunset as aids. Locate north star, face it, and then apply the old way of stretching arms, right toward the east and left toward the west. Mention use of shadows and blowing of smoke as means of deter- mining directions. Study wall map and apply knowledge. Locate a place and have children point to neighboring parts and tell directions. For more practical applica- tion, have pupils walk toward certain designated places. This exercise gives a personal relation to the facts. Its use makes pupils reahze that north is not always up nor is south always down. 442. Distance. — Actual measurements of familiar things must always be one way of acquiring the concept of distance. Time required in travelling, is another equivalent of distance, especially with city children. The average child will speak of the length of Brookyn Bridge as twenty minutes rather than a mile. Distance as an element of size in geography is likely to remain an imperfect estimate. 443. Maps. — The study of the schoolroom gives a larger conception of shape, size, location, cardinal directions, scale, and proportion. The intermediate points, northeast, southwest, etc., should be taught. The placing of pupils in the principal points in the room is a concrete way of sustaining interest. It gives reality to the exercise; and right here the pupils can begin to 210 METHODS IN EDUCATION use their constructive imaginations by making little journeys in the room. Name directions to and from which they travel. The map of the room requires another application of measurement according to a scale. Desk, library, and other large objects should be located on map, but the location of seats should be deferred. Too many items lead to confusion. This selection of im- portant objects is the first act in the formation of the habit of observing the essentials in later map study. The next step is simply a larger application of the ideas already gained. In cities, it may be a map of one floor of the school building; in rural schools, the yard is better because it puts pupils into contact with the realities of geography. The pupils' homes are still objective points of interest, but hills and valleys, woods and growing crops are also inviting forms of educative material related to the welfare of man. All these are interesting aids in fixing locations, applying directions, and training the pupils to image a map of all the points observed. 444. Models. — The exercises already suggested are means of training the observation. At the same time the memory is developed. When it is not possible to observe the actual forms of land and water, models and pictures are supplemental aids. Models may be made of clay, sand, putty, or paper. Clay and putty are serviceable for permanent illustrations. Moist sand is desirable because it can be used many times. Paper pulp is light and inexpensive, and it is easily colored to represent different elevations. The pulp is prepared by tearing paper into small pieces, soaking it, kneading it, and then draining off the water. It is easily worked into shape to represent land forms. Use glue or mucilage to fasten it to heavy paper or board. GEOGRAPHY 211 To illustrate rivers, lakes, or other forms of water, build the model upon blue or green paper or upon a pane of glass. Then mould the land forms but leave paper or glass exposed to illustrate water, 445. Constructive imagination. — The use of observa- tion as a process in elementary work in geography has already been shown. Likewise for the first uses of the memory in retaining geographical information. As sogn as pupils are required to think of forms or conditions which they have not observed, the constructive imagi- nation is brought into use. A familiar pond may be enlarged by the constructive imagination to make a lake; the neighboring hill can be increased in size till it becomes a mountain; the valley stretches to limits beyond the power of human vision, and it becomes a plain. All the facts observed in home geography are applied to locations in other parts of the earth; the streets, the houses, and the public buildings in the native village have to be transplanted and modified to make the image of a foreign city. Thus it is that in nearly every mental act in the broader study of geography the constructive imagination presents to the mind the images of things which can be thought although they are not actually observed. This power of the mind is also employed in constructing models, making maps, in getting the thought from oral or written descriptions, and in making commercial trips to the principal ports of the world. 446. Analytic and synthetic methods. — The analytic method of teaching geography begins with the globe as a whole. It divides the surface of the earth into land and water and then subdivides the surface into islands, peninsulas, continents, rivers, lakes, oceans, etc. The 212 METHODS IN EDUCATION advantages claimed for the analytic method are the following : 1. Whole to parts. 2. Early familiarity with the globe. 3. Better view of relative position, size, form, divisions of land and water. 4. The globe enables the teacher to explain causes of day and night, change of seasons, etc. 447. Synthetic method. — The synthetic method of teaching geography begins with the geography of the home and the schoolroom and then proceeds to the school yard, the neighborhood, and the larger pohtical divisions. It begins with the island, peninsula, valley, hill, river, or lake, which the child can see, and then pro- ceeds by use of the imagination to the other forms which the child cannot see. The advantages claimed for the synthetic method are the following: 1. Interest in familiar objects. 2. Known to related unknown. 3. From the near to the remote. 4. Concrete to abstract. 5. An inductive method. 6. It gives the pupil a fundamental geographical knowledge and enables him to pursue the study alone. In other words, it is a direct way to self-activity. 448. Both methods combined. — Both analytic and synthetic methods are used. The latter is used in beginning geography in 4A, the pupils making a map of the schoolroom and one floor of the school building as an introduction to the study of the map of the City of New York. Home geography covers location, nationali- ties and local history in such a way that the pupils become familiar with the industrial, social and civic rela- GEOGRAPHY 213 tions. The analytic treatment of the earth and its sub- divisions is also given in 4A, using the globe. Thus the advantages claimed for both methods are utihzed. 449. Excursions. — Excursions to fields, parks, and museums, to docks and water fronts, to centres of local industry, manufacturing estabhshments, and sources of supply, and to historical buildings, monuments, and tablets are recommended. Constant appeal should be m^de to the individual observation and judgment of pupils. — Introductory Note in Geography, New York City Course of Study. The mode of learning facts by means of excursions is a concrete approach to vivid ideas. A preliminary dis- cussion in the classroom prepares the mind for immedi- ate and active receptivity in the fields. The facts of local environment are learned so that pupils may begin early to adjust themselves to their environment. A second value of such facts is the acquisition of types of knowledge. These types are employed by comparison and contrast in studying similar facts or conditions in other parts of the world. Remember that the excursion itself is not the type of knowledge; the type is what is learned. Thus the study of a gas plant is a type for the study of other gas plants; one bicycle factory furnishes data for a type of knowledge in that hne. A third value of information acquired on excursions is economy in the act of learning. The lesson is concrete; the conditions are interesting; the class is under social stimulus; exercise, circulation, and respiration favor good physical support for mental activity. Fourth, the facts acquired do not admit adequate presentation within the scope of elementary text-books. Take, for instaince, a canal. The topic is the construe- 214 METHODS IN EDUCATION tion and operation of a lock. A quarter of an hour in observing the passage of a boat from a lower level to a higher level will give an intensity of impression that is not within the possibility of schoolroom teaching. Fifth, correlation of industries. Actual contact with the various unified forms of industry will tend to put the children into sympathy with the conditions requiring co-operative adaptation in later life. 450. McMurry on excursions. — A detailed treatment of excursions and types in teaching third and fourth grade geography is given in Special Method in Geography, by Charles A. McMurry. (The MacMillan Company.) Committee of Ten Quoted 451. Order of treatment. — The Report of the Com- mittee of Ten, page 211, suggests an order of treatment based on mental processes. (Quoted in sections 451 to 455 inclusive.) "Reduced to a sentence the scheme is: first, see; next, reproduce; then study the productions of others, and, meanwhile, ponder and reason on all. 452. Representative geography. — Immediately after the making of observations should come their reproduc- tion in the form of descriptions, sketches, maps, models, etc. The instruction of the teacher falls short of its highest efficiency if the early work is merely observa- tional and receptive. The great end of education is to create productive ability. One important form of this is representative production. Besides having value in itself, the description of features that have been seen and their representation by sketches, maps, or models reacts upon the observational work and induces a clear- ness, sharpness, and definiteness that it would not other- wise be Hkely to take. Not only this, but it leads the GEOGRAPHY 215 scholars to realize what maps, descriptions, etc., really mean. 453. Derivative or descriptive geography. — When pupils have gained true and vivid basal ideas by observa- tion and have, by reproducing these, acquired a realistic sense of the meaning of maps and an ability to read them, in the full and proper sense of the term, they are prepared to pass on to a formal study of descriptive geography. In . this, the observational and representative work of others than themselves is made the basis of study. The pupils are not now studying the earth's surface but ' sl description of the earth's surface.' 454. Rational geography. — It has already been urged that the pupils should be induced to observe changes and processes as well as the simple passive facts of geography, and that there should thereby be laid the foundation for an understanding of the origin, the devel- opment, and the future history of geographic features. This is the introduction of rational geography, as dis- tinguished from the mere noting and memorizing of facts. This phase of the subject, which leads the pupils into the reason of things, should be assiduously culti- vated, for it is the soul of the science. It should, how- ever, be carefully adapted to the capabilities of the pupils, particularly in the earlier stages of the study. They should not be forced beyond their capacity to compre- hend the nature of the agencies that have rendered geography what it is. On the other hand, there is an equal danger of underestimating the capacities of pupils to see into the reasons for natural operations. It is not recommended that rational geography be disassociated from observational and descriptive geo- graphy, but rather, on the contrary, that it be intimately 216 METHODS IN EDUCATION connected with these and that it be introduced so as to give them Ufe and significance. 455. Observational geography. — In the judgment of the Conference, observation should go before all other forms of geographical study and prepare the way for them; its object being (1) to develop the power and habit of geographic observation, (2) to give the pupils true and vivid basal ideas, and (3) to arouse a spirit of in- quiry and a thirst for geographical knowledge. This work of observation should begin with those features that lie immediately about the pupils and so fall easily within the reach of their direct study and ready compre- hension. In rural districts, the natural features of the surface will obviously form a large part of the study, while in cities, the artificial features must largely take the place of these. In the one instance, natural geogra- phy, as seen in the forms of the land, the hills, valleys, plains, meadows, divides, streams, lakes, etc., will pre- dominate, while in the other artificial, or humanistic geography will receive leading attention, as streets, railways, wharves, harbors, parks, plots, wards, etc.; but something of both these groups of subjects may be found and utilized in both localities. Neither should be neglected, for the pupils need not only to acquire clear ideas of the things by which they are chiefly sur- rounded, but type ideas of the things which characterize other localities and of which they need to form correct ideas without being able to see them. Observation, however, should not be confined simply to the passive fixed features by which pupils are surrounded. They should observe the agencies that produce surface changes, such as winds, rains, floods, thawing, freezing, cultiva- tion, etc. The temporary streams that follow heavy GEOGRAPHY 217 rains represent on a small scale many of the natural processes by which surface features are produced. From these immediate agencies, the observations should extend to the phenomena of the weather and the cHmate, such as temperature, winds, clouds, seasons, etc. ... As a step toward the study of the distribution of plants and animals, and an insight into their dependence upon temperature, soil, food, etc., the pupils should be en- couraged to observe the differences of plants on uplands, lowlands, marshes, etc., and upon sandy, clayey, gravelly, or stony ground, and to note the habitual dispersal of animals and insects in the neighborhood, and also their relations to each other, as in forming or frequenting forests, prairies, meadows, etc. As a step toward the study of the human elements in geography, observations should be made upon the population and its distribution, upon home occupations and productions, upon local political boundaries, as wards, school districts, city or town limits, etc., and upon the location of cities, villages, railways, canals, etc. 456. Concentric circles. — The arrangement of subject- matter in any course of study may be made so that the elementary facts of a subject are treated as fast as pupils are able to master those facts. Then in a later grade the more difficult facts are presented after a review of the elementary facts already mastered. This process of enlarging the scope of knowledge as pupils pass from grade to grade has been termed the arrangement in concentric circles. Many of the new text-books in the various subjects are made according to this plan. The old method attempted to master all essential knowledge of any part of a subject before passing to another chapter which dealt with another phase of the same subject, It is 218 ♦ METHODS IN EDUCATION claimed that the plan of concentric circles is in harmony with the interest and the ability of pupils. This arrangement in concentric circles, or cycles, is known as the spiral method in geography. This plan of arrangement is used in nearly all the modern courses of study, although there are some adverse criticisms of it. In teaching the circle of simpler facts, some teachers fail to give enough information, while others pass beyond the elementary circle into the fields of information which are supposed to be reserved for another grade. These two conditions are likely to make children show a lack of interest as soon as another teacher begins to review or enlarge the circle of information already covered. 457. Illustration of concentric arrangement. — The following outline for five grades illustrates the cycles in geography. 4A. Home geography, local history, the earth. Form and surface; the continents; the oceans; great islands and groups of islands; great seas, gulfs, and bays. 4B. The earth: motions, zones. Eastern and western hemispheres, world stories, duties of citizens and pubHc officials. 5A. The earth: seasons, latitude, longitude. General study of North America and United States. 5B. United States: representative states in each group. New York and the City of New York. 6A. South America, Canada, Mexico, Central America, and West Indies. Location of places associated with current events. 6B. Europe. Location of places associated with cur- rent events. , 7A. Review of United States and its dependencies. Places and current events. GEOGRAPHY 219 7B. Asia, Africa, Australia, and Island Groups. Places and current events. 8A. Mathematical and physical geography. Places and current events. 8B. Review of political and commercial geography. Places and current events. 458. Causal relations. — In the study of geography it is possible to memorize all the important facts about topography, climate, and human progress, but that knowledge would not be considered satisfactory in con- tent or method. Every part should be associated with cause and effect. Topography modifies climate and both topography and climate affect man. Man, in turn, converts many of the physical conditions to his own advantage. The tracing out of all these mutual conditions as causes and effects employs the reasoning powers in getting what is known as causal relations. 459. Causal series. — Recall the criticism of the old ways of teaching geography by making it a memory process. The explanation of causal relations already given is another way of showing that the modern teaching of geography appeals to the other powers of the mind. The processes required for reason and judgment are employed in all phases of the work from 4A through 8B. The arrangement of topics in such a way that the causal relations appear as a series gives rise to the term casual series. The following topics constitute a causal series: (1) Location, (2) resources, (3) industries and occupa- tions, (4) products, (5) commerce, (6) chief cities, (7) social development. See latest outline suggested in Plan of Study for 1907, section 466. 460. Man and nature. — Thus the interpretation of causal relations in geography involves the reciprocal 220 METHODS IN EDUCATION relations of man and nature. We quote from an article on Commercial and Industrial Geography by Superintendent Heeter of St. Paul, N. E. A. Report, 1907, page 508. " While cHmate and topography have operated singly and together in the distribution of life and both have played an important part, not only in the making of history, but in determining the customs and achieve- ments of every people, yet man has not been a slave to geographical conditions. He has gone forth to modify, to rise above environment, to multiply, and to subdue the earth, and there is a human, as well as a natural, interest in all this new study. 'Tis true, man has populated the earth, the North- land and the Southland, from Scandinavia to Siberia, from Abyssinia to the islands of the sea, but wherever he has gone, he has clad himself to meet the conditions of climate; he has built to withstand the tests of season; he has labored for wholesome food; and has forced the earth to yield up more than her native stores. The very form and character of his effort, as revealed by the apparatus in organization of industry, show not only the process of adjustment to native environment, but a determination and a success in rising above all natural limitations. Thus the Esquimau labors and invents, but not the same as the nomad of the desert, the planter of the flood-plain, the ranchman of the foot-hills, or the lumberman of the camps. The great double, question, then, confronting the student of geography today is, first, what physical and climatic conditions have directly influenced the different peoples of the earth, their modes of life, and their activities? Second, what have these people in turn done reacting against their geographical environment? GEOGRAPHY 221 Under the stimulus of man's inventive genius, along with the evolution of modern science and inventions, intercommunication has been made perfect, barriers have been broken down, regions once isolated have been connected, continents have been linked, the whole earth has become one vast neighborhood, and every man a neighbor. Here we see the interdependence of men, the East upon the West, the West upon the East, the North upon the South, and Europe upon America. Adverse conditions in one section affect all other sections. Civilized man everywhere is dependent upon all regions of the earth to contribute to his food, shelter, clothing, and culture; and a large part of civilized effort has been directed toward perfecting modes of travel, commerce, and intercommunication, until today streams of trade have opened into world-wide currents." 461. Types in geography. — A type in any study is a form of knowledge fixed in the mind. Such a form of knowledge becomes an apperceiving group for all other related knowledge. Thus in the study of geography it is possible to have the child master a characteristic mining section, or an agricultural section, or a manu- facturing section. Then when he comes to study other portions of the globe situated within the same general boundaries, his first inference will be that the conditions in those respective mining, agricultural, and manufac- turing sections are similar to the ones already studied. The analogy must be tested by finding a few conditions that mark a difference between the two sections. The advantages claimed for types as given by McMurry are the following: 1. Types are keys to larger areas of geographical knowledge. 222 METHODS IN EDUCATION 2. Realities are studies. 3. Thoroughly interesting and instructive. 4. The study of causes and causal relations. 5. Basis of a series of comparisons. 6. From home outwards. 7. Direct path to whole groups and sequences. Illustration of Type 462. Home city a type. — In 4 A grade the pupils make a thorough study of New York City. Note how this kind of treatment could be applied to Boston, Chicago, San Francisco, or any other city. Home Geography. — A plan of the schoolroom as an introduction of the study of maps; sketch plan of the school block, showing the position of the school building and the location of the classroom; the directions, north, south, east, and west indicated; plans drawn without reference to scale. Topography of the City of New York and vicinity; location of city with reference to the states of New York and New Jersey; division of city into boroughs and names of boroughs; direction of each borough from home borough; boundaries of the home borough and of Manhattan; land and water forms of the neighborhood; the harbor and water fronts. Location of main avenues and streets of home borough; names and locations of local bridges, tunnels, parks, and other important points of interest, with their attractions and the means of reaching them . Population. — Brief reference to nationalities com- posing it; occupations of the people illustrated by reference to neighboring farms, factories, shops, and to street and river traffic; transportation of people from the home borough to the business sections. GEOGRAPHY 223 Local history. — Stories connected with the history of New York told or read by the teacher or by the class; stories illustrated by reference to places and monuments of historic interest; biographical stories illustrating some of the great historic periods, as the settlement of Manhattan and neighboring territory; Dutch occupa- tion; the coming of the Enghsh; struggles with the French and with the Indians; New York during the Revolution. Department of the city as a manufactur- ing and commercial centre, e.g., Fulton's steamboat; the opening of the Erie Canal; the introduction of the telegraph; the laying of the Atlantic cable; the Brooklyn Bridge; consolidation; the Greater New York; the open- ing of the subway. Stories of distinguished citizens of the City of New York, such as Peter Stuyvesant, DeWitt Clinton, and Peter Cooper. Good citizenship. — Fire Department. Fire alarms; engine houses; duties of firemen; instances of heroism. Duty of Citizens. Care in the use of matches, kero- sene, gas, benzine, and other explosives or combustibles; care in regard to fireworks, bonfires, and rubbish; duty of keeping fire-escapes clear of encumbrances; fire- drills; means of egress from buildings; behavior at panics. PoHce Department. Enforcement of law; mainte- nance of order; control of crowds; protection of life and property; detection and prevention of crime; arrest of criminals; traffic regulation; instances of heroism. Duty of Citizens. Respect for pohce authority; appeal in case of danger; rendering assistance in main- taining order; conduct in the streets; ball-playing and stone-throwing — why forbidden ; protection of city 224 METHODS IN EDUCATION property. — From Syllabus, Revised Course of Study, 1905. 463. Comparison. — The study of geography by means of causal series, topics, etc., requires the constant use of comparison and contrast. But even aside from these specific methods involving the causes, many modern geographies present comparative tables for visualization. Some use dark lines of varying lengths to indicate the quantity of products. Others approach nearer the objective reality by presenting bags of different sizes to indicate the quantity of grains produced; barrels are used for wines, liquors, and other liquids. These tables whatever they may be, are simply another way of impressing geographical facts through multiple sense instruction. The memory alone is not required to carry the lessons of comparison. Illustration of Comparison North America 1. North America is an irregular triangle. 2. On its west coast there is a high range of volcanic mountains. 3. Parallel with the east coast runs a lower range. 4. The middle of the continent is occupied by a vast plain, from the Arctic Ocean to the Gulf of Mexico. 5. The St. Lawrence flows from west to east; the Mississippi from north to south. South America 1. South America is a regular triangle. 2. On its west coast there is a high range which contains many volcanoes. 3. Parallel with the east coast runs a secondary range. GEOGRAPHY 225 4. The middle of the continent is occupied by a vast plain from the Caribbean Sea to the La Plata. 5. The Amazon flows from west to east; the La Plata from north to south. This arrangement of facts is taken from DeGraff's School Room Guide, page 286. How to Study - 464. A plan suggested. — It is a rehef to a faithful teacher to get a plan that can be used without general revision. This does not mean that rigidity is welcomed as a characteristic in place of flexibility, but it does mean that the practical educator welcomes any suggestion based upon successful classroom experience. The fol- lowing six sections embody the recommendations by the Board of Superintendents in New York City in 1907, but the suggestions apply in New Orleans and Seattle as well as in New York. 465. Continents as wholes. — In studying the conti- nents as wholes, attention should be directed to their comparative sizes (North America being taken as the unit), relative positions, their general contour, their great mountain systems, their great rivers, their large seas, gulfs, and bays, and their important neighboring islands. Then should follow the main political divisions and the positions of important cities. 466. Plan for studying a country. — In studying a country the following series of topics, as far as they may be applicable to the country under consideration and in the grade in which the lesson may be given, is suggested: 1. Location as determined by latitude and longitude and with relation to surrounding countries and waters. Pupils should never be told the latitude and the longi- 226 METHODS IN EDUCATION tude nor required to memorize them, but should be trained to determine them by the inspection of a map. 2. Comparative size and shape. The area of the State of New York (about 50,000 square miles) may be taken as the unit with which the areas of all countries shall be compared. The compara- tive size should never be told, but should be made a matter of calculation on the part of the pupil. 3. Mountain systems and important ranges; slopes and plains. 4. River systems and important rivers. 5. Important cities, their location, and their com- parative population. The population of the City of New York, four miUions in round numbers, may be taken as the unit of com- parison. When learning about a city, the reason for which it is celebrated should be brought out. 6. Chmate, industries, products, and areas of pro- duction. 7. Form of government and general condition of the people as to education and ways of living. Under the head of ''Ways of Living" should be included housing, food, clothing, occupations, and use of animals. 8. Exports and imports, trade, particularly with the United States. 467. The recitation. — Most of the work in geography should be done in the classroom. Very little, if any, study at home is necessary. The lesson should generally begin with a study of a globe or a map. This should be followed or accompanied by the reading pertinent selections from the text-book or supplementary reader. The selections should be read aloud in class, and pupils GEOGRAPHY 227 should be expected to answer questions after a single reading. Then some time should be spent in copying the map roughly from the book or from the wall, indi- cating such phases of the subject as have been studied. The next lesson should consist largely in questioning the pupils with the map before them and in requiring them to make rapid sketches of maps from memory. This exercise is the best method of fixing geographical knowledge and of showing the pupil how accurate or inaccurate his knowledge is. It is, moreover, the easiest way to teach much of this subject, as well as the easiest way to test the definiteness with which the subject has been learned. Care should be taken to see that these maps are only sketches and that time is not wasted on the unnecessary elaboration of details. Neither tracing nor construction lines should be used. Sand or clay modelling may be used in the early grades to give a conception of the surface of a continent or a country. 468. Use of pictures. — A valuable aid to instruction in geography is a picture. The only true conceptions of certain elements of geographical knowledge are obtained by travel and observation. But travel and ob- servation for children are restricted within very narrow limits, and the best substitute is the picture. One picture is often worth volumes of verbal description, and at the present time there is scarcely any place or any feature of life or human activity of which a picture is not easily obtainable. Pictures are useful, however, only when children are trained not only to see and name the objects they contain, but to draw conclusions from them regarding the character of vegetation, the habitat and habits of animals, the ways of living and occupations of men, and other topics involved in the teaching of geography. 228 METHODS IN EDUCATION 469. Outlines by pupils. — In the higher grades, pupils should be exercised in making synoptic outlines of topics treated in the text-book. 470. Aids. — Globe; outline, commercial, United States geographical survey, topographic and census maps; weather charts, pictures, photographs, lantern slides, and other illustrative material; collections of minerals, rock, soils, seeds, raw and manufactured material; text-books, books of reference on geography, history, biography, travel, natural history; magazine articles, newspaper clippings, almanacs of the New York dailies, railroad and steamboat guides, and official reports. 471. Dr. Maxwell on geography. — In September, 1907, Dr. Maxwell dehvered an address before the principals of New York City. Sections 472 and 473 give the substance of his remarks on the revised syllabus in geography. See School Work, November, 1907, for an excellent abstracts of the whole address. 472. Suggestions to principals. 1. That you read and discuss with your teachers the Introductory Note, which explains the organizing princi- ple of the course and make suggestions as to method. 2. That you should take up lessons with your teachers as they will be expected to take them up with their pupils. These things require special attention to the following details: (a) How to use a globe. See section 484. (6) How to use a map. See section 502. (c) How to study the text of the geography. See section 504. (d) How to study a picture. Following plan suggested : Select a picture, see the items it contains, draw con- GEOGRAPHY 229 elusions as to character of vegetation, occupations of men, ways of living, etc. 473. Results that are essential. 1. In learning about a place, a pupil should be able instantly to point to it on (a) a map with names, (b) map without names, (c) place it on a map rapidly sketched by children. 2. Tell why it is distinguished. 3. To make rapid computations as to relative size; continents with North America; countries with New York State; cities with New York. 4. To tell the latitude and longitude of a place from inspection of a map; and to locate a place, the latitude and longitude being given. 5. To make a synoptic outline of a given portion of the text. To meet criticism, I would suggest that both teachers and children should be required when mention- ing any city in the United States to mention along with it the state in which it is located. Suggestions for Devices Some of these have already been mentioned, but we present them all under this heading so that the teacher may view the topics as a whole. 474. Concrete aids. — Moulding-board, globe, maps. See section 470. 475. Outline maps. — The time required for elaborate work in making the outlines of various states or countries is no longer considered useful in the study of geography. Outline maps may be secured from publishers and then the filling in becomes a valuable act of learning. Only the most important points deserve location on the maps. 230 METHODS IN EDUCATION The use of such map-making is simply one means of impressing through visuahzation and motor activity. 476. Product maps. — Product maps to illustrate resources. Concrete interest is attached to this kind of work as long as pupils are encouraged to place actual resources such as grains, minerals, kinds of trees, etc., on the map. 477. Scrap-book. — Have a bulletin or scrap-book for interesting articles brought by the children. The latter is recommended for permanent use. The teacher may find it necessary to reject some of the material selected by the children, but after a little experience the children will themselves be able to select what is worth preserving. Such a book becomes a permanent source of interest and information for succeeding classes. 478. Pupils as examiners. — Have pupils prepare suitable review questions at home. The abuse of this practice seems to be the only valid objection to this kind of constructive work. All the general acts in the school are tending toward habituation of a desired kind, and so there seems to be no good reason why pupils should be denied the right to take an active part in mak- ing the questions for review or for examination. The teacher's supervision is needed at all times, but that is no reason for rejecting all the work of this kind. A thorough justification may be found in a little actual experience. 479. Class discussion. — Assign topics for discussion by individuals. Limit the number so that the whole recitation need not be given to this kind of training. A few topics intelligently discussed will give variety to the exercise and also stimulate a wholesome interest in this kind of original research. Do not permit pupils to hold GEOGRAPHY 231 notes while speaking; encourage them to remember as much as they can. Have the pupil who is speaking face the class. 480. Debates. — Have debates in grammar grades. These debates serve as a valuable kind of review. The pupils are required to select the essential facts, to weigh them in comparison with other facts, and then to use their reasoning powers in defending what they hold to be the facts of most importance. The following subjects for debate are suggested: Germany vs. United States; Limited Monarchy vs. Republic; Eastern United States vs. Western United States, taking the Mississippi River as a dividing line; Railroads vs. Steamships in the Devel- opment of Commercial Prosperity. 481. Commercial trips. — These trips are journeys from one port to another. Their purpose is general review. Pupils must name the ports, the steamship lines connecting, the cargo, the cities passed, the status of respective nations, the favorable or unfavorable climatic condition, ocean currents, return cargo, etc. Encourage pupils to sketch outline map to indicate the journeys made. 482. Geographical cards. — Many excellent series of geographical cards are issued by the various publish- ing houses. Some of these cards are intended only for review, while others furnish interesting information of literary, historic, and scientific value. For personal use, teachers can make such cards covering the specific work of their own grade. 483. Competition. — The kind of interest sustained by spelling matches and other competitive drills can likewise be applied in review in geography. An interest- ing application of this kind of drill is the assigning of 232 METHODS IN EDUCATION each child to one country in Europe, for example, and then asking him to be ready to present a complete defense of all the advantages of his country. The blackboard may be divided into sections so that each child may write a list of the important points in his defence. 484. The globe an essential. — Every class in geog- raphy should have a globe. Better yet if every pupil can have one during certain recitation periods and study periods. No child can learn all his geography by per- sonal study of the earth itself, and so a globe should be made the most useful objective aid in all stages of the work in geography. Expensive globes are not necessary ; in fact, complex and elaborate representations are con- fusing. A large globe can be made of clay, paper, or wood. Then paint the surface black and observe the advantage and delight in using crayon to illustrate the point of the early lessons in geography. , 485. Uses of the globe. — Following are some of the specific uses of the globe in teaching: 1. Shape of the earth. The earth is an oblate sphe- roid. Then show the flattened surface at the poles. To carry the suggestion further, illustrate the flattening process by whirling a ball of moist dough on a wire or rod as axis. 2. Axis, poles, equator. 3. Rotation of earth. This will give foundation for later teaching of causes of day and night. • 4. Revolution of earth. This will lead to causes of change of seasons. 5. Inclination of axis, zones, ecliptic, latitude, longi- tude, meridians, and parallels. 6. Distribution of land and water. Draw line around globe and observe which hemisphere has the more land. GEOGRAPHY 233 7. Relative position of continents, countries, oceans, seas, etc. 8. Relief globe for illustrating surface. 9. Commercial routes to show the world's highways of commerce. 10. Use the globe in every development lesson to remedy defective ideas arising from studying a flat map. 486. The shape of the earth. — It is a difficult matter for pupils to understand all the facts used to prove that the earth is a sphere, but this difficulty is not a valid reason for dropping that work altogether. Pupils can understand some of the proofs; later in school hfe more proofs will seem clear; and during all the geography work, the pupils will be making useful inferences be- cause they have faith in the conclusion. This topic is a valuable one because it invites thought all through Ufe. Lesson Outline on Shape of Earth I. Aim. To prove that the earth is a sphere. II. Preparation. The very announcement of the aim arouses curiosity. Additional interest may be awakened by having a cube, a cardboard disc, a wire hoop, a large globe, and a small globe for each pupil. III. Presentation. The proofs involve personal experience and derived information. 1. Horizon is always a circle. This proof is a matter of observation. It is true for all locations. Use wire hoop to illustrate. Take any point within hoop, keep hoop in the plane of vision, and the limiting line of vision is always circular. 2. When ships are approaching, masts are seen first, 234 METHODS IN EDUCATION then the lower part of the masts, and finally the whole ship. This is likewise a matter of actual observation. Illus- trate by moving objects on the globe. 3. New stars come into sight as we reach new latitude. This is information from the experience of others. Show that this change in the sky may be due to the curved surface of the earth. Use pointer held against object moved on globe and observe arc described by end of pointer. N.B. These three proofs simply indicate that the earth has a curved surface. 4. The earth has been circumnavigated. This is a fact in history. Recall Magellan's voyage from Spain across the Atlantic, through the Straits of Magellan, over the Pacific to India, around the Cape of Good Hope, and thence back to Spain. That voyage in 1519 and 1520 was the first complete circuit of the globe. Show commercial routes around the world. Show by cardboard disc that the circumference is a way leading back to any starting point; but a passage over the edge of the plane surface of the card would not lead back. Recall fear of sailors on first voyage of Columbus. They thought they would drop off the flat surface west of Spain and never be able to return. 5. Earth's shadow on the moon in an eclipse is always a circle or part of a circle. None but a spherical body can cast a circular shadow in any position. Illustrate this by holding cube in the sun. Likewise with disc, pencil, pointer, book, etc. Observe shadow of pupil. The shape of the shadow is like the shape of the body casting the shadow. Briefly explain eclipse and show pictures of eclipses. GEOGRAPHY 235 6. Analogy. All the other planets are seen to be spherical, and it is not probable that the earth is an exception. This fact about other planets is verified by astrono- mers. Use of powerful telescopes is an interesting topic. Note. — These are proofs that the earth is a sphere. The following proofs are intended to demonstrate the flattening at the poles; in other words, the earth is an oblfiite spheroid. Proofs 8, 9, 10 should not be given in elementary work in geography. 7. It is a law of all rotating bodies that they rotate upon their shortest diameter. If a spherical body in a fluid state be rotated, its axis of rotation will become its shortest diameter. 8. By actual measurement of the arcs of meridians, it is found that a degree increases in length towards the poles. This shows that the arcs near the poles are arcs of larger circles. 9. A pendulum vibrates more rapidly near the poles than at the equator. This is due to greater force of gravity. 10. Bodies increase in weight when moved from the equator to the polar regions. This is partly due to gravity, as in 9. IV. Conclusion. The earth is an oblate spheroid. Its polar diameter is 26.48 miles shorter than its equa- torial diameter. Climate 487. Extension of the term. — The comprehensive use of the word climate requires a study of temperature, moisture, and all the modifying conditions of each. Temperature embraces the variations of heat and cold; 236 METHODS IN EDUCATIOINJ weather relates to daily temperature; climate means an average of weather conditions during an extended period. Moisture is water in any of its forms. 488. Conditions affecting climate. — The conditions affecting climate can seldom be considered alone; they modify one another. Younger pupils cannot under- stand all of the facts at first, but later study will utilize what is understood in the early lessons. These modifying conditions are often studied in relation to causes and effects. 1. Latitude. CHmate becomes colder as distance increases north or south from the equator. The region of the equator receives the vertical rays of the sun; the regions north or south receive heat from oblique rays; the polar regions are deprived of heat and light for certain periods. This difference in vertical and oblique rays of the sun is due to the inclination of the earth's axis. The earth's radiation of the heat received is the fundamental condition to be considered here. 2. Altitude. The general rule is that cold increases with altitude. Three hundred feet make a difference of one degree. Rapid radiation of heat is the principal cause. 3. Proximity to the sea. Effect is toward uniform climate; cooler in summer, warmer in winter. The sea absorbs heat and radiates heat more slowly than the land. Hence, cool breezes from the sea in summer, warm breezes in winter. 4. Prevailing winds. Climate is modified by heat, cold, and moisture distributed by winds. Sea breezes carry much moisture; land breezes are dry winds. 5. Position and direction of highlands. Highlands modify climate by shutting off hot or cold winds; by GEOGRAPHY 237 condensing moisture till it falls as rain; and by inter- cepting moisture-bearing winds. 6. Slope of country. Note how slope may favor climate under each of the five conditions already mentioned. 7. Nature of the surface. Forests equalize tempera- ture and prevent droughts and floods. Deserts and sandy soils radiate heat rapidly; clay soils retain heat and moisture. Large areas of cultivated land absorb and radiate heat more rapidly than grazing lands. Bogs, marshes, and other lowlands tend to cool the air and cause fogs. Rocky surfaces heat and cool quickly. 8. Ocean currents. See Gulf Stream, Japan Current. Illustrations of Climatic Influences 1. Western Alaska. Inference from latitude and altitude, cold; but proximity to sea, warm winds, and westerly slope favor mildness of climate. 2. Newfoundland same latitude as Ireland. New- foundland cold by latitude, by Arctic current, by prevailing winds; Ireland has warm climate on account of Gulf Stream, winds, nature of surface. 3. The great deserts of Utah and Nevada are caused by the position and direction of the Sierras; moisture shut off and precipitated. 489. Forms of moisture. — Since moisture has so much to do with climate, it is necessary to consider the forms of moisture, their causes, and a particular explana- tion of rain. 1. Water vapor is a name given to moisture in an invisible form. Water which passes into the air by evaporation may be said to exist as water vapor. 2. Dew is one form of condensed vapor. If air con- 238 METHODS IN EDUCATION taming water vapor be cooled, the vapor will approach saturation, since the lower the temperature, the less the capacity for water vapor. On clear, calm nights the soil and vegetation radiate heat; the surrounding air becomes cooler; hence, vapor is condensed into small drops of water. The temperature at which condensa- tion occurs is the dew-point. 3. Frost is frozen dew. Frost is formed when the dew-point is below 32 degrees Fahrenheit. 4. Fog. A visible mass of vapor on or near the ground is fog. Condensation is caused by the meeting of warm air and cool air. Thus the Newfoundland fog is caused by the warm air from the Gulf Stream meeting the cool air from the Arctic Current. 5. Clouds are visible masses of vapor floating in the air. 6. Mist is vapor falling in very small drops. 7. Rain is condensed moisture which falls when it becomes heavier than the atmosphere. 8. Hail is frozen rain. 9. Snow is frozen vapor. 10. Glaciers are rivers of ice. 11. Icebergs are portions of glaciers broken off and floating in the ocean. 490. Rain. — The four processes requiring explana- tion are evaporation, condensation, saturation, precipi- tation. I. Evaporation. Familiar facts from observation. 1. Steam is condensed vapor coming from heated water. 2. Heat from the sun or from other sources turns liquids into water vapor, and then the water vapor rises in the air. GEOGRAPHY 239 3. Water evaporates from clothes hung on a line. 4. Ink evaporates from wells. 5. Hands become chapped in spring because winds cause rapid evaporation. 6. Some ponds and brooks dry up in the summer. 7. Place dish of water in the sun and notice the effect. 8. Roads, sidewalks, and porches dry rapidly after a rain. Sun and wind hasten evaporation. 9. During hot afternoons in summer, the sun can be seen '^ drawing water"; i.e., actual evaporation can be observed. 10. Definition. The process of moisture passing into water vapor, under the action of heat, is evaporation. 11. Condensation. 1. Steam is not strictly water vapor since steam is visible. Water vapor, partially condensed by contact with cool air, is steam; and further condensation into water can be produced by having the steam come into contact with cold glass, slate, or other surface. 2. Moisture from the breath condenses on cool window panes. 3. Moisture condenses on the outside of a pitcher of water. 4. When pupils say they see their breath on a cold day, they see only the condensation of the moisture in their breath. 5. Definition. The process of water vapor or other forms of moisture passing into water, under the action of cold, is condensation. III. Saturation. Condensation of moisture in the atmosphere is caused by the cool surfaces of forests, hills, mountains, or by cool currents of air. Saturation 240 METHODS IN EDUCATION denotes simply the extent of condensation; it is all the moisture that the atmosphere can hold. IV. Precipitation. When saturation causes the moisture to become heavier than the air, the moisture falls as rain. This condition is called precipitation. Summary for Amplication 1. Heat of sun converts water into water vapor. The greater the heat, the greater the evaporation. 2. Hot air can hold more water vapor than cold air. 3. When hot air containing water vapor becomes cooler the vapor condenses into clouds. 4. The clouds become saturated by the uniting of the particles of water, and then rain falls as soon as the weight is more than the air can sustain. 5. Rainfall is constant in a belt about five degrees wide near equator; periodic, north and south of the constant belt; variable, beyond the limits of the periodic belts. 6. Rains purify the air, modify cHmate, clean the surface of the earth, and help sustain all animal and vegetable life. 7. Notice the circulation of water: Rains supply springs, brooks, rivers, and all other sources of moisture; springs, brooks, and rivers unite to supply larger bodies of water; evaporation furnishes moisture in the form of water vapor for the air; water vapor condenses into clouds, particles unite and fall as rain. Think how this circulation is a natural way of sustaining the conditions required for agriculture, manufactures, commerce, and the leisure joys of life. 491. Glaciers. — This lesson need not be difficult if teachers will distinguish known and unknown. GEOGRAPHY 241 I. Preparation. Recall hill, mountain, snow-capped summit of mountains; the melting, moving, and falling of snow on roofs, hills, and known mountains; successive thawing, snowing, and freezing on skating ponds; the familiar processes of wetting and packing snow in making houses, forts, snow-men. II. Presentation. Most of the facts are famihar. Larger applications are required. -1. Formation. Heavy snowfall on mountains during long winters. Summers too short to melt all the snow. Year after year snowing, thawing, melting, packing, and freezing continue. Thus the immense mass of snow and ice is formed into a glacier. 2. Movement. The slope of the mountain, the thaw- ing, and the weight of the glacier will tend to cause a movement. Amount, one foot or more in a day. The top of the glacier moves faster than the bottom, the centre faster than the sides. Why? Tall, narrow glaciers move more rapidly than broad ones. Why? 3. Action of the glaciers. Huge rocks are torn away by the sides and bottom of the glaciers. Some of these rocks are crushed and distributed as soil, while others, badly scratched, are left in the pathway of the glacier. Such rocks are found on Long Island and in many parts of New England and New York . 4. Norway, Sweden, Switzerland, and Alaska are the homes of glaciers. The western coast of Norway is a series of beautiful fiords caused by glacial action. III. Drill. Whether named as application or con- tinued presentation, this lesson is made more vivid by the following. 1. Pictures of glaciers. 2. Pictures of fiords. 242 METHODS IN EDUCATION 3. Stereopticon views. 4.' Magazine articles on life in the Alps. 5. Blackboard drawings. This subject is adapted to crayon illustration. 6. Geography readers and other correlated material. 7. Allied topics for collateral reading or for future lessons: Crevasses and moraines; the Ice Age in North America; icebergs. 492. Icebergs. — See lesson on glaciers. Icebergs are parts of glaciers. When the forward part of a glacier moves into the ocean, the force of the water lifts up the submerged part and breaks it off. This detached mass of ice then floats away as an iceberg. Ice is only a little lighter than water, and so only one-eighth of the iceberg remains above the surface of the water. The course of icebergs is directed by winds and ocean currents. Ice- bergs cool the temperature, cause fogs, and endanger navigation. 493. The seasons. — Pupils living in the temperate zones are familiar with spring, summer, autumn, and winter, but many pupils never fully understand summer and winter in the frigid zones and wet and dry seasons in the torrid zones. A season seems to stand for fixed temperature within definite zone boundaries. But as climate is the result of many modified causes, so the seasons yield to local conditions as we pass from zone to zone. Facts for Lesson 1. The sun illumines but half the earth at once. 2. The earth revolves around the sun once in 365 days. 3. The earth's axis is inclined 23J° to the plane of its orbit. GEOGRAPHY 243 4. The earth's axis always points in the same direc- tion. The north pole points toward the north star. 5. Temperature depends upon the direction, duration, and distance of the sun's rays. Inferences Different parts of the earth's surface mil receive dif- ferent degrees of heat during the year. These differences may be stated in describing each of the seasons. See geography or drawings. Description of Seasons 1. Spring. On the 20th of March the sun's rays are vertical at the equator; the circle of illumination intersects the poles; days and nights are equal every- where, and h«at is increasing in the northern hemisphere. This is the vernal equinox and the season is called spring. 2. Summer. On the 21st of June the sun's rays are vertical at the Tropic of Cancer; the circle of illumina- tion extends 23J° beyond the north pole and falls short 23 J° of the south pole; days and nights are longest in the northern hemisphere and shortest in the southern; heat is greatest in the northern hemisphere. This is the summer solstice and the season is summer. 3. Autumn. On the 22d of September the sun's rays are again vertical at the equator; the circle of illumination intersects the poles; days and nights are equal as on March 20; heat is decreasing in the northern hemisphere and increasing in the southern hemisphere. This is the autumnal equinox and the season is autumn. 4. Winter. On the 21st of December the sun's rays are vertical at the Tropic of Capricorn; the circle of illumination extends 23 J° beyond the south pole and falls 244 METHODS IN EDUCATION short 23 J° of the north pole; days are longest in the southern hemisphere and shortest in the northern; heat is greatest in the southern hemisphere. This is the winter solstice and the season is winter. 494. Zones. — Divisions of the earth's surface, cor- responding to the amount of heat received and to the varying length of days and nights, are zones. The lesson on the seasons gives the essential facts used in this lesson. This is simply a classification of those facts. 1. Torrid Zone lies between Tropics of Cancer and Capricorn. 47° or 3250 miles wide. Torrid means hot; this zone is the hottest portion of the earth. Days and nights nearly equal. Two seasons, wet and dry. 2. North Temperate Zone lies between Tropic of Cancer and the Arctic Circle. 43° or 3000 miles wide. Days and nights vary in length. Temperature varies; four seasons. 3. North Frigid Zone is north of the Arctic Circle. Width from Arctic Circle to north pole 23J° or 1625 miles; modern texts speak of the widths as 47°. Oblique rays of the sun part of the year. Days vary in length from twenty-four hours to six months. Two seasons, summer and winter. 4. South Temperate Zone is bounded by Tropic of Capricorn and Antarctic Circle. 43° wide. Four sea- sons opposite in time to North Temperate Zone. 5. South Frigid Zone. Size similar to North Frigid. Days and seasons opposite to North Frigid. 495. Isotherms. — Isotherms or isothermal lines are lines drawn upon a map or globe connecting all places having the same average temperature. Thus the GEOGRAPHY 245 isotherm of 50° Fahrenheit passes through New York at 40° latitude and London at 50° latitude, making a dip of 10° in latitude. The true climatic zones do not correspond to the astronomical zones already discussed. The Torrid Zone is bounded by 70° F.; the Temperate, by 70° F. and 32° F.; the Frigid is below 32° F. It is interesting to have the class follow a few isotherms around the earth and ascertain the causes for variation in latitude. Such an exercise will apply the facts under causes of climate. Latitude and Longitude 496. — A lesson outlined. — This topic is so important that it seems prudent to suggest material for class work or examinations. I. Aim. To understand latitude and longitude as means of locating places on the earth. II. Preparation. Conversational exercise about familiar ways of locating things. Numbers for rooms, coat hooks, houses; aisles and rows of seats in the school- room; avenues and streets in the city. Show plan of regular section of a city where streets and avenues are at right angles. None of these ways adapted to earth as a whole; hence, necessity for another way. III. Presentation. Have circular disc, blank globe, maps, and mapped globe. Draw axis and equator on circular disc and blank globe. These give starting points for measuring. 1. The name of the equator is known. Measure north and south in inches. Show impractical use of such standards as inch, rod, or mile. Tell that the degree is the unit and that every circle contains 360°. This number was chosen because it is divisible 246 METHODS IN EDUCATION by all numbers from 1 to 12 except 7 and 11. These facts must be accepted; they do not admit development. 2. For latitude, tell that the equator is starting point for measurement north or south. Hence, places on the equator have no latitude; they are marked 0°. Now draw a circle passing through the poles; ehcit that the north pole is a terminus in measuring north latitude, that the south pole is a terminus for south latitude; that the distance from the equator to either pole is one- fourth of the whole circle, or 90°; that the limits of latitude are 0° and 90°. 3. Parallels. Lines can be drawn parallel to the equator for convenience in indicating latitude. Call such lines parallels. Why? 4. Definition. The distance in degrees north or south of the equator is latitude. 5. For longitude, another starting point evidently is required. Tell pupils that the meridian passing through Greenwich, England, is the Prime Meridian. Prime means first; meridian means midday because all places on it have midday at the same time. 6. Draw Prime Meridian on black globe or indicate it on mapped globe. Two kinds of longitude, east and west. Have two pupils move objects from Prime Meridian east and west around the equator and thus observe that the maximum east or west longitude is one-half way around the earth, or 180°. 7. Meridians. Lines are necessary for indicating longitude; hence, the meridians. 8. Varying length of degrees of longitude. Observe meridians on globe and maps; mark meridians and cut sections from apple, watermelon, or other spherical forms. GEOGRAPHY 247 Make pupils see that greatest length of a degree of longi- tude is on the equator; at the poles, 0°. 9. Definition. Distance in degrees east or west from the Prime Meridian is longitude. IV. Applications. 1. Practice in reading latitude and longitude at top and bottom of maps. Here explain that meridian of Washington is also used. 2. Find actual latitude and longitude of specified cities and countries. 3. Give latitude and longitude of certain places and have pupils find places. 4. Location of ships at sea. All ships have chro- nometers showing accurate time at Greenwich. For instance, suppose the sun indicates 10 a.m. when the chronometer indicates 3 p.m. Since any spot on the earth's surface passes through 360° in 24 hours, each hour is equivalent to 15°. The difference in time be- tween chronometer and sun is 5 hours, or the equivalent of 75°. Hence, the ship is in 75° west longitude. The longitude is west because the time by the sun is earlier than the time by the chronometer. Reverse the facts and the longitude would be 75° east. 497. International Date Line. — If a man starts westward from London to travel around the world, he must set his watch back one hour for every 15° passed over if he wishes to have .the correct local time. This would require twenty-four changes during the journey around the world, and thus he will lose twenty-four hours or a whole day. If he starts eastward from London, he would set his watch ahead twenty-four times, and thus he would gain a day. 248 METHODS IN EDUCATION To overcome such differences, the nations have agreed upon a place where time shall be changed. That place is the 180th meridian east and west from Greenwich. Suppose the two men start from Greenwich near London, one going eastward and the other westward. The one travelling eastward will find the time twelve hours later than when he started, while the one traveUing westward will find the time twelve hours earher. So the latter in crossing the line on Wednesday must call the day Thursday; while the one travelling eastward in crossing the line on Wednesday must call the day Tuesday. 498. Standard time. — The railroads of the United States have agreed upon scheduled places for changing time. Following are the divisions: 75th meridian. Eastern time. 90th meridian. Central time. 105th meridian. Mountain time. 120th meridian. Pacific time. It is evident that the difference in time between any two of these divisions is one hour. 499. Volcanoes : Concrete presentation. — One device for giving pupils a concept of volcanoes is to observe coke, ashes, and iron slag, which are known products resulting from the action of heat; to explain the forma- tion of the earth by the process of cooling of the surface while the interior still remained hot; to make drawings to illustrate earth's crust, heated interior, and cracks in earth's crust; to show picture of active volcano; and to read or give vivid description of the action and results. This plan gives the general idea of a volcano without much emphasis upon details. Another presentation. — This plan involves a scien- tific treatment of the topic. In matter and method it GEOGRAPHY 249 is suited to older pupils. Heat of the interior of the earth is explained and proved as follows: 1. Hot springs are evidence of interior heat. Some found as far north as Iceland. 2. Geysers are another indication of interior heat. 3. Increasing heat in mines. Heat increases about one degree with every sixty feet of descent into the earth. 4. The nebular hypothesis regarding the formation of^ the planets explains the existence of the heated interior and the cooling crust. In the process of cool- ing the contraction causes many fissures, foldings, and openings in the crust or surface of the planet. Action of volcanoes. Water from the surface of the earth passes through the openings into the heated interior; the heat expands the water into steam, and this added power causes an explosion or eruption. The matter thrown out during an eruption is lava, or melted rock, pumice stone, water, steam, sand, mud, cinders, and ashes. The opening through which the materials are forced is the crater of the volcano. Noted volcanoes. Mauna Loa and Kilauea in Hawaii, Chimborazo in South America, Hekla in Iceland, Etna in Sicily, and Vesuvius near Naples in Italy. Graphic aids. 1. Pictures of extinct, dormant, and active volcanoes. 2. Drawings of vertical section showing base, cone, crater; the process of mountain building around crater; the contour of the volcanic mountain and the distribu- tion of ejected materials. 3. Maps showing location of principal volcanoes. 4. Specimens of pumice stone, lava, ashes, etc. 5. Narration, description, and illustration of the destruction of Pompeii. 250 METHODS IN EDUCATION 6. Stereopticon views. Definitions. A volcano is a mountain or hill, usually more or less conical in form, from which lava, cinders, steam, sulphur gases, and the Hke are ejected; — often popularly called a burning mountain. — Webster. This definition is scientifically inaccurate. A volcano is not necessarily a mountain; the mountain is the result of the accumulation of material ejected by vol- canic action. Again, a volcano is not a burning moun- tain; the explosion is not a process of consuming material by burning. A volcano is a hole in the earth's crust from which steam, lava, or ashes are or have been thrown. — Dexter and Garlick's Object Lessons in Geography, page 155. A volcano is essentially a vent in the surface, through which rises some kind of molten rock, which, upon accumulating, builds a conical peak. — Tarr^s Elemen- tary Geology, page 329. Illustration of Eruption of Vesuvius Large glass vessel, small bottle of red wine, clay or sand, water. Form miniature mountain on bottom of vessel; make small hole in cork of wine bottle and then cover bottle with sand; put water in vessel. When ready, stir the water. The water removes sand from hole in cork and the wine ascends in a whirhng plume. — McKay^s Magic Experiments, page 30. 500. Winds. I. Circulation of the atmosphere. The air is very elastic and so it is easily put into motion by changes in temperature. Heat causes air to expand, become hghter, and rise. This upward current of warm air is replaced by heavier cool air which in turn rises after becoming GEOGRAPHY 251 heated. Apply this explanation to the large areas in the equatorial regions and notice four great movements in the general circulation of the atmosphere: 1. The inflowing surface winds. 2. The uprising heated current. 3. The outflowing winds at high elevations. 4. The descending air at considerable distance north and south of the equator. ^11. Relation of air pressure and wind. The ris- ing column of warm air pushes away the air above it, thus decreasing the barometric pressure ; but the reverse is true in regard to pressure when the cooling air becomes heavier by condensation. Then it follows from the last topic that wind and air pressure -ftFe-elosely related. 501. Trade winds. I. The name. The name trade winds is given be- cause commercial vessels take advantage of the aid given by these winds. II. Location. In Atlantic Ocean 8° to 29° N. and 3° N. to 28° S. In Pacific Ocean 2° to 25° N. and 2° to 21° S. latitude. It is sufficient to say about 30° north and south of the equator. Cause. Cooler air rushing in to replace rising air in equatorial regions. See explanation in circulation of atmosphere. III. Direction. From the northeast in the northern hemisphere; from southeast in the southern hemisphere. Such incoming air tends to blow from north and south; but the earth's surface at the equator is moving east- ward at the rate of seventeen miles a minute, and so the wind lags behind. IV. Effects. 1. Aid navigation. Columbus followed this route. 252 METHODS IN EDUCATION 2. Coming from cold regions, they absorb moisture and thus cause deserts. 3. Absorbing much moisture from the ocean, they produce abundant rainfall on sloping coasts. 4. The meeting of so much warm air at the equator produces an upward movement over an area nearly 400 geographical miles wide. This area is the belt of equa- torial calms. How to Study a Map 502. Importance. — This is only one more phase of teaching pupils how to study. Lay aside theoretical discussion and join a healthy class in studying Asia. The response will convince you of the direct value of community effort. Here are some of the real conditions in an effort of this kind: 1. Geography is disliked by some pupils because it has not been well taught. The pupils have not been taught how to use the text-book. 2. Every pupil has a geography. The ownership of the book or the right to use the book is a native impulse waiting for invitation to react, according to James and Thorndike. The handling of the book gives employment to the hands, — another suggestion of free- dom from mischief. The coloring of the map appeals to the eye. In brief, such presence of material means a kind of business that appeals to a healthy class. 3. The teacher works with the pupils. There is a natural interest in such mutual observation, interpreta- tion, and discovery; and a derived or acquired interest follows for all pupils who experience for the first time the joy of finding how much can be learned without reading even one line of the text. GEOGRAPHY 253 503. The process of studying a map. — A large globe, a map of Asia, a map of the world, and a relief map of Asia are ready. Light, heat, ventilation, and comfortable position are physical requisites. PreUminary questions on globe and maps will secure attention and thereby prepare the minds for united and individual effort. Such questions will determine comparative location, size, and shape; location of highlands and lowlands; general direction of mountains and peninsulas. Now turn to individual maps; eagerness guarantees activity. The map study gives information on these topics. 1. Actual location by latitude and longitude; land and water boundaries. 2. Size. The largest continent; the largest moun- tains, rivers, seas, bays, countries, peninsulas; and, by inference, the largest population, forests, animals. This inference requires later proof from text. 3. Surface. The location, direction, extent, and names of mountains; the three great slopes as indicated by direction of flow of rivers; the names of rivers and the bordering waters ; important lakes and seas. 4. Climate. Probable conditions by comparison with North America; apphcation and probable results of each of the causes affecting climate. Here, again, is another invitation to later use of the text to verify inferences. 5. Countries and their chief cities; apparent means of commercial intercourse. 6. Industries, products, and commerce. Map study alone cannot give the accurate knowledge required, but it can correlate old knowledge and also make pupils think and justify their thoughts in advance. 7. The people. Prior information is considerable. Note vast extent of lands of the different peoples. 254 METHODS IN EDUCATION Pupils' results from studying the map: 1. Social pleasure. 2. Self-satisfaction in progress. 3. Prior knowledge recalled, applied, correlated. 4. Desire to study text to verify conclusions. 5. Consciousness of increasing power in studying. How to Study the Text 504. Difficulties. — There are certain difficulties in teaching the intermediate grades and it is well to consider first the reasons why pupils do have such difficulties in using the text in geography. 1. Poor teaching. It is a safe rule that says pupils should use text-books as soon as books can be used advantageously. But notwithstanding this view, some teachers do not require pupils to use the books furnished. The teachers make notes from the books, write the notes on the board or dictate them, have pupils copy and then memorize. This plan robs the pupil of his right to learn to do by doing; it is a waste of time; it exalts the mem- ory; it develops a habit of absolute dependence upon the teacher. 2. Defective books. Some text-books are badly planned. Pupils have to search in three or four parts of the book to find the required facts. Some books are not well arranged. The matter may be found in one place, but topics are not given; or, if topics are given, the order is neither logical nor pedagogical. Other books are not adapted to the capacities of the pupils; scientific style, or undue emphasis of causal relations when the causes are not understood, or the presentation of a con- fusing amount of details. 3. Inactive pupils. This condition may be largely GEOGRAPHY 255 due to poor teaching and defective books. The pupils do not feel a necessity for such knowledge. In the section on how to study a map, a way of arousing a desire for study of text has been suggested. 505. The Process of studying the text. — The six topics followed in the study of the map make a topical series for guidance in studying the text. Whether the arrangement of the text is in that order or not, the pupils are working under definite aims. The pupils must classify the facts under the topics; the efforts must be systematic ; and the mental result should be a tendency toward a habit of thinking. 506. Suggestions for the aid of pupils in studying the text. 1 . Pupils must feel the need of the facts in the printed matter. 2. Pupils should have a guide in their study, such as topics, questions, etc. 3. The teacher should work with the pupils to see that they acquire proper habits of application and in- terpretation. There is too much scattering of energy. 4. Have pupils read a portion of the text, tell ex- plicitly what the author means, and comment upon it or otherwise apply it. It is a very valuable exercise in observation to have pupils read exactly what is printed, give its precise meaning, and then express a personal opinion upon it. 5. Proof. The printed text must disprove or verify the conclusion reached in the study of the map. Here is authority vs. opinion. Judgment and reasoning are required in every complete act in this kind of study. The map might suggest the tundras as an inviting home for man, but the text describes those mossy swamps as 256 METHODS IN EDUCATION suited only to nomadic tribes who manage to live upon fish and fur-bearing animals. 6. Comparison. The study of North America and Europe has habituated pupils to associate climate, occupations, and productions according to zones. Such types of knowledge are used in map studies; but the text must furnish the conclusive facts to enable the pupil to ascertain the truth by comparison and contrast. Tabu- lated facts in parallel columns give a mode of visualizing truth in the field of world geography. As in proof, here, too, the text must be used for accuracy. 7. Synopsis. Critical study of the printed matter is insisted upon in each of the foregoing suggestions, Another means of mastering the text is analysis by out- line. The value of this exercise is fully presented in the chapter on composition. 8. Abstract. Another way of making the thought of another a part of one's self. See chapter on composi- tion. 9. The text is a source of information for individual discussion and class debates. 507. Characteristics of modern text-books. 1. Enrichment; physiography. 2. Pertinent illustrations. 3. Unit areas vs. unrelated facts. 4. Heuristic questions. 5. Inductive development. 6. Political and industrial relations exalted. 7. Topical arrangement. 8. Causal series, cycles, comparison. 9. Types as apperceptive bases. 10. Correlation with science, history, and literature. CHAPTER XIII HISTORY AND CIVICS 508. An institutional subject. — Butler and Spencer have advocated institutional training as a desirable preparation for life. John Dewey, Horace Mann, and others have come out strongly for citizenship as a worthy ideal. The subject-matter of history and civics is com- ing more and more into use as suitable means of helping pupils toward the ideals advocated by leading educators. The suggestions quoted in the following eight sections are pertinent. 509. Early work in history. — In the lower elementary grades, topics introductory to history will be found in the fables and myths and in literature and geography lessons. As pupils in the earlier years take an intense interest in events associated with life and endeavor, the subject-matter of the lessons in history should be chiefly biography and the record of events which have visibly shaped or influenced the destinies of man. Only a brief sketch of each topic is expected; no notes should be dictated by the teacher; no home study should be re- quired of pupils in grades below the eighth year. The reading of library books should be encouraged. 510. Geographical background. — The teacher should see that pupils have a proper geographical background for all historical events. Appropriate use should be made of pictures, reference books, and maps to give a 257 258 METHODS IN EDUCATION fit setting to the narratives, to show the pohtical and physical boundaries, to indicate territorial growth and expansion, and to illustrate the progress and purposes of movements in warfare. The judgment of the pupil should be exercised in tracing the causes as well as the progress and outcome of great historic movements. 511. Current events, anniversaries, excursions. — Attention should be given to current events and to his- toric anniversaries, as Lincoln's Birthday, Washington's Birthday, Decoration Day, Independence Day, and Thanksgiving. In order to make the subject of history real and vivid, pupils should be encouraged to visit the Metropolitan Museum of Art, the American Museum of Natural History, the museum of the Brooklyn Insti- tute, the historical and general libraries. Civics 512. Members of society. — Pupils should be taught in all grades, as far as they may be made to understand their responsibihties and privileges as members of society, and that as such they owe duties to the school, to the family, to the neighborhood, to the city, the state, and the nation. In this way they may be led to comprehend the principles of government and their individual duties in connection with it. The necessity for obedience to authority should be dwelt upon, as also the moral obligation of working with the various departments of the government and not against them. Wherever possible, the reasons for conduct should be explained. If the child knows the reason for any law, he will obey that law more readily. 513. Topics for discussion in all grades. — In all grades there should be frequent discussion under these HISTORY AND CIVICS 259 headings: Obedience to law; Why laws are made; Who makes the laws? Who enforces the laws? Why are law-breakers punished? 514. Importance of local ordinances. — Principals and teachers are urged to lose no opportunity to impress upon pupils the importance of city ordinances that are specially applicable to local conditions. Pupils should be led to see that even slight departures from the stand- ard of order and good administration become very serious matters when many persons engage in them, and that, therefore, each individual should be careful to avoid acts, such as throwing paper and fruit skins into the streets, which, though trifling in themselves, would, if they became general, tend to impair the clean- Hness and health of the city. In teaching the ''duties of citizens and public officials," special attention should be directed to the work of the departments that come under the immediate observation of pupils. 515. Government by the people. — In the higher grades of the elementary course pupils should be led to appreciate the force of Bryce's statement that ''the greatest problem that free peoples have to solve is how to enable the citizen at large to conduct or control the executive business of the state." It is very important that all young people should be made to understand that in this country government is not something apart from the people, but that it is established by the people them- selves, and that there are orderly ways provided for giving effect to the will of the people. 516. Aim of history and civics. — The educational aim of civics as of history is to give a body of ideas and a trend of action that will assist the child to become an intelligent and a patriotic citizen. 260 METHODS IN EDUCATION John Fiske says: " The child should be so trained that he will always retain something of interest in reading history, something of power in following up a line of ordinary investigation, something of a disposition to seek for the underlying causes of events, something of a grasp of the mighty tendencies and movements of his- tory, and some inkling of that conception of history that makes it a teacher of the present out of the wealth of its past." 517. Result sought. — First, to make the present full of meaning by showing pupils its origin in the past, to help them properly to understand the present, to develop truth, reason, and high ideals. Second, to develop patriotism by causing the pupils to feel a responsibility in preserving and upholding the institutions founded by their ancestors. Along the line of patriotism is habitua- tion to civic requirements. 518. Habituation to civic requirements. — In discuss- ing the ideals of education, citizenship is mentioned as one advocated by Horace Mann and John Dewey. For those who do not wish to consider education a prepara- tion for the hereafter, the ideal of citizenship furnishes a satisfactory standard for effort; and for those who wish to make the supreme aim of education a preparation for the life to come, the ideal citizen may be considered one whose hving in this life is a good preparation for the hereafter. The teacher who can influence his pupils to habituate themselves to adapt themselves to the require- ments of the community in which they live, is doing all that can be expected from him under the general pur- poses of history and civics. 519. Definition of history. — Locke says that " His- tory is the science of the development of men in theii' HISTORY AND CIVICS 261 activities as social beings." A German writer calls history ''the politics of the past, and poHtics the history of the present." Mace (page 9) says: ''His- tory deals with the life of the people in the process of growth." 520. Value of the study of history. — While we have not thought it necessary to mention specific values of the subjects since all the subjects are deemed worthy of places in the course of study, special mention should be made of the ethical, patriotic, and practical value of history rightly taught. The ethical value may be chiefly derived from the study of the lives of great men as taught to children. See section 524. The patriotic value has been alluded to in section 516. Probably the consensus of opinion has established patriotism as the important reason for the study of history. This may be awakened by striking events which appeal to a pupil's feelings, illustrations of the beauties of one's country, deeds of illustrious men, the early struggles of the people, victories both military and civic, so that the pupil will have a pride in belonging to a country which has so many claims on his admiration. The natural interest awakened by historic places, buildings, scenes of battles, and peace conferences develop a love for the past so that these future citizens, in the changes which must necessarily come to a progressive country, do not lightly relinquish the old, for the new. Its practical value lies in the fact that history runs on in much the same channels that it has with the Anglo- Saxon race for hundreds of years. We touch the history of our fathers in all present-day national questions. Therefore as Bourne (page 81) says, ''The surest road to a comprehension of our country, its institutions and its 262 METHODS IN EDUCATION relations to the world lies through history." It intro- duces pupils to the world of men and makes them ac- quainted with motives and actions. In its different phases, its pohtical is represented by the government, its religious by the church, its educational by the school, its industrial by the occupations, its social by the family. The pupils are shown how great movements have been made and the effect of these. For the more thorough understanding of the present, they must know the past. By this knowledge their own judgment is exercised in regard to present questions. 521. The historical sense. — The historical sense is not a sixth ''sense," nor a ''faculty"; it is simply a feeling that the past can be rightly interpreted only when the student lays aside his own prepossessions, and seeks in the past itself a means of understanding the forces which moved the men of a bygone age, and when he enters sympathetically into the spirit which gave dignity to their institutions. — Bourne, The Teaching of History and Civics, page 9. A fully developed character, such as is the aim of all education to inculcate, is lacking in one rich field, if it does not feel that historic sense which causes respect for past institutions and even places of historic note, though these may no longer be useful. The nation's historic sense, as shown in Holmes's Old Ironsides, was mani- fested in its opposition to the destruction of the battle- ship Constitution in 1833. 522. Extent of history. — In the elementary school, a good rule is to cover the history of our own country and as much of the history of other countries as affects our own. This is not a narrow view. It embraces a general knowledge of Enghsh history, some French, a HISTORY AND CIVICS 263 little German and Spanish history, and some reference to the history of other countries. 523. Method of teaching history. — Here again we face the problem of classifying ways or processes, as already discussed in chapters VII and VIII. Perhaps the easiest mode of adaptation is to conform to the suggestions and plans of approved text-books in his- tory and civics until the effort of educators can secure for history the uniformity that has been secured for geography. Bourne's The Teaching of History and Civics is authority on methods. His liberal encour- agement to teachers is illustrated when he says, page 168, if the teacher ''can succeed in leading his pupils to study historj^ to comprehend it, to acquire the habit of reading historical literature, his method is sound." 524. Method in the lower grades. — The study of the hves of particular men, in connection with the different events in their careers, has been found a fascinating source of interest in history. This is especially true in the lower grades where most of the history is taught biographically. In regard to this, two hints may be given. One which does not detract from the interest in the grade and which is a benefit in the higher grades is this: Teach stories in regard to noted men and the events which group themselves about these men in chronological order. The second is an exception to the first, but it suggests itself because of the interest which naturally attaches to it: Teach an event upon the anni- versary of the day when it occurred. The work of the fifth and sixth years would naturally be to put together events, or men and events, to recognize that there is a relation between these, and to build a skeleton into which later knowledge may be fitted. 264 METHODS IN EDUCATION The worth of biography is well expressed in Foote and Skinner's Explorers and Founders of America from which book these ideas are taken. The story of a na- tion's progress is largely written in the lives of its great leaders, and if we wish to create in boys and girls an interest in history and in historical reading we must appeal to their love for life and action. Great leaders exemplify in themselves the ideals and purpose of the people whom they lead, and through a study of their lives young people may come to know something of the causes which make for national success or failure. A good example of a great leader will lead the class to see in him our country's progress. All the religious zeal, the self-denial and the devotion to duty, which characterized the era of colonization and settlements is told in the lives of founders and the early leaders of the colonies. Customs and manners may be gained from study of characters. If associations are carried on in this way, the child will have some appreciation of the causes which led to the industrial and social development of a great people, some quickening of imagination, and some admiration for courageous perseverance in the face of difficulties and some respect for duty. If we kindle these qualities of mind and heart, we shall make our children good citi- zens and lead them to see that they can make their lives sublime. 525. The teacher's preparation. — The ideal teacher of history is one who has been especially trained for this work. Unless a teacher has a broad view of his subject and can grasp the whole situation, as a teacher of many subjects cannot do in all of them, the proper relation of parts cannot be well maintained. But it is HISTORY AND CIVICS 265 possible for every teacher to be reasonably well pre- pared, and for this purpose a brief plan is suggested. Take any good text-book like Fiske or Gordy for the United States. After a thorough reading, note the periods into which, in your own mind, the history natu- rally divides itself. Compare your own impressions with some good outline, such as Kingsley's or McLaury's, and then decide upon a composite outline for class use. T^ke whatever period is to be studied and subdivide it before you conduct the recitation. Two illustrations are given. Illustration I. Revolutionary period. 1. Causes which led up to this. 2. Objects of British. (a) To separate the colonies. (6) To cut off colonies from the south. 3. How this was accomplished. Under each of these large divisions there would be several subdivisions. Illustration II. Under the large topic of the Period of Settlement are several subdivisions. One of these is The Settlement of Rhode Island. 1. Purpose of Settlers. To found a place of refuge for those w^ho suffered religious persecution in Massa- chusetts. 2. Chief Settlers. (a) Roger Williams. Founder of Providence. Banished from Massachusetts because of religious views, — separation of church and state and that no one should be obliged to support the church. (h) Anne Hutchinson. Founder of Portsmouth. Banished from Massachusetts because of religious views. 266 METHODS IN EDUCATION 3. Government. (a) Obtained a very liberal charter from the King similar to that of Connecticut. (6) Perfect religious freedom. A caution to be observed is to keep your bearings. Do not let detail lead away from the large theme. If time is limited, an outline already prepared may be used. Do not make it dead by mathematical precision, but let the human element, the feeling in regard to eventS; make it mean something and keep it alive. Beyond this, in order to intensify his interest and make his subject real, the teacher should read at least one of the original historical documents, as Bradford's His- tory of the Plymouth Colony, or Sources relating to the Norse Discovery of America. These may be found in any well equipped library. The teacher will feel fully repaid for the reading by the power he feels in teaching a subject which he knows from the original documents, and will realize the practical value because it furnishes one criterion for the selection of text-books which are true to facts. 526. Topical method. — This method would be the one naturally followed by a teacher whose preparation has been similar to that just described. It is necessary for the guidance of the teacher to have at least a plan of work for the term mapped out by topics. The supreme value of the topical method is exempli- fied in the work in history. One view of this method presents a whole lesson under a series of topics arranged in logical or chronological order. These eight or ten topics, for instance, furnish a guide to whatever the pupil is expected to do in that recitation. Another view of the topical method selects HISTORY AND CIVICS 267 one general topic for the subject of the recitation and then there are a few subordinate topics assigned to be covered in the various ways of conducting the recitation. One topic may be set for oral or written review; another may cover the required work in collateral reading; another may be for general discussion to develop the pupil's power of expression and his sense of sound judg- ment; while another may be the direct preparation for the work of the succeeding days or weeks. Whatever the arrangement of the topics may be, the aim should be definite assignment, to direct pupils toward what they should try to learn, where they may find informa- tion, and how they may make that information a part of their own mental possession. 527. Text-book method. — Here again we must dis- sent from the adverse criticism of the use of text-books. The text-book is the source of information for every pupil, and no teacher has a right to deprive the pupil of his right to use his own activity in the field of educa- tion, nor can any teacher take the place of an accepted text-book in this or any other subject. More adverse criticism of text-books is not needed; some devotion to the ideal in teaching pupils how to study a text-book is what is needed. To attain this ideal the teacher -should be the master of the text-book, not a slave to it. In this as in the topical method important events are to be emphasized, and minor details and connecting events omitted altogether or kept in proper perspective. Doubtless the best results can be secured by a combina- tion of these two methods. The text-book is certainly necessary even though the topical method be used. 528. Source method. — The source method of teach- ing history, as the word source implies, requires students 268 METHODS IN EDUCATION to consult the original documents from which history is written, and then form their conclusions upon that material. This method applied in the elementary schools would be presented in a text-book not in narra- tive form, but in the form of summaries, tables, and brief reproductions of the original documents. For elementary pupils, this method cannot be commended. The pupils lack the foundation knowledge for forming an opinion on the material furnished and, besides, they have not yet acquired habits of study that will enable them to interpret the materials without a great deal of collateral reading. The collateral reading in connection with an authorized text-book in the class may introduce the pupils to the source method in some lines of investi- gation. Selections read by the teacher from original sources serve a twofold purpose; they put that life into history which can only result from making it real, and they introduce children to the field of original sources. Selections from the following are of especial interest to pupils of United States History in the seventh and eighth years: Beverly's History of Virginia, and Josiah Quincey's Figures of the Past. As the study of history in the elementary school is not supposed to be intensive, only a mere introduction to source literature is all that can be recommended; otherwise, the regular work of the course would be neglected. 529. Collateral reading. — " The object of collateral reading is twofold: it supplements a text-book, giving the student additional information and describing the same events from new points of view; and it also cul- tivates the student's interest in history as literature." This is Bourne's opinion as stated on page 158. Gordy advises the use of a short list of good references rather HISTORY AND CIVICS 269 than the reading of many books. He advises that each pupil read one good reference book in addition to the text-book. Probably many teachers have noticed the shock that a young pupil experiences when for the first time he finds text-books disagreeing. This is an oppor- tunity to make him realize that books are written by men; that in the main historical points men agree; but that in minor details the author may give his own point of view, or present information that is not authoritative. Another advantage derived from collateral reading is the skilful use of books. Too many pupils in the elemen- tary schools are entirely helpless if asked to look up a cer- tain topic. History offers a greater opportunity than any other subject for practice in getting definite information. 530. Open text-book recitation. — ''An excellent sug- gestion is that of 'open text-book recitations/ in which with their books before them, pupils are asked questions on cause and effect, on relations with previous lessons, etc.; answers may, if necessary, be written out and corrected in class. Such an exercise trains pupils to take in the thought of a printed page, and to grasp the essential points. "Such a system tends to encourage the habit of applying what one knows to a new problem. Still more helpful in the same direction are the off-hand discussions and impromptu debates which spring up in an eager class, and which should be encouraged by every good teacher." — Committee of Ten. 531. Cause and effect. — Whatever the method of recitation may be, the training of the judgment will require pupils to trace the relations between cause and effect in all the great events of history. See causal series in geography, section 459. 270 METHODS IN EDUCATION Events are meaningless without their settings. The cause, the event, the effect are what arouse interest, demand thought, appeal to reason and judgment. 532. What should be memorized. — '' How far should pupils be expected to memorize? 'A few things should be learned by heart and, when forgotten, learned again, to serve as a firm ground-work upon which to group one's knowledge: without knowing the succession of dynasties, or of sovereigns, or of presidents, or the dates of the great constitutional events, the pupil's stock of information will have no more form than a jelly-fish.' But those few necessary facts ought to be clearly defined as only a framework to assist the memory." — Com- mittee of Ten. Taking an application in United States history, we suggest that pupils learn thoroughly the names of the presidents with dates of administrations and the political party to which each belonged. In the study of the constitutional period, this will be found to be indis- pensable as a framework for all important facts of recent history. The learning of long lists of dates is no longer considered a legitimate part of history. The memoriz- ing of particular dates in relation to epochs or periods is all that is essential, with one or two others which mark the important event in some movement. The dates which are learned should be learned accurately. Gordy says dates are valuable in giving perspective to reveiw work. 533. Verbal repetition. — It is not necessary to give much space to reasons why verbal repetition of the matter in the text is not the way to teach history. This kind of recitation is the cause of severe criticism against •the teaching of the past; but a little experience with HISTORY AND CIVICS 271 teachers of this decade leads to a commendation of their tact and judgment in matters of this kind. Only poems, national songs, and prose selections, which have been written with reference to some historical event, are to be committed to memory for verbal repetition. 534. Correlation. — Correlation with geography has already been mentioned. Literature is another study that can contribute a large share of interest and use. Masterpieces in poetry and prose often present the facts of 'history under the charm of literature. Lincoln's Gettysburg Speech is an apt illustration of the correla- tion of oratory and history. ''The teaching of history should be intimately con- nected with the teaching of English: first, by using historical works or extracts for reading in schools; second, by the writing of English compositions on sub- jects drawn from the historical lessons; third, by com- mitting to memory historical poems and other short pieces; fourth, by reading historical sketches, biographies, and novels, outside of class work." — Committee of Ten, page 164. 535. Reviews. — Our point of view was expressed in a general way in section 134. That view has particular application to history. Good teaching will require a summary at the close of each recitation; the assignment of home study will be largely a matter of review rather than advanced preparation; the making of outlines of the matter covered in the regular text or of the matter in collateral reading is another valuable exercise; and extemporaneous speaking upon assigned topics or brief written summaries during the recitation period will tend to systematize the whole work under some comprehen- sive plan of presentation. 272 METHODS IN EDUCATION As.de from this daily review, when a period has been covered it should be given a general review in order to see that the pupils hold the subject as a unit and also to strengthen the impression. This review should not be a restudy of the subjects as presented in the original lessons but should be attacked in a fresh way. This will avoid loss of interest and help the pupil to organize his knowledge more thoroughly. Illustration After the completion of the study of the Civil War take up the history of slavery. This has already been studied in connection with the period of colonization, in the provision for the non-interference with the trade until 1808, in the effect produced upon it by the inven- tion of the cotton-gin, in the Missouri Compromise, and in the question of whether new states should be admitted as slave or free. In the review, let slavery be taken connectedly. For such a review excellent results can be gained by the preparation of outlines by the pupils. Gordy suggests three kinds of reviews: 1. Reviews may be chronological, but must connect and associate each one with some important event. 2. Reviews may be biographical. Noteworthy events may be associated with the names of men. 3. Reviews may be geographical when association of events is to be with places. Topical reviews are thus defended in Cornman and Gerson's Topical Survey of United States History: " Sound psychological and pedagogical consideration demands that this review should not consist of mere repetition, but should, as far as possible, be presented HISTORY AND CIVICS 273 in a fresh guise, and aid the pupil in organizing the knowledge which he has already acquired. The various elements of the matter to be reviewed should be closely interrelated, essential features emphasized, and a broader range of view disclosed, so that the knowledge as a whole may form an apperceptive system to which future acquisition may be readily related." 536. Use of outlines. — This plan is advocated as one of the best means of teaching pupils how to select and CQinprehend the essential points in the printed text. It is difficult at first, and needs the personal direction of the teacher; but a little practice in it gives a con- sciousness of growing power so that the pupil will soon be anxious to follow this kind of individual work. Out- hnes prepared for guidance in study would, of course, obviate the making of similar outhnes by the pupils. Teachers differ in their views of the value of such out- lines in connection with the study of advanced lessons, but there is almost unanimous opinion in favor of the outhnes in reviewing a part or the whole of a subject. Cornman and Gerson's Topical Survey of United States History is excellent for reviews. 537. Note-books. — Elaborate notes are not useful to the elementary pupils. The mere copying of long ex- tracts is not a prudent investment of time or energ}^ Use note-books for the following purposes: 1. Summaries of work. Similar to that described in sections 525, 526. 2. Progressive maps. 3. Review questions or topics. 4. References in connection with collateral reading that appeal to the owner of the book. 538. The use of maps. — The geographical maps are 274 METHODS IN EDUCATION absolutely necessary to fix the location of the principal places studied in history. This is one means of corre- lating history and geography. One caution to be ob- served is that the map shall not have too many places located upon it. Confusion must be avoided. 539. Progress maps. — A helpful means of stimulat- ing visualization is the use of progress maps. Outline maps can be secured from publishers and so pupils need take no time in marking the limits of latitude, longitude, and boundaries. That part of map-drawing has httle educational value. The progress map will then contain the location of the few principal points under considera- tion. Thus in the study of the early years of the Revo- lutionary War the map will have the location of Boston, Saratoga, New York, Princeton, Trenton, Philadelphia, and Yorktown. A line may indicate Washington's route across from Long Island up the Hudson and then down through New Jersey. 540. Debates. — History furnishes material for the frequent use of short debates. The value of such exer- cises is evident to all experienced teachers. 541. Questions prepared by pupils. — This plan of promoting self-activity and co-operation has been em- phasized, from time to time, in this book. Personal experience is the justification for such commendation. Gordy, in his notes To The Teacher, says: " The pupils should be required to prepare a written question on every lesson. The value of this simple device in leading them to note the working of cause and effect cannot easily be measured. If pupils have not been trained to ask such questions they may at first be diffident about it. They will also ask questions that call for yes or no or for single-word answers. With a httle judicious help, HISTORY AND CIVICS 275 however, they will soon begin to ask searching questions that will stimulate the interest of the entire class." 542. The use of illustrations. — The word illustra- tions in this topic has reference to the pictures or other illustrations in the text-book itself. One essential of any good text-book is that it shall not be overloaded with details. So, too, of the use of pictures. The illustrations are intended simply to strengthen the matter already given in the printed text. The limit to be- observed is the truthfulness and the usefulness of the illustrations inserted. 543. Collection of prints and pictures. — In speaking of school decorations we advised the use of a few superior paintings in place of a large number of cheap prints and pictures. The same caution may be applied to history. It is suggested that a large scrap-book be used for keep- ing the prints and pictures instead of posting them on the walls of the schoolroom. 544. Excursions. — Fortunate is the school that is located within the field of historic experience. Excur- sions under the plan described for teaching geography cannot fail to produce satisfactory results in impressing the facts through the aid of concrete interest. 545. Dramatization of historic events. — Teachers can hardly be expected to put the historic material into dramatic form for presentation in rhetorical exercises, but it is possible to secure such material already drama- tized. Such exercises in school will be found one of the most valuable means of promoting a healthy school spirit. A little play called the Continental Congress, in which pupils take the parts of those who adopted the Declaration of Independence, may be mentioned as an illustration of this phase of the work in history. 276 METHODS IN EDUCATION 546. Use of mnemonics. — Anything so artificial is not approved as a method of teaching; but it is a device that may have some value for some pupils. The follow- ing illustration suggests an ingenious and helpful way of remembering the events connected with slavery agi- tation. Notice that the first letters of the seven lines spell slavery. Sixteen hundred nineteen — Introduced 1619. Law prohibiting slaves imported — 1808. Admission of Missouri — 1820. Violent opposition to annexation of Texas — 1845. Emancipation Proclamation — 1863. Rebellion the outgrowth — 1861-5. Year of 1865 — Thirteenth Amendment. 547. How to arouse interest. — The summary of the last tw^enty-six sections will present a number of points of view on the teaching of history. A condensed expres- sion of the substance of these points of view will give the means of arousing interest in teaching the subject to elementary pupils. 548. Civics. — This is part of the life of today. At a very early age the child comes into contact with civil government. Just as in the study of history, first he learns disconnected facts in regard to city government, also in regard to home and school laws, election, taxa- tion, political parties. In the seventh and the eighth years these isolated facts are gradually brought together in a whole represented by the national government. The laws of state, county, town, city, school, and family are fitted into this whole. 549. Local government. — The study of the forms HISTORY AND CIVICS 277 and uses of local administration is a part of the early work in all the grades in New York City. It is what is called institutional presentation of history and civics. To impress the utility of such government, many of the schools have adopted forms of pupil self-government to represent the departments in the larger municipal organ- izations. Wherever the school may be, it is possible for pupils to study the government related to them. 550. Process of legislation. — Another means of increasing civic knowledge is for pupils to make a special study of the three departments of government in the state and in the nation. The history of a bill from the time that it is introduced until it has been under judicial approval is one of the valuable topics in relation to his- tory and civics. Turning the class or the school into a legislative body for this purpose is one concrete method of presenting the work. 551. Institutional study of history and civics. — In the five kinds of inheritances mentioned in Butler's definition, the institutional inheritance is found. The American tendency is strongly in favor of such training. 552. Common mistakes in teaching history and civics. 1. A pupil sometimes receives a good mark because he is a fluent talker, rather than because he knows and can connect facts. History offers many avenues to inaccuracy and a teacher must be constantly on his guard. 2. Past events are kept in the past. Make them real by bringing out how they touch the fife of today. 3. Events are often left hanging in space. This may be avoided by the use of maps, by connecting events either logically or chronologically, and by giving atten- tion to periods of time. 278 METHODS IN EDUCATION 4. Indefinite assignment of lessons. This may be avoided by the use of topics with their subdivisions. 5. Too much prominence given to wars. Many great questions are fought out and decided in times of peace. 6. Taking sides. State facts. Do not warp the judgment of pupils by such strong partisanship that they believe that England had no excuse for the attitude she assumed toward the American colonies before the Revolutionary War, that the southern people were all rebels in 1861, and that the north contained all the men of principle. Views sufficient to arouse interest and enthusiasm should be given, but proper justice to both sides should be shown. 7. Making the study too critical. It is not necessary to spoil the enjoyment of and perhaps decrease the inter- est in history by raising a doubt as to the truth of a likely story. History should not be studied critically in the elementary school. CHAPTER XIV READING 553. Value. — Excellence in all other branches of school work is dependent upon ability to read well, and hence the basic importance of reading. But aside from its importance in the acquisition of knowledge in school, reading is a means of pleasure for ourselves and others during later life. Appreciative reading of good Hterature gives strength and refinement to character, and assures continued development of intellectual power through the use of the mental faculties. 554. Characteristics of books formerly used. — The use of the terms old education and new education is indefinite, partly because there is no distinct dividing line and partly because the former term is frequently associated with adverse criticism. A condemnation of the old is a popular argument for the new. It would be nearer the spirit of true teaching, however, to give full credit to the achievements of the past by using those achievements as a foundation for progressive develop- ment. There is nothing in matter or method that is entirely new; and surely child nature is the same, but we understand it better. Adaptation is the mark of modern improvement. In speaking of the old and the new books in reading, there are differences which can be precisely stated. The old books had selections possessing intrinsic merit, but 279 280 METHODS IN EDUCATION the selections taken together did not make a unified whole. They lacked that continuity that is deemed essential for persistent development. The books were compilations of unrelated and unclassified fragments. Following is a summary of the leading characteristics: 1. Graded words and exercises without reference to content. 2. Moral stories. 3. Information readers. 4. Patriotic selections. 5. Literary masterpieces. 555. Complete works vs. selections. — The accepted point of view is quoted from an approved answer in a recent English examination. ''Another reform of great consequence has taken place during the past fifteen years in the teaching of reading. The movement had its origin in the conviction on the part of President Eliot and others that reading was too formal; that reading is but a means and not an end, and that so soon as the mechanical elements are mastered it should be used as a vehicle to transmit the contents of literature to the child. This reform, which was greatly assisted by the discussions and reports of the 'Committee of Ten' and the 'Committee of Fifteen,' has revolutionized the school readers and the courses of study throughout the length and breadth of the land. Courses of study in the elementary school now demand, in the upper grades, the critical and appreciative study of masterpieces of literature, and the school readers are no longer made up of ' useful information ' and twaddle on moral subjects invented by the compilers of readers. But they contain, even in the lowest numbers, pieces that possess genuine literary merit. So that instead READING 281 of reading about Janets Doll and Jack^s Top, the boys and girls of the second and third grades read the poems of Longfellow, Field, and Gary. In the secondary and collegiate courses similar changes have occurred. Formerly, courses in literature consisted largely of the mastery of treatises about literature and its creators. Now they consist of the concrete, first-hand study of entire masterpieces representing authors or types of literary form. The changes may be summed up by saying that the courses in English have been infinitely enriched by placing the emphasis on the subject-matter of literature rather than on the mere form of mechanical aspect. " 556. Guiding principle today. — The one great prin- ciple that determines correct methods of teaching read- ing is from the whole to its parts. This principle is applied all through the elementary grades. 557. Types of reading matter used at present. 1. Nonsense rhymes, such as Mother Goose. Rea- sons in favor — play in education, pleasure, interest; against — content lacking. 2. Literature of familiar things, such as toys, games, food, domestic animals. 3. Stories of primitive life of the race, early civiliza- tion, animal life, concrete heroism, Homer, Indian life, etc. Apply culture epoch theory. 4. Fairy stories. Imagination sees the good and the beautiful. Should stories be condemned because the true is lacking? No. 5. Fables. Literary inheritance. 6. Myths. The story in education. 7. Bible stories. 8. Poetry. 282 METHODS IN EDUCATION 558. Principles determining the selection of reading matter. — The twofold relations of the individual and the community are factors for constant consideration. The mental requirements of the individual must be satisfied; the sociological or community interests must not be neglected. Hence, the two determining principles in the selection of reading matter are the psychological and the sociological needs. Such needs require 1. Material simple in thought and form. 2. Familiar words. 3. Suitable content. 4. Adaptability to individuals. Analytic Methods 559. Analytic methods of teaching primary reading: word, sentence. — The word method in reading teaches a large number of words as wholes by associating the words with familiar things. The words are recognized at sight without knowing the speUing. Pupils have ideas when they enter school; they know many objects; they use many words; and so this method aims to teach pupils to recognize the words which are used in familiar language. 560. Word method. — The advantages claimed for this analytic method are the following: 1. The word is mastered by the eye. 2. It is from the known to the related unknown, as children can talk words when they enter school, and now they learn that the word is a picture and also a sign of some objective thing. 3. Alphabet, spelling, and syllables are learned in- cidentally. 4. It is natural because languages are developed one word at a time, the word being the unit of language. READING 283 Disadvantages of the word method: 1. Mastery by the eye alone is not a pedagogical advantage; multiple sense instruction is better. 2. Habit of guessing. 3. Incomplete without phonics, spelling, and writing sentences. 4. Considering the sentence as the unit of expression, the word method violates the principle from the whole to its parts. 561. Sentence method. — This analytic method begins with sentences and works down to words and letters. Two advantages are claimed: 1. The sentence is the unit of our language, since every complete thought must have a sentence for its expression. 2. Interest, apperception, and self-activity used in constructing and interpreting sentences. Disadvantages of the sentence method: 1. Incomplete without the study of words, letters, and phonics. 2. Not suited to simultaneous teaching where dull pupils are present. Synthetic Methods 562. Meaning. — The accepted meaning is given in section 210. Compare also sections 209, 211, and 212. 563. Alphabet method. — The alphabet method teaches the letters first. Sooner or later the letters must be learned as they are instruments of knowledge in the child's mental equipment. It is, then, an advan- tage to learn them as soon as possible. But usage does not favor this method because (a) it violates the principle of going from wholes to parts; (6) it is 284 METHODS IN EDUCATION neither the interesting nor the natural way of learning a language. 564. Phonic method. — The learning of the sounds of the letters is not approved as the first step in learning to read. These are the reasons for disapproval: 1. Some letters have too many sounds. 2. Some letters are silent. 3. The two arguments against the alphabet method. 565. Advantages of phonic training. 1. Pure tone. 2. Distinct articulation. 3. Power to read new words and pronounce them correctb^ Analytic-Synthetic Methods 566. Distinction not accepted. — The two classifica- tions, analytic method and synthetic method,, are not accepted as distinct methods by all educators. We have already directed attention to the point that there can be no complete mental act without both analysis and synthesis; and, under this interpretation, we may reject any method that claims to be strictly analytic or syn- thetic alone, or we may show that the classification is defective. The latter is preferred. In the Psychology of Number, by McLellan and Dewey, we found an exposition of the mental process in passing from a vague whole to the definite. A similar psycho- logical process is fully explained in McLellan's Applied Psychology. If every child's mind passes through that process, then every method of teaching primary reading is analytic, even though the distinctive steps are syn- thetic. Hence, any of the approved methods discussed in this chapter may be called analytic-synthetic. READING 285 567. Combination methods. — A liberal view of teaching primary reading includes the best features of the four methods mentioned. Thus the methods are made analytic-synthetic. Then add writing to co- ordinate motor activity; and, as another form of motor reaction, use dramatic expression as a means of interpre- tation through the aid of action. 568. Dramatization. — The value of dramatic ex- pression is a modern contribution to primary reading. It need not be limited to primary reading, however, nor should it be. We have frequently emphasized the worth of oral expression in recitations, declamations, discussions, and debates. Here we add one more sug- gestion in regard to using the dramatic instinct of chil- dren in all grades as a means of individual and social interpretation, expression, and impression. In the N. E. A. Report for 1907, page 485, there is a short article on Dramatizing by T. C. Blaisdell, Professor of English Literature, State College, Lansing, Michigan. We quote three paragraphs and some of his suggestions : '' But why should not dramatizing be a potent factor in education? Children have an imagination far more vivid than have youths or adults. Left to themselves, unhampered by teachers and curriculum, children un- consciously become actors of power and dramatists of real human interest. To illustrate: A few days ago I attended the out-of- door flag-day celebration of a two-room rural school. The program had been left to a committee of five girls. They had of course the conventional recitations and songs, a violin solo, choruses, etc. But finally came an announcement that caused an expectant rustle among the fifty or sixty children and 286 METHODS IN EDUCATION the few visitors sitting on the sloping hillside. Charades were announced, and we were to '' guess." They were not charades, however; they were effective Httle dramas, conceived entirely by the girls, without rehearsals, and, so far as I could learn, without any schoolroom experience in dramatizing. The Betsy Ross home during the mak- ing of the first flag was shown, the conversation between General Washington and his aides, and the famous flag maker, being given with a vividness that caused silence even among the boys of the somewhat restless audience. But the chief work of art was yet to come. Our young friend Malcolm was seen mounting his pony. He and his pony are a unit. And when he came crashing through the trees and in front of the audience crying " The British are coming! Be ready! Be ready! " he brought his audience to their feet. They cried out in their excite- ment, *' Paul Revere! Paul Revere! " The dramatizing was done with vigor, and was received with a dehght that does not pass. Will not Malcolm read of the famous ride of Paul Revere with a new power when next that poem is called for in the reading-class? And will not every boy and girl who saw the little play have a deeper under- standing of the real meaning of the original ride and read of it with added joy and with more dramatic skill? " 569. Arguments for dramatization. 1. Children are eager to interpret hfe; hence, the desire to play stories, poems, songs, and home or vaca- tion incidents. 2. Visualization. Pupils comprehend better after seeing; they become better readers and better appre- ciators of literature. 3. Overcomes self-consciousness. The enthusiasm is a powerful social stimulus. READING 287 4. Clearer images formed. Better talking and writ- ing. 5. Strengthens the speaking voice, gives ease of bodily carriage, increases desire for knowledge, brings teacher and pupils into closer relations, and exalts the function of pleasure as a factor in education. 6. For reference, see Sara Cone Bryant's How to Tell Stories to Children; also, the books cited in 570. McCloskey Method 570. Features. — This method of teaching reading combines the advantages of the four methods discussed in the preceding sections and also correlates reading and language. Special emphasis is placed upon the content of the reading matter. Some of the leading features are summarized : 1. The choice of matter that appeals directly to the interests of the pupils. Live objects are selected, such as, the story of The Kid, from the Jewish Talmud; The Ox; The Little Red Hen; The Little Pine Tree; The Little Boy Blue. 2. The vivid telling of stories by the teacher. The oral treatment of the story is the first step in the teaching. The story is told three times: first, to give an idea of the whole; second, to give the children a chance to fix the essentials in their right order; third, a rapid telhng to bring all the parts together again. For suggestions for oral work with stories, see DeGarmo's Essentials of Method, pages 94-107; McMurry's Method of the Recitation, pages 26-29; McMurry's Special Methods in Primary Reading, pages 1-46. 288 METHODS IN EDUCATION 3. The use of script forms in introducing the thought expressed in a sentence. Tliis process combines the sentence method and the word method. 4. The transition from script to print. This puts the child into the use of text-book or printed sheets early in his school career. It gives him a chance to begin to help himself. 5. Oral language lessons based upon the written and printed sentences already treated. A reproduction of the material already covered gives the teacher an opportunity to make use of the dramatic instinct in the children. This dramatic rendering of the little stories is not strictly a part of the McCloskey method but it is used successfully by a large number of teachers who are using the other points of advantage in the McCloskey method. The written language work follows closely after the first oral language work, and absolute accuracy in getting capitalization and punctuation is required from every pupil. The progress in the line of structural composition is one of the marvellous results of this method of teaching. 6. Introduction of phonic lessons. After fifty or sixty words are thoroughly known at sight, the pupils are able to grasp the words as wholes and then the work in phonic analysis is introduced. The method of phonograms and blending is used. 7. The letters of the alphabet learned and used. This summary of features shows that the McCloskey method does use the sentence method, the word method, the phonic method, and the alphabet method, but they are used in the reverse order from that advocated in some schools. The principle from the whole to the parts is rigidly observed in this method. READING . 289 Ward Method 571. Self-help. — This method is a combination of the word method and the phonic method. Later the other two methods are utihzed in the reading lesson. The aim of the Ward method of teaching reading is to make the child independent. The phonic drill during the first two years of the work aims to give the child a key to the language so that he will be able to help him- self in all the work in reading after the second and third years. 572. Sight reading and drill. — The oral work in the Ward method is divided into three distinct lines of drill : 1. Sight reading from the blackboard. 2. Drill on phonograms. 3. Drill on blend. In the first half year of school the children are taught to read eighty-two words by sight reading and in every instance the teacher must see that the children under- stand what they are reading. In teaching a word the actual process of teaching is not done until after the children have been tested to see that they have the gen- eral thought conveyed by that word. These words are used in sentences from the very beginning and are fre- quently drilled upon in conversation or story. Along with this sight reading there is much drill upon phono- grams and the blend. 573. Features. 1. The presentation of phonograms in a rational order. A phonogram is a written or printed representa- tion of a sound; as, f, 1, m, n, r, ing, ings, ight, ights. A word phonogram is a sight word used as a phonogram; as, ail, at, old. 290 METHODS IN EDUCATION 2. The teaching of an initial stock of phonograms before any phonetic reading is done. 3. Thorough training in phonetic blending before any reading is done. This training aims to prepare the sense of hearing for quick, accurate perception. 4. Gradual introduction of phonetic words into the sentences used in the reading lessons. A sight word is a word that has been taught as a" whole. Such words are recognized by the sight alone. A phonetic word is a word that the children are to read by means of com- bining the phonograms. The blend or blending is the union of simple or combined sounds into words. Aldine Method 574. A general outline. — The actual procedure in the Aldine method is indicated by this outline: I. Preparation. 1. Telling of the story. 2. Dramatization of the story. II. Actual Reading. 1. Writing of the rhyme on the board. 2. Picture study. 3. Repetition of whole rhyme by individuals while pointing to the several words. 4. Instant recognition of the rhyme words pointed to promiscuously by the teacher. 5. Recognition of rhyme words written promiscu- ously on the board. 6. Drill with sight word cards. 7. Drill on sentences from the chart. 8. Seat work from the rhymes. III. Phonetics. 1. Initial consonants (no diacritical marks). READING 291 2. Vowel combinations and type words used with initial consonants to form word families. 575. The method justified. — We have secured a brief exposition of Aldine Reading from one of the originators of that plan: * 'Aldine Reading as a plan or method is based on the natural interests, the spontaneous activities, the re- sponsive and creative imagination, the feelings and the knowledge of children living the active, happy life of childhood. Into this life Aldine Reading comes not as a task that is artificial, foreign, and distasteful — a drudgery to which children must submit because they are little; into the child's life Aldine Reading comes as a delight, as a most fruitful resource, offering varied and undreamed- of opportunities for joyful childish activity, growth and happiness. Hence the not uncommon occurrence of a child's suddenly discovering in surprise that he has learned how to read, that he can read, that he is reading, and that he likes to read! He had never realized that he was learning that difficult art. '^ But there is no magic about Aldine Reading. Like the marvellous achievements of applied science, its success depends upon the simple principle of understand- ing and utilizing, instead of ignoring and antagonizing nature. The child's nature furnishes the key, the sure guide to all the method there is in Aldine Reading. What does the child like — to see, to hear, to do? Does he hke stories, rhymes, pictures, ' make-believe ' games? All these he gets and takes part in from the very beginning. What subject, what content, must these stories, pictures, plays, and games have? Must they be full of simple action, full of appeal to the imagi- nation, with now and then a touch of mystery and won- 292 METHODS IN EDUCATION der? Must the actors be animals and children and simple folk, fairies and personified objects of nature, with a strong bond of sympathy running through, uniting all and making them natural associates and playmates? All these simple requirements of childhood are satisfied in Aldine Reading. ''The three fundamental elements of the power to read well are (1) a reading vocabulary composed at first of words and expressions already in familiar use in the spoken vocabulary; (2) the habit of instantly asso- ciating suitable thought and feeling with printed symbols and, in oral reading, of expressing naturally and effec- tively those thoughts and feelings; and (3) the power and the habit of mastering new language and thought independently. These three are developed constantly from the child's first day in school. Every exercise of every description contributes to this end, some exercises developing chiefly one, some another of these elements. '' Here we may barely indicate a few of the most important means employed to develop the three elements of power essential to good reading, as given above. Al- though all these elements are developed at the same time, in the beginning they are emphasized in the order named; as factors in making good readers, however, their relative importance would place them in the reverse order. ''The initial reading vocabulary is acquired through the rhyme, the story, pictures, objects, and dramatizing; these, as means to the acquisition of a vocabulary, are of importance in the order named. The habit of associating suitable thought and feeling with printed symbols and, in oral reading, of expressing naturally and effectively those thoughts and feelings, is formed READING 293 and fixed through dramatizing, the story, pictures, the rhyme, and conversation; these serve this purpose in about the order given. Just how all these objects and exercises are correlated and made to serve effectively in the development of the first two elements on which good reading depends, is explained in the Teacher's Manual: " The service of the exercises centring about these objects and ideas is not limited to the development of the first two elements of good reading; they also con- tribute to the development of the third and, in its far- reaching effect, the most fundamentally important of the three factors that determine good reading, the power and the habit of mastering new language and thought independently. In the development of this third factor, however, particularly so far as it has reference to the independent mastery by the child of the pronunciation and the thought of new words, most reliance is placed upon the treatment of phonics. Space permits here only the statement that children do learn in an in- credibly short time to read independently and fluently anything that is within the range of their understanding. And they can read what they are capable of understand- ing wherever it occurs, in books, papers, magazines, and manuscripts; they are not limited at any time to specially prepared books; diacritical marks — that abomination of children's readers — have no place in the Aldine. For the full explanation of the treatment of phonics reference must be made to the Manual. " The most fundamental principle in Aldine Reading is that the child shall apply from the beginning and con- stantly the knowledge that he has; that the teacher shall never do for the child what he can do for himself; and that all help given shall help the child to help himself. 294 METHODS IN EDUCATION This one principle of independence, variously stated from various standpoints, pervades every exercise, whether it be reading, phonic drill, dramatizing, or picture study; it pervades equally all the variety of interesting and pur- posive seat work which contributes materially to the development of good reading. Aldine Reading is vastly more important than any mere method or device for acquiring mastery of the mechanics of reading — it does lead to that mastery speedily; it is all-round, rich, sound education for the primary child; and withal, it is a joy to child and teacher, as all primary education ought to be." 576. Summary of advantages claimed 1. Analytic system. 2. Increasing interest stimulated. 3. Self-rehance promoted. 4. Abundant drill furnished. 5. Power of expression stimulated. 6. Self-activity always utilized. 7. Visualization constantly used. 8. Aesthetic appreciation developed. 9. Associative laws followed. 10. Systematic arrangement. 11. Enables pupil to read alone from books at home within the first ten weeks of the school year. McCloskey and Aldine Combined 577. Eclectic tendency. — A choice of what seemed best in the McCloskey and the Aldine methods has given us a combination method as applied in a Brooklyn school. This method has not been tested above the third grade, but still it is a type worthy of consideration. The McCloskey reading was abandoned in this grade READING 295 because, at the start, it was found that the length of the sentences was too much for the beginners. The chart with its pictures, the stories suggested in the manual, the phonetic and sight word cards of the Aldine System aid the teacher in presenting the subject and help to hold the pupil's attention. Since this sys- tem is based upon a series of rhymes, it works nicely into the McCloskey System. The Aldine Manual is adhered to for directions, and each lesson is conducted along the following lines: 1. Story is told by the teacher with the aid of the picture on the chart. 2. Dramatization by the children in which the rhyme to be learned is repeated as often as possible. 3. Rhyme is written on the board and drilled upon so as to associate the written form with the spoken word. The first rhyme consists of four different words. The second one has six new words. These ten words form a basis for numerous drill sentences in which the rhyme is eliminated. The sight word cards are used for the drills in recog- nizing the words already taught. These cards seem particularly good because the script form is on one side and the printed form on the other. When the children have mastered about six stories and are able to recognize readily the written form of the rhymes, print is introduced. The rhymes being known by heart, the printed form is easily learned. At this point the primer is started. For a certain number of pages the work is identical with that on the chart. The print being smaller, the pictures colored and the book itself something new, interest is still maintained. Phonetics are a part of the work, consonant sounds 296 METHODS IN EDUCATION only being employed in the first grade. The phonetic cards also are well planned, one side containing the capital and the small form of a letter and the other side the small form and a word beginning with that particu- lar letter. 578. Good reading defined. — Interpretation of the author is good reading. The analysis of this definition will show that it covers all of the mental and the physical quahfications of good reading. The physical qualities are articulation, enunciation, pronunciation, pitch, modulation, time, accent, and inflection. The general position of the body and the holding of the book con- tribute much to these quahties. The mental quahties are the results of an application of the physical qualities so that the selection may be properly expressed. This interpretation expressed involves emphasis, placing of rhetorical pauses, fluency, and feeling. 579. Physical difficulties. 1. Distinct articulation and enunciation. Appeal to imitative faculty of child, the teacher being the model; have individual and class drills on difficult sounds and combinations hke th in with, t in first, r in frog, k in sink. 2. Modulation of voice. Work for pure speaking tones, the teacher being the model again. 3. Weak attention. Have short, interesting lessons, and stop before interest wanes. Physical conditions often determine the duration of sustained interest. Timidity, bashfulness, and laziness should also be considered as causes. 580. Mental difficulties. 1. Association. Reading calls for a threefold effort: the idea in the mind, the spoken words, and the symbols READING 297 representing these words. This association requires time, as required by DeGarmo's Law of Successive Clearness. 2. InteUigence. Strive to get intelhgent reading, not a mere pronunciation of words. See the term appreciative reading in section 586. 581. Reading to pupils. — In the lower grades the teacher's aim is to serve as a model in interpretation and expression, and, consequently, to arouse an interest in reading. The instinctive response through imitation is very strong. Aside from this desired reaction, the educative effect is powerful because the teacher's reading brings the content within the comprehension of the children. As the pupils advance in the grades the teacher's reading to them is not for the purpose of direct imitation by the pupil, but to increase interest and maintain a standard of good reading. 582. Meaning of words. — The meaning of words should be learned through the context rather than from formal definitions. For various ways of teaching the meaning, see sections 289 to 295 inclusive. How to Arouse Interest in Reading 583. Information and drill. — The substance of this section is in harmony with what was said about prepara- tion as one of the formal steps. See section 223. It has been suggested that, beginning in the second grade, '' The reading lessons proper should be preceded by (1) such conversations as may be necessary to prepare the minds of the pupils for the appreciation of the subject- matter, and (2) exercise which will insure the prompt recognition of the form and the meaning of new words." 298 METHODS IN EDUCATION This second suggestion emphasizes the importance of drill as a means of reviving and clarifying old concepts to make them ready to blend with the new. 584. Removing difficulties. — This process is a con- tinuation of the work in the last section, but the responsi- bility of finding and removing the difficulties must be shifted from the teacher to the pupils as soon as the pupils are capable of doing the work. In the fourth grade, for instance, pupils should use the diacritical marks as aids in the pronunciation of difficult words, and in the intelligent use of the dictionary. In all of this work, guidance is the function of the teacher, and consciousness of increasing power to help himself is the desired state of mind of the pupil. Every selection in reading has certain difficulties, and it is imperative that pupils acquire an effectual habit of removing the difficulties that are obstacles to good reading. But here we meet a pedagogical question: Does good reading require the removal of all difficulties? If so, is not practice in reading sacrificed to collateral research? We may leave this question unanswered and direct our attention to the following difficulties and remedies : 1. New or difficult words. For a general treatment of teaching the meaning of words, see sections 289 to 295 inclusive. 2. Allusions and figures of speech. The teacher must be prepared in advance to explain whatever the child cannot find for himself. For allusions, give refer- . ence to pupils, if possible, and encourage them to look up the answers. 3. Words, phrases, or clauses out of the natural order. The first treatment of this difficulty of order in a sentence READING 299 is to lead pupils to arrange words, phrases, or clauses in the natural order, or the order commonly used in speak- ing. Then see why inverted or peculiar order is used in the selection. Is it for emphasis or climax? 4. Ellipses, especially of verbs. Use suggestion just made, namely, look for the usual form of expression. Try to discover the contrast between the elHptical ex- pression and the full expression. What is gained by ellipses? 5. Words used under poetic license in advanced gram- mar grades. Teacher must explain and then have pupils notice such uses thereafter. 585. Enlarging native interests. — In the interme- diate grades, teachers should give informal talks on books to read at home, being guided in recommendations by tastes and interests of the individual pupils. This suggested reading may develop an acquired interest that will lead to usefulness and culture. Teachers have frequently reclaimed wayward children by tactfully recommending a book that satisfied youthful interest, even though the book was not in the prescribed reading for the grade. After an initial effort of this kind, the assignments can gradually make a transition to the literature of the grade. Judicious assignment means what all good teaching means, — an adaptation to the needs of the pupils. 586. Appreciative reading. — In the first part of this chapter we spoke about the modern use of complete works in place of abstracts. It is the privilege of pupils to become familiar with all of Snow-Bound, Evangeline, Deserted Village, The Bunker Hill Oration, and other masterpieces that thrill the youthful mind by a realistic conception of human fellowship and literary power. 300 METHODS IN EDUCATION One reading is not likely to arouse a lasting interest; and so three readings are advised, each having a specific yet related purpose. Have one rapid reading to get conception of the piece of literature as a whole; part of the reading may be done by teacher, part by pupils in class, and part by the pupils at home. A second reading should clear away the difficulties in meanings, and pupils should try to get the thought and feehng rather than the form of the selection. The third reading is for effective oral rendering of those parts of the selection which make special appeals to the pupils' imaginations and sympathies. I^v The three readings constituted what was formerly called critical reading of masterpieces. Now we call it appreciative reading, or interpretative reading, because the practice of critical study has produced another step in intellectual advancement. 587. Oral reports. — The practice of giving occasional reports of collateral reading or other special assignment has the value already attributed to oral discussions and debates. Expression is a correlative of impression. 588. Memorizing. — The recitation of selected por- tions of masterpieces need not be associated with drudg- ery and timidity. The boy who voluntarily commits to memory one hundred lines of the Deserted Village will not have to be told that Goldsm.ith's theme was close to the life of the people. Teach pupils how to memorize a selection, give them frequent practice in facing the class, and then one phase of interest in reading will be maintained by the pupils themselves. 589. Silent reading. — A large part of the work of school and of life depends upon the power of reading silently. As all good reading means an interpretation of thought, it follows that the teacher's duty is to show READING 301 pupils how to get the thought from the printed page through the process of silent reading. This may naturally follow the ability to do good work in oral reading, but special exercises to test the children upon the work in the reading lesson and in the library books are recom- mended. Articulati07i 590. Violations of articulation. — Articulation has reference to the distinct utterance of the sounds of the letters and syllables constituting a word. This distinct enunciation is violated in four different ways. 1. Suppression of a syllable; as, ev'ry for every, reg'lar for regular, and mem'ry for memory. 2. The omission of sounds; as, readin for reading, swif'ly for swiftly, and Feb'uary for February. 3. The substitution of sounds; as, ufford for afford, judgmunt for judgment, modist for modest. 4. Blending of the termination of one word with the beginning of another; as, this sworld for this world. Accent and Emphasis 591. Definitions. — Accent is the stress of voice placed upon a syllable; emphasis is the stress of voice placed upon one or more words in a sentence. The difference in accent is illustrated by the pronunciation of words, thus: conduct, meaning behavior, is accented on the first syllable; conduct, to lead, is accented on the second syllable. 592. Emphasis illustrated. — Emphasis is frequently denoted in books by the use of italics, small capitals, or large capitals. But these indications are not always used, and so the interpretation of the piece to be read 302 METHODS IN EDUCATION requires the student to place the emphasis so that the meaning of the author will be properly expressed. We give two illustrations from the Union Fifth Reader, by Sanders : '' Liberty and Union, Now and Forever, One and Inseparable." Treason! cried the speaker; treason, treason, TREASON, re-echoed from every part of the house. Absolute emphasis is the kind just illustrated. It belongs to the important words in a sentence, irrespec- tive of contrasting emphasis. Antithetic emphasis depends upon contrasting parts of a sentence. " People do not lack strength; they lack will.'^ Inflection 593. Meaning and kinds. — The word inflection means a rising or a falhng of the voice in reading or speaking. The four kinds of tones classified under inflection are the monotone, the rising inflection, the falling inflection, and the circumflex. Strictly speaking, the monotone is not an inflection at all because there is no rising or falling, but for convenience it is classified with the other three kinds of tones. Following is an illustration for each kind of tone. 594. Monotone. ^' Thy will be done." 595. Rising inflection. The noisy geese that gabbled o'er the pool, The playful children just let loose from school; The watch-dog's voice that bayed the whispering wind, And the loud laugh that spoke the vacant mind; These all in sweet confusion sought the shade. And filled each pause the nightingale had made. READING 303 In these lines from the Deserted Village, use rising inflection on pool, school, wind; falling on shade and made. 596. Falling inflection. Brutus. Go to; you are not, Cassius. Cassias. I am. Brutus. I say you are not. Cassius. Urge me no more; I shall forget myself. Have mind upon your health; tempt me no further. — ^From Jidius Caesar. Falling inflection on to, not, Cassius, am, not, more, myself, health, further. 597. Circumflex for underscored words. And this man has become a god, and Cassius a wretched creature. Modulation 598. Kinds : pitch, quantity, quality. — Modulation has reference to the variations in the voice in speaking and reading. Modulation is both mental and physical and it depends upon the emotional interpretation of the selection to be read. Modulation is expressed in three different ways. Pitch has reference to high or low tones of the voice; quantity means the volume or the loudness of the tones; quality has reference to the kind of tone. Pitch is easily distinguished by associating it with the musical scale. Quantity is measured by the volume of the sound, as soft or loud; and by the time, as slow or quick. Volume has reference to the stress; time has reference to the movement. Illustrations of the principal characteristics under quantity are given below. Number (1) is high and loud; (2) very loud; (3) quick; (4) soft; (5) very 304 METHODS IN EDUCATION loud; (6) plaintive; (7) and (8) slow and low. Selection and application taken from page 44, Union Fourth Reader, by Sanders. (1) The combat deepens ! (2) on ! ye brave ! (3) Who rush to glory, (4) or the grave! (5) Wave, Munich! all thy banners wave! And charge with all thy chivalry! (6) Ah! few shall part where many meet! The snow shall be their winding sheet, And every turf beneath their feet (7) (8) Shall be a soldier's sepulchre! — Campbell. Quality of Tone 599. Meaning. — Quality relates to the kind of tone. Under ordinary classifications there are the four kinds. Sanders, an authority followed by nearly all the modern books, gives four definitions which we shall quote: 600. Pure tone. — The pure tone is a clear, smooth, sonorous flow of sound, usually accompanied with the middle pitch of voice, and is adapted to express emotion of joy, cheerfulness, love, and tranquillity. Example Hail! beauteous stranger of the wood, Attendant on the spring, Now heaven repairs thy vernal seat. And woods thy welcome sing. 601. Orotund. — The orotund is a full, deep, round, and pure tone of voice, peculiarly adapted in expressing sublime and pathetic emotions. READING 305 Example It thunders! Sons of dust, in reverence bow! Ancient of Days! Thou speakest from above: Almighty! trembhng, hke a timid child, I hear thy awful voice. Alarmed — afraid — I see the flashes of thy lightning wild, And in the very grave would hide my head. -602. Aspirated tone. — The aspirated tone of voice is not a pure, vocal sound, but rather a forcible breathing utterance, and is used to express amazement, fear, terror, anger, revenge, remorse, and fervent emotions. Example Oh, coward conscience how dost thou affright me! The lights burn blue. It is now dead midnight; Cold, fearful drops stand on my trembling flesh. 603. Guttural quality. — The guttural quality is a deep, aspirated tone of voice, used to express aversion hatred, loathing, and contempt. Example Tell me I hate the bowl? Hate is a feeble word: I loathe, ABHOR, my very soul With strong disgust is stirred. Whene'er I see, or hear, or tell, Of the dark beverage of hell. Pauses 604. Grammatical and rhetorical. — Rhetorical pauses are those made in reading, irrespective of the construe- 306 METHODS IN EDUCATION tion or the punctuation of the passage. Grammatical pauses are those made in accordance with the construc- tion and the punctuation of the passage. The former is illustrated: Sweet was the sound | when oft at evening's close | Up yonder hill 1 the village murmur rose I 605. Control of the breath. — As in all other school work there are two conditions to be considered, the physical and the mental. We have already spoken about the necessity of good physical conditions in each child and the consequent mental conditions. Good breathing requires proper position in sitting and standing. It involves practice in deep breathing and the general poise of mind and body. The child that is taught to breathe deeply will soon form the habit of breathing in that way most of the time. When he comes to the prac- tice in oral reading, the breathing will then take care of itself and his attention can be given to the mental qualities of good reading, while the breathing will supple- ment his interpretation by means of the oral expression. The ordinary ''setting up" exercises in physical culture are intended to put the body into physical conditions for effective breathing in all school work. 606. Extensive and intensive reading. — Extensive reading refers to the amount of reading done by the pupil; while intensive reading relates to the depth of the interpretation made. The present tendency is toward extensive reading. Stanley Hall and some other educators advocate the mastery of one good book in literature rather than the promiscuous reading of books. The latter may seem to satisfy the desires and views of the child, but there will be a lack of classified material READING 307 or an utter forgetfulness of the matter read. Intensive reading of a few good books will enable the pupil to get the thought of the author, to become familiar with the author's style of writing, and to form ideals worthy of imitation. There are arguments in favor of each kind of reading, but a personal opinion favors the latter kind. 607. Home reading. — The class library is designed to supplement school work and to furnish the teacher with such material as will attract the children to books, create a love for good literature, and encourage the habit of reading outside of school hours. A good rule to be followed in the selection of books is the one laid down by Dr. Hill in The True Order of Studies: '' The most instructive reading for a person of any age, old or young, is that in which the author's tone of thought is above the average tone of the reader's thought, and yet not beyond his grasp." The pupils should have convenient access to the hbrary for reference work and general reading. They should be encouraged to draw books and take them home. Books should be kept not longer than two weeks without renewal; and such books as are in great demand should not be retained by a pupil more than one week. — New York Course of Study. 608. Literature and character. — This topic is in- serted here to emphasize the need of more direction regarding what children shall read. The teacher of ordinary reading is supposed to give the child the power to interpret good literature, but her task does not end with that part of the work; she must supplement those efforts in teaching by trying to direct the child into habits of reading a kind of literature that will form character for life. 308 METHODS IN EDUCATION 609. Patriotic selections. — There are two views regarding the teaching of patriotism. One mentions specific virtues in civic life and then proceeds to teach the necessity of having these virtues. This teaching is done largely through biography and history. The tendency toward imitation of the lives of great men and women is the principle upon which this kind of training rests. The other view is through the self-activity of the pupils in organizations for pupil self-government and in the supplementary reading of chosen selections which convey the highest ideals in American life. The latter process is the one that justifies the use of patriotic material in the course for reading. Such material exalts civic virtues, which are treated abstractly in the first view of patriotic training, but the teacher does not preach the necessity of following every one of these virtues. She hopes, however, to have the pupil, through the interpretation of the literature, recognize the ideals and feel it a duty and a pleasure to strive to attain such standards. 610. Biography. — In the chapter on history we spoke of biography as a correlated means of making historic events emphatic. A similar use may be found in reading. The selections in literature will have a stronger personal relation as the child becomes acquainted with the lives and characteristics of the author. This point of view alone justifies the use of a certain amount of biography as a part of the suitable material in the course in reading. How to Memorize a Selection 611. The selection. — Choose a selection that will appeal to the interests of the class. It may be necessary READING 309 to educate the children to appreciate certain kinds of prose or poetry. In this process of education teachers should select material that will suit the children during the various steps in their development. 612. Copy in .sight. — Use a selection that may be found in the books of the class so that each child may have a copy for his own use. If this is not possible, write the whole selection on the board so that it may be easily seen from any part of the room. 613. Biography of author. — Bring out the essential facts in the biography of the author. 614. Occasion of writing. — Show the conditions which led to the writing of the selection. 615. Business-like attack. — Don't make a long in- troduction in trying to arouse interest. Make the teach- ing of the selection a matter of business which every child in class ought to respect. The very fact that the selection has been chosen for this purpose is enough to invite respectful attention; and the facts brought out in the biography and in the conditions at the time of writing the selection are enough to interest an average class. 616. Physical comfort. — Have the pupils take a comfortable position, fix attention upon the matter on the board, and prepare themselves for concert work. 617. The memorizing. — The teacher should diriect the lesson by having all pupils read the whole selection through once. Then take it by stanzas or paragraphs, and then the third time begin upon the sentences. Concert memorizing of a certain amount of the selection is made by means of visualization. Concert drill and individual drill follow. 618. Unifying review. — Review frequently from the 310 METHODS IN EDUCATION beginning so that pupils may hold the parts in their relation to the whole. Do not prolong the work to the point of fatigue. Grade selection according to the abihty of the class to memorize, and stop when the complete selection is mastered. The completion of the process may be assigned for home work. 619. Rhetorical exercises. — The practice of having rhetorical exercises, from time to time, is to be com- mended as a useful exercise in school work. Those who have read the substance of this book do not need an extensive answer to this question. Such exercises are a kind of oral summary of the leading points in all the lessons; but as a means of bringing out the dramatic element in expression they have a far greater value. From what has been said about class discussions, debates, etc., students can summarize the points of value in rhetorical exercises. 620. Adaptation. — We have emphasized the necessity of adaptation all through the grades in the elementary schools and so that general principle can be applied to every exercise in the course in reading. 621. Variety. — The law of variety is a physical and a mental necessity. It is the one valuable point in the avoidance of fatigue. As the reading matter is one external means of adapting variety, it is not necessary to offer a longer defence of its use. 622. Correlation. — Since reading is necessary as a basis for all studies, it follows that reading must be correlated with all studies. It is not necessary, however, to make the recitation periods in reading lose their character as such in the effort to cover the work in geography, grammar, arithmetic, or other studies. READING 311 Memory Gems 623. Limitations. — To what extent should pupils be required to memorize gems from literature? What should be the characteristics of such memory selections? A minimum assignment should be prescribed for every grade in the elementary school. The selections are intended to aid pupils in thought and expression rather than to serve as mere training for the memory. Each sele'ction has the merit (a) of being adapted to the grade, (h) of teaching some desirable lesson, (c) of possessing literary excellence. New York City Suggestions lA At least four lines of poetry per week, or an equivalent amount of prose, should be memorized by every pupil. The selections may be made from the following list: Little Pussy — Taylor. The Dewdrop — Sherman. Who has Seen the Wind? — Rossetti. Sleep, Baby, Sleep (two stanzas) — From the German. The Rain is Raining All Around — Stevenson. The Wind — Stevenson. Boats Sail on the Rivers — Rossetti. Mother Goose Rhymes: Humpty Dumpty. Mistress Mary. Little Jack Horner. Little Bo-Peep. Little Boy Blue. Baa, Baa, Black Sheep. Rock-a-by, Baby, Thy Cradle is Green. Rock-a-by, Baby, on the Tree Top. .This Little Pig Went to Market, etc. iB The Sunbeams — Poulsson. Over in the Meadow — Wadsworth. Hush! the Waves are Rolling in — Old 312 METHODS IN EDUCATION Gaelic Lullaby. What Does Little Birdie Say? — Ten- nyson. The Baby — MacDonald. The Golden Rule — ■ New England Primer. Robin Redbreast — AUingham. Twinkle, Twinkle, Little Star — Taylor. Nonsense Alphabet — Lear. Mother Goose Jingles: Sing a Song of Sixpence. I Saw a Ship a-SaiUng. I had a Little Sister. Peter Piper. As I Went Through the Garden Gap, etc. Thirty White Horses. Little Nancy Etticoat. The House That Jack Built. 2a The Swing — Stevenson. Bed in Summer — Steven- son. Who Stole the Bird's Nest? — Child. Daisies — Sherman. Seven Times One — Ingelow. The Rock- a-By Lady — Field. All Things Beautiful — Alexander. Proverbs and Maxims. 2b Don't Kill the Birds — Colesworthy. Ariel's Song, '' Where the bee sucks." — Shakspere. My Shadow — Stevenson. Dutch Lullaby — Field. Windy Nights — Stevenson. Lady Moon — Houghton. Stop, Stop, Pretty Water — Follen. The Land of Story Books — Stevenson. 'Thanksgiving Day — Child. Proverbs and Maxims. '3a I Live for Those Who Love Me — Anon. The Brown Thrush — Larcom. The Tree — Bjornsen. Wishing — AUingham. The Owl and the Pussy Cat — Lear. The Violet — Jane Taylor. Hiawatha's Childhood — Long- fellow. Hiawatha's SaiUng — Longfellow. Proverbs and Maxims. READING 313 3b The Child's World — LiHiput Lectures. Marjorie's Almanac — Aldrich. A Visit from St. Nicholas — Moore. The Owl — Tennyson. The Captain's Daugh- ter — Field. Sweet and Low — Tennyson. Proverbs and Maxims. 4a The Night Wind — Field. The Children's Hour — Longfellow. Jack Frost — Gould. Robert of Lincoln — Bryant. ''He Prayeth Best " — Coleridge. The Wreck of the Hesperus — Longfellow. 4b The Fountain — Lowell. September — Jackson. The Village Blacksmith — Longfellow. The Mountain and the Squirrel — Emerson. Barefoot Boy — Whittier. Drill exercises, as in 4a. 5a The Landing of the Pilgrims — Hemans. The Day Is Done — Longfellow. '' Under the Greenwood Tree " — Shakspere. A Sea Dirge — Shakspere. Woodman, Spare That Tree — Morris. The Gladness of Nature — ■ Bryant. Excelsior — Longfellow.. The Arrow and the Song — Longfellow. 5b The World Wants Men — Anon. Aladdin — Lowell. Psalm of Life — Longfellow. To the Fringed Gentian — Bryant. The Planting of the Apple-Tree — Bryant. Paul Revere's Ride — Longfellow. Barbara Frietchie — Whittier. Today — Carlyle. 314 METHODS IN EDUCATION 6a Orpheus with His Lute — Shakspere. The Destruc- tion of Sennacherib — Byron. A Man's a Man for A' That — Burns. The Minstrel Boy — Moore. Abou Ben Adhem — Hunt. The First Snow-Fail — Lowell. Nobility — Gary. Sheridan's Ride — Read. Song of Marion's Men — Bryant. 6b The Spacious Firmament — Addison. Burial of Sir John Moore — Wolfe. The Builders — Longfellow. Old Ironsides — Holmes. One by One — Proctor. '^ Breathes there the Man " — Scott. The Blue and the Gray — Finch. The White-Footed Deer — Bryant. 7a Fiftieth Birthday of Agassiz — Longfellow. To a Waterfowl — Bryant. The Finding of the Lyre — Lowell. The Year's at the Spring — Browning. " It is not growing like a tree " — Jonson. Daybreak — Longfellow. Bannockburn — Burns. 7b Thanatopsis — Bryant. Gharge of the Light Brigade — Tennyson. Hohenlinden — Gampbell. " Good name in man and woman " — Shakspere. " Farewell, along farewell to all my greatness " — Shakspere. The Bugle Song — Tennyson. " There was a sound of revelry " — Byron. 8a " Thou, too, sail on " — Longfellow. '' The quahty of mercy '*' — Shakspere. The Ghambered Nautilus — READING 315 Holmes. My Heart Leaps Up — Wordsworth. The Brook — Tennyson. Sound the Loud Timbrel — Moore '' I wandered lonely " — Wordsworth. The Concord Hymn — Emerson. Opportunity — Sill. Warren's Ad- dress — Pierpont. Bunker Hill Oration — Webster. Po- lonius's Advice — Shakspere. 8b Liberty and Union — Webster. To a Skylark — Shdley. Elegy — Gray. The Forest Hymn — Bryant. Commemoration Ode (Division VI.) — Lowell. On His Bhndness — Milton. The Way to Heaven — Hol- land. Sandalphon — Longfellow. '' This was the noblest Roman of them all " — Shakspere. Gettysburg Ad- dress — Lincoln. '' What is so rare as a day in June " — Lowell. CHAPTER XV ARITHMETIC 624. Changing points of view. — During the last ten years the teaching of mathematics has had more vigorous and authoritative discussion than any other subject in the elementary schools. The investigative efforts have produced a new psychology of number and new concep- tions of methods, reconstructed text-books representing new types in content and arrangement, and established public recognition of the pertinent value of the history of mathematics. When we consider that arithmetic was co-existent with the needs of man, it is surprising that evidence of systematic reconstruction is not found in the earlier epochs of intellectual activity. But regrets are needless since students are privileged to share the ben- efits of modern scholarship. For references, see list of books at the end of this chapter. 625. Quantity, measurement, mathematics. — One notable feature of the new conception of mathematics is the close relation of arithmetic to life. This relation has always existed, but it has not been recognized in theory and application. The fundamental idea in each of the three topic headings in this section is found in the needs and hmitations of mankind. Our wants are many, but provision for their supply is limited and secured only by labor. Time and energy are limited. It comes about, consequently, that the question how 316 ARITHMETIC 317 much enters largely into life. How much do I need? How much can I get? How much of my time shall I give to this portion of my task, and how much to that? How much is mine? How much is yours? These and a thousand other similar questions are very insistent. Success in life depends largely upon the wisdom and accuracy with which we answer them. A more specific illustration of this quantitative side of life is found in the historic experiences of the race. Take the pioneer farmer's problem, for instance. Land must be cleared and plowed and planted. The crop must be cultivated and harvested, a barn to store the grain and a shelter for family and stock must be built. Many other tasks must be performed. All these are essential parts of his one great task. Not one can be neglected, but almost any one might absorb all of his time and energy. He might build so large as to have no time for other things. He might clear so much land as to have no time left for plowing and so on. He must decide how much time he can give to any one part of his task and yet do justice to all the rest. In each separate task he must decide how much to undertake so that he may finish the task in its allotment of time. All thi^ is true under the primitive conditions; and as social organization develops, the question how much becomes far more insistent and frequent. Definitions That aspect or property of the outside world that presses upon us the question how much may be thought of as quantity. The process of determining the answer to the question how much is measurement. It is not always or gen- 318 METHODS IN EDUCATION erally a simple process of laying off a unit. That is, of course, always involved, but the entire process gen- erally involves also considerable computation guided by knowledge of geometrical or physical laws. The science of quantity is mathematics; and, therefore, mathematics is the science that treats of measurement and all the geometric and physical laws that measure- ment involves, and the application of those laws in computation, as well as the art of computation itself. 626. Definition of number. — The answer to the ques- tion of quantity, the result of the process of measure- ment, is number. This is identical with the definition found in many arithmetics: '' Number is that which answers the question how many or how much.'' The question how much always resolves itself into how many, according to Psychology of Number, page 71. Number is, then, that in which our ideas of quantity become definite. The following definition regards the origin as well as the use of number: Number is a product of the way in which the mind deals with objects in the operation of making a vague whole definite. — McLellan and Dewey, page 32. Note that this definition considers the concept of number as the result of a mental process showing quantity. Other Approved Definitions 1. A number is that which is applied to a unit to express the comparative magnitude of a quantity of the same kind as the unit. — Glashan, Arithmetic for High Schools. 2. Number is the abstract ratio of one quantity to another of the same kind. — Newton. ARITHMETIC 319 3. Number is the ratio of one quantity to another quantity taken as a unit. — Euler. Disapproved Definitions 1. ''Number is a symbol." Entirely abstract; wrong, not in the mind. 2. "Number is identical with things; it is a property of objects." Wrong, as concept of number can exist only in the mind. It is because objects have been used to develop the idea of number that these definitions have been used. While we put number into objects, we derive our idea of number from the objects themselves. 3. ''Number is a collection of units." Smith, page 100, says this definition is " scientifically worthless." But some educators hold that the first number concept is a collection of units, the ratio idea not developing clearly until later. This definition as quoted does, of course, exclude one as a number. Conclusion The consensus of opinion favors the definitions making number identical with ratio. The definition quoted from McLellan and Dewey is generally accepted. Another authoritative source is Smith's The Teaching of Elementary Mathematics. The quotations used by Smith on pages 99, 100, and 101 are serviceable here: The notion of number is not the result of immediate sense-perception, but the product of reflection, of an activity of our minds. We cannot see nine. We can see nine horses, nine feet, nine dollars, etc., that is, we see the horses, the feet, the dollars, if they are presented to us; that there are exactly nine, however, we cannot 320 METHODS IN EDUCATION see. If we wish to know this we are forced to count the things; and since we usually do this with the help of our eyes, the idea has got abroad that we see number. — Fitzga, Die naturliche Methode des Rechen- Unter- richtes in der Volks- und BUrgerschule, I. Theil, Wien, 1898. Number is generated in the mind by the seiSe-percep- tion of a group of things supposed to be alike. — Smith, page 101. A careful observation shows us, however, that there are no objects exactly alike; but by a mental operation of which we are quite unconscious, although it holds within itself the entire secret of mathematical abstrac- tion, we take in objects which seem to be alike, rejecting for the time being their differences. Here is to be found the source of calculation. — Laisant, La Mathe- matique, pages 15, 18, 19, 31. 627. Counting and measuring. — There is much dis- cussion about whether counting or measuring should come first in teaching number. Both are required, but the New York City course of study mentions counting first. This use of the term counting includes the four fundamental operations; the old notion of counting meant a mastery of the numbers 1, 2, 3, 4, etc., in a narrower sense. Measuring is simply a form of activity, a kind of reaction. It implies learning by doing; it is concrete; it is empirical; it should be definite work rather than educative play. Measuring stimulates interest if the pupil understands what he is doing when he is measuring; but he cannot have any definite con- cept of measurement until he counts by using some unit of measurement, such as foot, yard, pint, dime, etc. Hence, ''all counting is measuring and all measuring is ARITHMETIC 321 counting," as is said in McLellan and Dewey's Psychol- ogy of Number, page 48; also in Smith's The Teaching of Elementary Mathematics, page 104. When we count books in a hbrary, we measure the Ubrary; and we meas- ure our weight by counting the number of pounds. Counting is measuring a magnitude composed of dis- cernibly distinct units; measuring is a method of counting the units into which a magnitude, outwardly continuous, may conceivably be divided. *The difference between counting and measuring is that in ordinary counting we use an undefined unit, a kind of vague measurement; as, 10 apples, 5 books. This counting of 10 apples or 5 books becomes definite only when weight or value, i.e., measure, is known. The two processes help each other toward the same object, determination of quantity. 628. Arithmetic and its aim. — Arithmetic is a Greek word meaning literally science of number, and that is its traditional definition. But the word is used by us to describe the mathematics of the elementary school course, which is necessarily much more and at the same time much less than the science of number. What we thus call arithmetic might more properly be called the elements of mathematics, since the elements of geometry and physics have as legitimate a place in it as number, although the number element is large as compared with other elements. The subject-matter of arithmetic must be mathematical operations, processes, principles; but the aim of arithmetic is not so much the mastery of those processes and principles, as their application to the problems of measurement in the world about us. That application means the mastery of our material surround- ings, familiarity with the quantitative side of nature, 322 METHODS IN EDUCATION insight into the world we Hve in, and command over its resources. The authorities for this view are McMurry, page 19; Smith, Chapter II and page 89; Harris, in Educational Review, Vol. 9, page 231; Young, page 203, for statement of aim of teaching arithmetic. The obvious aim is to give accuracy and facility in simple computations and a working knowledge of prac- tical applications; but, as Young points out, the teacher who works for no other end will miss a thousand oppor- tunities to invigorate the pupil's power of thought. All the practical usefulness of arithmetic can be attained without sacrificing its value in cultivating habits of observation and reflection. The Scotch Education Department memorandum on Teaching Arithmetic in the first years states as the first aim of the teacher: The development of the pupils' interest and inteUigence through the solving of concrete problems with a clear understanding of the processes involved; and, as the second aim, the gradual perfecting of the machinery for the manipulation of abstract num- bers. It should be added that a definite aim is the most important thing connected with method. {Smith, pages 1 and 110.) 629. Utility of arithmetic. — It thus appears that ''arithmetic is the indispensable first step toward all science of nature." ''Historically it was the first tool of thought that man invented in the work of emanci- pating himself from thraldom to external forces." "It is a powerful instrument for the regulation of social intercourse." The utihty of the subject of study that occupies this position is obvious, and nearly all nations have put special utilitarian value upon it. Smith points out that the utility of mathematics for the individual in ARITHMETIC 323 helping him to earn a Hving has been overrated. That is in a measure true, but it is also true that, in a larger sense, the utility of mathematics as a means of correlat- ing the child with the world he is to live in cannot be overrated. For further discussion, see Educational Value of Mathematics, Frank A. Hill, Ed. Rev., Vol. 9, page 349; also W. T. Harris, Ed. Rev., Vol. 9, page 242. 630. Important historical facts. — The Roman nota- tion was used in Europe during the classical times and up to the fifteenth century. That notation served clumsily and inadequately the purpose of recording number, but was of no use for assisting computation. For this latter purpose some form of the abacus, in which counters in different grooves represented units of the various decimal orders, was used. Thus, both the teaching of arithmetic and the method of computation were objective. About 1500 A.D., the Hindoo, commonly called the Arabic, system was adopted. This furnished an ideal means of assisting computation, and teachers, perceiving that their objective devices were no longer needed for computation, supposed that the devices could be dis- pensed with altogether. Arithmetic came to be a thing of symbols exclusively, and so also did the teaching of arithmetic. The teaching of arithmetic became the inculcating of a vast body of rules for juggling with digits. This was the age of rhyming arithmetics. It was hoped that if the rules were turned into rhyme the pupils would more easily remember them. Not until shortly before the beginning of the nine- teenth century was there a return to a more rational system. The great reformer was Pestalozzi. He reso- lutely made sense-perception the basis of all number 324 METHODS IN EDUCATION work and' insisted that arithmetic should not be a matter of rules and traditions, but a rational process from beginning to end. His reforms were bitterly- assailed and opposed, and only partially adopted. The battle still goes on. Compare for example the radically different views of objective teaching in the early school years as given in the New York City Syllabus and the 1910 State Syllabus. A brief summary of historical views shows that thinkers have been contributing point by point what some recent writers seem to consider entirely new. A grouping of these respective contributions gives the substance of modern ways of teaching. Consult Smith for full presentation. 1. Busse. Number pictures: number cards of today. 2. Pestalozzi. Observation = perception, (a) Know numbers rather than figures. (6) Objective presentation; remove objects before drill. (c) Much oral abstract drill. 3. Tillich. Special blocks: ratio. See Speer method. 4. Kranckes. Concentric circles. 10, 100, etc. Spiral methods. 5. Grube, 1842. All processes simultaneous. 1 to 10 first year. 6. Tank and Knilling; counting, (a) Numbers needed for counting. (6) Use number series. 2468, etc.; count objects, then memorize. (c) Counting is basis of all elementary operations. 7. German spiral method based on concentric circles. 8. Arithmetic in rhyme. 9. All arithmetic based upon measurement of lines. ARITHMETIC 325 10. All arithmetic based upon paper folding. 11. Rein. Correlation. (a) Familiar objects in home, nature study, literature, etc. (6) Series and method units. (c) Formal steps of instruction. 631. Method in arithmetic. — It would be impossible to form one composite method from the various lines of thought in mathematics. There is no unified historic development. We must look to recent psychological conclusions, as stated in the first section of this chapter. Four opinions will help to strengthen the opinion on general method as expressed in Chapter VIII. 1. There is no subject taught in the elementary schools that taxes the teacher's resources as to methods and devices to a greater extent than arithmetic. There is no subject taught that is more dangerous to the pupil in the way of deadening his mind and arresting its development if bad methods are used. — W . T. Harris in Editor's Preface to the Psychology of Number. 2. ''Sound methods are methods that capture the interest, supply the will with motives, enlist the reason- ing powers, favor original thought, and put the student on his intellectual mettle." ''The methods need to be so graded as to give the student the consciousness of power." — F. A. Hill, Ed. Rev., Vol. 9, page 350. The problem of method is always the same : — to interest the pupil, to induce research, to continually give him the notion, the illusion if you will that he is discovering for himself the things that are being taught him. — M. Laisant, quoted by Smith, page 109. Enough has been said to show that one of the easiest things in the teaching of arithmetic is the creation of 326 METHODS IN EDUCATION ''Method" — and one of the most useless. We may start off upon the idea that all number is measure, and hence that arithmetic must consist of measuring every- thing in sight — and we have a ''Measuring Method." It will be a narrow idea; we shall neglect much that is important; but if we put energy back of it we shall attract attention and will very likely turn out better computers than a poor teacher will who is wise enough to have no "Method," in this narrow sense of the term. Again, we may say that every number is a fraction, the numerator being an integral multiple of the denominator in the case of whole numbers. From this assumption we may proceed to teach arithmetic only as the science of fractions. It will be hard work, but, given enough energy and patience and skill, the children will survive it and will learn more of arithmetic than may be the case with listless teaching on a better plan. We might also start with the idea that every lesson should be a unit, and that in it should come every process of arithmetic, so far as this is possible, and we could stir up a good deal of interest in our "Unit Method." Or, again, we could begin with the idea that all action demands reac- tion, and that every lesson containing addition should also contain subtraction; that 6+4= 10 should be followed by 10 — 6 = 4 and 10 — 4 = 6; and that 2 X 5 = 10 should be followed by 10 -^ 2 = 5 and 10 -^ 5 = 2. By sufficient ingenuity a very taking scheme could be evolved, and the "Inverse Method" would begin to make a brief stir in the world. This in fact has been the genesis, rise, and decline of Methods; given a strong but narrow-minded personality, with some little idea such as those above mentioned; this idea is exploited as a panacea; it creates some little stir ARITHMETIC 327 in circles more or less local; it is tried in a greater or less number of schools; the author and his pupils die, and in due time the Method is remembered, if at all, only by some inscription in those pedagogical graveyards known as histories of education. — Smith, Monograph on The Teaching of Arithmetic, 1909, page 23. 632. Methods of teaching the concept of number. — It is unnecessary to outline in detail the first steps in teaching pupils to count. Most pupils have a concept of number long before they enter school; all they need is drill in wider application of their knowledge. Some teachers use splints in this drill; others use pencils, rulers, books, or the pupils themselves. The various devices are outlined in the next section, but through all the variety runs the uniform principle of concrete presentation. The first idea of number is never abstract. Slowly through the years of experience the mental process of abstraction produces the abstract concept of number. Four suggestions for concrete teaching are mentioned in the course of study. 1. Scoring. This is simply a way of indicating the early impressions of number. The Arabic numerals are not so easily made as groups of vertical lines, thus: 1 2^ 3 4 / //' /// ////• The drawing of such vertical lines to represent num- bers is called scoring. 2. By measurements and comparisons. Actual use of pint and quart, five-cent piece and dime. Compari- son of groups of objects. 3. Use of toy money in business operations. 328 METHODS IN EDUCATION 4. Use types in concrete problems. Here are the suggestive types: (1) If there are 3 apples in one group and 2 apples in another, how many apples are there in both? (2) If 3 apples are taken out of a group of 5 apples, how many apples remain? (3) If there are 2 plants in a row, how many plants are there in 3 equal rows? (4) If 2 plants are placed in a row, how many such rows are required for 6 plants? (5) If 6 plants are placed in 3 equal rows, how many plants are there in each row? " Exercises in counting should aid in column addition and in a mastery of the multiplication tables. Com- parisons and objective measurements should lead pri- marily to thought, rather than to over-much figure work. Oral work should precede and accompany all written work in every mathematical operation. Small numbers should be used in the illustration of principles." The counting in the first term is limited to counting by I's to 200, and lO's to 100. Later the pupils receive much drill in counting forwards and backwards by 2's, 3's, 4's, 5's, etc. This is the process that gives the foundation for the tables in the' four fundamental operations. This paragraph relates to New York City practice. 633. Concrete number operations, order of succes- sion. — We quote from the Scotch Memorandum. " The pupil must first learn the sequence of names in the number series, and be able to count a succession of objects one at a time. He should then be taught by concrete examples to perform the four operations with small whole numbers which may be slowly increased in ARITHMETIC 329 magnitude as he advances. In addition to ordinary objects employed at this stage of the instruction it is useful to associate small numbers with geometrical forms, such as are seen on cards or dominos, as these forms not only give a picture of the number itself, but show the various ways in which it is made up." E.g., notice that in the form we have pictured all the possible ways in which seven can be made up. ''The common units of every-day life should be gradually introduced; e.g., the money units, the units of time, of length, of weight. The pupil should handle the coins and know their value. The clock should be used for the units of time. The units of weight should be used practically until the pupil has a clear idea of each unit and can give a fair estimate of a length or weight without actual measuring or weighing except to correct or verify his estimate. The units so introduced will give scope for the application of the four rules to problems of an every-day type." 634. Summary of modes of concrete number opera- tions. — Notice that both measuring and counting are used in each of the devices in this summary. 1. Counting visible objects, as chairs, birds, houses, children, apples, etc. 2. Other objects, as tooth-picks, buttons, beads, pen- cils, fingers, etc. 3. The abacus, cubes, blocks, squares, etc. 4. Demonstrative devices, as distribution of papers, books, the marking off of positions at board, the paging 330 METHODS IN EDUCATION of books, counting time on the clock, attendance records, thermometer; in home geography, counting houses, making maps, etc. 5. Standard units, as gallon, pound, dollar, bushel, barrel, day, dozen, cubic foot, etc. Variety, practical units, ratios, and fractions from use of these. 6. Number pictures made of dots, lines, etc.; dom- inos. 7. In decimal scale, splints or tooth-picks in bundles of lO's and lOO's. 635. The use of a book by pupils. — The safe rule for the time of introducing a text-book in any subject is this: A book should be introduced as soon as children are able to use it to their own advantage. The average child is not capable of reading well during the first term of school life and so there is little or no advantage for him in trying to use a text-book in arithmetic. For this reason, the work of the first term is largely oral, but as soon as the child is able to make any use of a text-book in arithmetic he should be given that privilege. The work in mathematics should not depend largely upon the hearing; it is another instance of multiple sense instruction. The interpretation of a printed problem requires more mental effort than the interpretation of a problem written on the board or dictated by the teacher. In the last two ways the pupil depends upon the assist- ance from the teacher. Devices for Drill in Primary Grades 636. A distinction repeated. — All these suggested devices are only different ways in method; they are not methods in arithmetic. Devices of any kind are in- tended to attract and maintain attention. Curiosity, ARITHMETIC 331 competition, and success are likely to secure interest. Different devices satisfy a desire for variety, and some of these have permanent value in being ready for use at any time. It is understood, of course, that these devices cover all the four fundamental operations — - addition, subtraction, multiplication, and division. 637. Cards. — Number cards having the combina- tions on both sides of the card. 638. Charts. — Charts made with rubber pen. Fig- ures large enough to be seen from any part of room. 639. Mimeograph work. — Copies made by mimeo- graph admit many uses. Some copies may contain the same work for the whole class; other copies may have a few additional problems for the faster workers; a third kind may have different work for each pupil. 640. Text-books. — A good text-book — no other kind should be used — has scores of examples suited to drill purposes. Use the book. Teachers may now secure separate books for each grade, and these are excellent supplements to the class text-book. 641. Board. — Special work on the blackboard. The advantage is the probability of satisfying the exact needs of the class by adaptation; the disadvantages are temporary use and eye-strain. Every class has some pupils who cannot easily read blackboard work. 642. Circle. — Figures outside circumference; num- ber in centre. 643. Square. — Similar to arrangement in 642. 644. Drawing. — Two vertical lines crossing two hori- zontal lines at right angles, giving places for nine figures. Vertical, horizontal, and diagonal drill. 645. Dictation. — Dictation under limited time for answers. 332 METHODS IN EDUCATION 646. Competition. — Competition under recorded time after definite assignment of work. 647. Decimation. — This device uses ten as a basis in each of the four fundamental operations. Following is a table in counting: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Build to 100 101 102 103 104 105 106 107 108 109 and then drill down and up. Decimations in Combinations 0+1=1 7+8 = 15 9+4 = 1^ 10+ 1 = 11 17+8 = 25 19 + 4 = 23 20 + 1 = 21 27+8 = 35 29+4 = 33 30+ 1 = 31 37+8 = 45 39+4 = 43 40 + 1 = 41 47+8 = 55 49+4 = 53 etc. etc. etc. Subtraction Multiplication 99 — 6 = 93 3X 6= 18 89 - 6 = 83 3X 16= 48. 79 - 6 = 73 3 X 26 = 78 69 - 6 = 63 3 X 36 = 108 59 - 6 = 53 3 X 46 = 138 etc. etc. 648. How to mark papers. — This topic brings up the question in regard to marking what is right or what is wrong, and also the use of per cents, letters, or other means of indicating the worth of answers. Another question arises here, namely, if the answer is incorrect, ARITHMETIC 333 shall we allow anything for right methods of operation? In all problems accuracy is the first test of an answer. Answers are either right or wrong. The simple oral work cannot justly be marked upon any other basis. Later in the life of pupils it may be that the processes should be given some consideration, but the business demand for a correct answer is a criterion always to be kept in mind by the teacher. The use of letters or figures is a matter for individual decision. "649. The nature of the problems. — In speaking of the various kinds of elementary work we have insisted that the material should be adapted to the capacities of the pupils as well as to the needs of the course of study. These same principles apply in the primary arithmetic. Use problems that are adapted to the actual experience of the child. Such problems are the ones that produce interest at the same time that they give the requisite drill in the work. It is advisable to use problems that are related to the common forms of industry and other forms of life, but in the first grade it is probable that the interests of the children will require a simple presentation of experience in regard to games, toys, home life, etc., more than to the industrial phases of the community. Regarding the method of doing the work, both oral and written practice should be put into use as early as possible. Regarding abstract and concrete examples, both kinds should be used. Accuracy may result from using concrete problems alone, but rapidity can never be acquired without fre- quent drill on abstract numbers. Much of the work should, of course, be concrete, but as soon as the chil- dren are able to perform abstract number operations, a part of the daily drill should be devoted to rapid com- 334 METHODS IN EDUCATION putation in abstract work. A few minutes each day through all the grades should be set aside for oral com- putation. It is suggested that in the written work a time limit be set so that each child may be judged accord- ing to his recitation. It is not expected that all pupils will be able to solve the same number of problems in the limited time. 650. Opinions on drill. — Mechanical precision with abstract numbers can be accelerated, without detriment to the intelligence, by a well arranged summing up of the results already obtained in concrete cases. — Scotch Memorandum. Teachers are seriously attempting at the present time to co-ordinate the interests of the children, the needs of society, and the mathematical powers in each of the grades from the first year through the elementary school. ■ — Smith, Monograph on The Teaching of Arithmetic, page 17. See Young, page 131. 651. The fundamental operation. — The fundamental operation of arithmetic is counting. All other arith- metical operations are simply devices for speed by using remembered countings instead of going through the detailed. Herein is the hint furnished the teacher for the first lessons in arithmetic. Let the child construct gradually out of his countings his own tables of addition, subtraction, and multiplication, and fix them in his memory. — Harris, Ed. Rev., Vol. 9, page 243. 652. Hint from experience of the race. — It is inter- esting to reflect that the concrete problems that they differentiate as addition, subtraction, multiplication, measurement, and partition, came to primitive man unclassified ; and he solved them all by counting without realizing that they were of different classes. Take three ARITHMETIC 335 illustrations, the second and tlie third together being the inverse of the first. 1. If a wild savage chief wants to distribute 6 fresh- water clams apiece to 4 warriors, how many must he have to distribute? 2. If a chief wants to deal out 18 clams to as many as he can, giving 6 to each, how many will receive clams? 3. If he wishes to distribute 18 clams equally to 3 meUj how many will each receive? All of the intricacies and mysteries of measurement and partition are wrapped up in the last two problems, but the savage chiefs solved them all by counting, and so can the small boy. The practice is justified also by the culture epoch theory of education. Addition 653. A kind of counting. — This is another applica- tion of counting. Some writers speak of addition as a synthesis of the elements of knowledge gained in the first number concepts. But addition is so closely related to the first work in counting that it is not necessary to try to set limits between the two kinds of mental operations. Counting by I's is addition; and surely the counting by 2's, 3's, etc., is giving results in addition, whether called so or not. The first addition tables are the combinations of num- bers of one order with 1 and 2 : 123456789 23456789 iiiiiiiil 22222222 sums found by counting objects; the value of each num- ber and of each combination, as 3 and 2 are 5, 2 and 3 336 METHODS IN EDUCATION are 5, should be recognized at sight without counting the combinations memorized. A continuation of the drill in addition gives forty-five combinations of digits, taking two figures in each com- bination. 654. The forty-five combinations. — Following is the complete list as it is taught in the first two years of school: 1 2 3 4 5 6 7 8 9 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9 2 2 2 2 2 2 2 2 3 4 5 6 7 8 9 3 3 3 3 3 3 3 • 4 5 6 7 8 9 4 4 4 4 4 4 4 5 6 7 8 9 5 5 6 6 5 7 6 7 7 5 8 6 8 7 8 8 5 9 6 9 7 9 8 9 9 655. Automatic habits. — After all of these combina= tions whose sum is 10 or less are thoroughly memorized, ARITHMETIC 337 and special attention has been given to the combinations making 10, then proceed as follows: 1. 10 + 1 = 11, 10 + 2 = 12, 10 + 3 = 13, etc., to 10 + 10 = 20. 2. Then in any such sum as 13+ 5, proceed thus: 13 + 5 = 10 + 3 + 5 = 10+8. 3. To pass from a number in the first decade to a number in the second decade, as 8+7, proceed thus: 8+7=8+2+5= 10+5= 15. Or after special attention has been given to series 6+6, 7+7, 8+8, 9+9, the following method may be used: 8+7 = 1+7+7= 1+14= 15. These are methods of using known combinations to discover new combinations in constructing the tables without taking the trouble to count up. A combination of methods is not only possible but desirable, as the ultimate aim is to suppress the intermediate and secure the result in one step automatically, which can be more easily effected if the intermediate step is variable. — Scotch Memorandum. 656. Two fundamental facts. — As soon as the sum of two numbers involves the process of ''carrying," two fundamental facts must be taught: 1. Ten units make one ten. 2. Place gives value to a figure. The practice in counting by lO's is a preparation for both these facts, and the drill on addition giving sums from 10 to 20 will impress the truth. 657. Decomposition. — When the sum is 20 or more, it may be helpful to show units and tens by decomposi- tion. This process is not approved by some educators, but it is inserted here for the use of those who wish to teach it. 338 METHODS IN EDUCATION 1. 16+' 5= ? Then 10 units 16 = 1 ten + 6 units + 6 units 16 = 10 units + 6 units. + 5 units + 5 21 units. 21 ans. 2. 24+ 13 = ? Then 20 units 24 = 2 tens + 4 units + 4 units 13 = 1 ten + 3 units. + 10 units 24 + 3 units +13 37 units. 37 ans. 3. 87+36= ? Now we meet the fact that ten tens make one hundred. 87 + 36 ds tens units 8 7 3 6 11 13 1 2 3 123 ans. 658. Algorisms. — This is a word relating to the form of work, i.e., the arrangement. The column or vertical arrangement is preferred, since so much column addi- tion is required in life. The psychological habit of vertical addition is, therefore, more important than the habit of horizontal addition. Both are combined for proof in the grammar grades. The proof of addition in the primary grades is made by reversing the order of adding. If the first process was from the bottom to the top, then for proof begin at the top and add down. Equation. — The horizontal form of expressing an example in addition gives an equation, thus: 32+19= 51. In other words, the expression of equality in mathematics is an equation. The part before the sign of equality is ARITHMETIC 339 the first member; the part after the sign of equahty is the second member. The equation is a kind of algorism. 659. Laws or principles of addition. 1. Only like numbers can be added. 2. The sum is the same in kind as the addends. 3. If the like orders of units be added separately, the sum is the sum of all the numbers added, since the whole is equal to the sum of all its parts. 4. If the sum of the units of any order contains units of a higher order, these higher units must be combined with units of like order. Subtraction 660. Relation to addition. — As addition is consid- ered synthesis in counting, subtraction is analysis in counting. Addition and subtraction may be taught together, using subtraction as the inverse of addition. Sticks, pencils, and other concrete devices are used as material, and the child measures the difference in the groups by counting. Considerable facility in rapid sub- traction should be secured in the easy combinations before introducing the necessity of " borrowing." De- composition will be used again to explain the relations of units, tens, and hundreds in subtraction. It is only one step from the known process in addition. 661. Decomposition to explain borrowing. 35- 18=? 35 = 3 tens + 5 units = 30 + 5 = 35 = 2 tens + 15 units = 20 + 15 = 35 35 18 = 1 ten + 8 units = 10 + 8 = 18 - 18 1 ten + 7 units = 10 + 7 = 17 17 ans. 340 METHODS IN EDUCATION 662. Equal addition to explain borrowing. — A few years ago the method of equal additions was widely used among the disciples of Pestalozzian number. It is not used much today, although the axiom still holds; namely, If equal numbers be added to unequal numbers, the difference between the unequal numbers remains unchanged. 35 - 18 = ? Or 35 - 18 35 + '10 = 3 tens + 15 units = 30 + 15 = 45 18+10=2 tens + 8 units = 20 + 8 = 28 1 ten + 7 units = 10 + 7=17 35 -18 35 - 18 = 17 ans. Or 17 ans. This operation has combined the use of decomposi- tion with equal additions to make the number of units in the minuend greater than the number of units in the subtrahend. 663. Complementary addition in subtraction. — This method is an application of addition, thus: 764 - 478 286 ans. Instead of saying 8 from 14, we observe that 6 added to 8 will make 14, and the process becomes 8 + 6 = 14, 8 + 8 = 16, 5 + 2 = 7. This method is mentioned by Smith in the next para- graph. ARITHMETIC 341 664. Four ways of performing subtraction. — In subtracting 297 from 546, we have the two 546 old plans, both dating from the time of the 297 earhest printed text-books, at least. 249 The calculation is substantially this: (1) 7 from 16, 9; 9 from 13, 4; 2 from 4, 2; or (2) 7 from 16, 9; 10 from 14, 4; 3 from 5, 2. But we have also a more recent plan: ^3) 7 and 9, 16; 10 and 4, 14; 3 and 2, 5. To this might be added a fourth plan, which has some advocates: (4) 7 from 10, 3; 3 and 6, 9; 9 from 10, 1; 1 and 3, 4; 2 from 4, 2. All four of these plans are easily explained, the first rather more easily than the others. But the third has the great advantage of using only the addition table in both addition and subtraction, and of saving much time in the operation. It is the so-called ''Austrian method" of subtraction. The fourth plan, while a very old one and possessed of some good features, is so ill adapted to practical work as to have no place in the school. It is hardly necessary to say that the old expressions ''borrow" and "carry" in subtraction and addition are rapidly going out of use; they were necessary in the old days of arbitrary rules, but they have no advocates of any prominence today. — Smith, The Teaching of Elementary Mathe- matics, page 121. 665. Principles of subtraction. 1. Only hke numbers can be subtracted. 2. If the units of each order in the subtrahend be taken separately from the units of hke order in the minuend, the sum of the differences equals the entire 342 METHODS IN EDUCATION difference of the given numbers. Axiom: The whole equals the sum of all its parts. 3. If both minuend and subtrahend be equally in- creased the difference will not be changed. 666. Proof of subtraction. — Add difference and sub- trahend; or subtract difference from minuend to get subtrahend; or cast out 9's. Multiplication 667. Special case of addition. — This process is treated as synthesis in taking one number a certain number of times. Multiplication is a short form of addition, or, more strictly speaking, is a special case of addition, namely, that in which the several addends are equal; and in which consequently another memory device, namely the multiplication table, is possible. 668. Counting. — For first steps, arrange and count concrete objects as in addition and subtraction. 669. Decomposition. — Use decomposition again to explain multiphcation by one figure. 28 = 20 + 8 28 20 X 3 = 60 3X 8 X 3 = 24 28 X 3 = 84 Decomposition to explain multiplication by two figures. 67 67X 3= 201 23 X 67 X 20 = 1340 67 X 23 = 1541 This work may be arranged in another form: 201 1340 ARITHMETIC 343 Multiplying by 3 units we have 201 units; gy multiplying by 20 units we have 1340 units. 23 X The sum of these partial products is 1541 units. Since 1340 units = 134 tens, we omit the cipher, and write 134 as tens. This shorter process gives the final form. thousands hundreds tens units 6 7 2 3X 2 1 13 4 670. Justification. — These three examples are justi- fied by the third principle of multiphcation in section 675, or rather by a principle of which that third prin- ciple is a special case, namely, that the product of a number by the sum of two other numbers is equal to the sum of the products obtained by multiplying that number by each of those numbers separately. This is the distributive law of multiplication, and is an axiom or a fundamental assumption verified by all experience. It is useful, in impressing this truth, to multiply by 20 first. The method is just as easily grasped by gy the small child. It impresses the fact that in 23 V multiplying 67 by 23 we are multiplying by 20 rrrr and by 3. It has the advantage of doing the » most important part of the work first — a procedure that is always commendable. In fact, the method is insisted on for the last named reason in Elson and Short's First Book in Mathematics just published by Heath. 344 METHODS IN EDUCATION 671. Multiplication by factors. — Variety is one advantage, a means of proof is another, and a practice 3546 in analysis of numbers is a third. Another X 24 justification is the associative law of multipli- Qc^^g cation. This process illustrates the law: 3546 ^ g X 24 = (3546 X 6) X 4 = (3546 X 4) X 6 = T-— — 3546 X (4 X 6). This is another important ^ law which may be regarded as axiomatic in character and a fundamental law of the science of number. 672. Justification by commutative law. — The com- mutative law is equally important and good for varietj^, for proof, and for knowledge of the properties of number. According to the first principle in section 675, the mul- tiplicand and multiplier may be interchanged. 67 23 23 X 67 X 201 161 1340 138 1541 1541 673. Commutation, association, and distribution. — A statement of the three laws may be helpful to some students. The laws relate to arrangement and analysis of numbers. The law of commutation says the product is the same, independent of the order in which the numbers are multiphed. 5X6X7=7X6X5=6X7X5. Likewise in addition. 5+6+7=7+6+5=6+7+5. The law of association, applied to multiplication, says that the use of brackets makes no difference in the process. ARITHMETIC 345 2X3X5=6X5=10X3=15X2. But the use of brackets in combined addition and sub- traction does make a difference. 5 + 6 X 7 = 47 (5 + 6) X 7 = 77. The law of distribution uses analysis by a kind of decomposition of numbers. 5=2+3. Then 4X5=4X2+4X3= 20. a{h + c) = a6 + ac. The product of the sum of two numbers by a third equals the sum of the products of the numbers by the third number separately. 3(5 +4) =3X9=3X5+3X4. The important apphcation is 25 X 33 = 25 X 3 + 25 X 30. 674. Multiplication tables: mode and order of learn- ing. — Learning these tables by the memory process alone is condemned. All the work in counting by Ts, 2's, 3's, etc., is a preliminary preparation. The com- binations in the four operations are another aid; and then the use of acquired knowledge in measuring with foot-rule, yard-stick, toy money, pints, quarts, etc. — all help the pupils to construct the tables out of personal experience in counting and measuring. The order of learning the tables is not that of the old books. An easy order is as follows: lO's, 2's, 5's, 4's, 8's, 3's, 6's, 9's, 7's. This order starts with lO's as the easiest; then the 2's are not difficult; the 5's easily unite with the lO's and the 2's; so, too, the 4's and the 8's, and then 3's, 6's, and 9's. The 7's are not closely related with any other table; but by leaving the 7's till the last, all the combinations in the 7's are then covered by 346 METHODS IN EDUCATION the other tables. Other opinions favor a different order of procedure, but McMurry upholds this one. 675. Principles of multiplication. — When either fac- tor contains more than one figure, the principles are as follows: 1. The product is the same, whichever factor is used as multiplier. 2. If one factor be units of the first order, the product will be the same in kind as the other factor. 3. If units of each order in the multiphcand be taken separately as many times as there are units in the mul- tiplier, the sum of the products equals the entire product of the given numbers. 676. Proof of multiplication. — Divide product by multiplier to get multiphcand; or invert order of factors and multiply; or cast out 9's. 677. Concrete and abstract numbers in multiplication. — This is the place for discussion of terms concrete number and abstract number. A concrete number is a number with the name of the unit designated. MuU tiplicand may be either concrete or abstract, but multiplier must be abstract. Even if multiplicand is ab- stract, the multiplicand and multiplier must be different kinds of numbers, i.e., refer to units of different sorts; the multiplicand refers to units of some sort, though the sort is not designated, and the multiplier to units • not of the same sort, but to repetitions of the group represented by the multiplicand. Illustration If 3 pencils cost 2 cents apiece, how much will the 3 cost? Answer, 3 times 2 cents. Is it 3 pencils times 2 cents? Absurd; not 3 pencils times 2 cents. ARITHMETIC 347 but 3 times 2 cents, because the 2 cents must be repeated as many times as there are pencils. Even in concrete problems, such as that just discussed, multiplication is commutative as is shown by the fol- lowing analysis. If the 3 pencils had cost 1 cent apiece, the 3 would have cost 3 cents; but, since each costs 2 times 1 cent, the three will cost 2 times 3 cents. It appears, then, that multiplier and multiplicand may be interchanged, but that the multipUer in becoming multiplicand takes on the concrete character of cents and the multiplicand in becoming multiplier loses its concrete character and becomes times. , Division 678. Nature of division. — An analytic process, the inverse of multiplication; i.e., the process of finding one factor when product and the other factor are given. Division may also be regarded as repeated subtraction of divisor from dividend. 679. Measurement and partition. — In speaking of product in the preceding paragraph, product is the dividend and the known factor may be either multi- plicand or multiplier. As emphasized in section 677, the multiplicand is presumably concrete, the multiplier always abstract, and at any rate numbers referring to different kinds of units. Arising from these conditions, two cases of division may be distinguished: (1) measure- ment, or that in which a number, the multiplicand, is repeated in a number of the same sort, the product, and in which the problem is to find how many times, the multiplier; (2) partition, or that in which the number of times is given, and the problem is to find the multi- 348 METHODS IN EDUCATION plicand. The first case is like physical measurement and hence the name. In the second case, partition, if the operations were to be performed actually instead of symbolically it would be seen to be measurement after all. Distrib- ute 52 cards to four people and find size of each pile. The problem is of course to find one-fourth of 52, i.e., partition, but the method is to deal a card to each of the four people and then determine how many times this process of dealing out four cards from the 52 can be repeated, which process is evidently measurement. Hence, McLellan and Dewey contend very strenuously that there is no such thing in arithmetic as partition. (Psychology of Number, page 123.) 680. Short division. — Short division is only the in- verse of the combinations in multiplication. Long division. — Long division by decomposition (distributive law). 684 2=? 600^ -2 = 300 80- -2 = 40 4- -2 = 2 684- 1-2 = 342 ans. Other forms. 342 2)684(342 6 8 • 2)684 6 8 8 4 8 4 4 4 A more difficult example. ARITHMETIC 349 We say 674 = 6 hundreds, 7 tens, 4 units. 2)674(337 6 hundreds -f- 2 = 3 hundreds. Bring down 6 7 tens; 7 tens -r- 2 = 3 tens and 1 ten re- 7 maining. 1 ten and 4 units = 14 units; 14 g units -i- 2 = 7 units. The quotient is 3 hun- ^ dreds, 3 tens, 7 units, or 337. ^^ 681. Division by factors (associative law). 3864 -^ 24 = ? 4 )3864 6)966 161 ans. 682. Laws or principles of division. 1. Dividing a number by one of its factors gives the other factor. 2. When the divisor is an abstract number, the quotient and the dividend are Uke numbers. 3. When the dividend and the divisor are hke num- bers, the quotient is abstract. 683. Proof of division. — To prove division, multiply quotient and divisor to reproduce dividend. 684. Grube method : characteristics, advantages. — The leading characteristic of this method is that it tries to teach the four fundamental processes with each num- ber before the next number is taken up. It is an appli- cation of the old idea of teaching in ^'concentric circles.'' Advantages claimed: simplicity and thoroughness. . 685. Objections to the Grube method. 1. A unit not a fixed thing. The natural beginning of number is a whole — needing measurement, while Grube says that one thing is the natural beginning. 350 METHODS IN EDUCATION 2. Different processes are not equally difficult. 3. Free range among higher numbers excluded. 4. Synthetic only; memory drill. These four objections are from McLellan and Dewey. The following are from Smith, page 91 : 1. It carries objective illustration to an extreme, studying numbers by the aid of objects for three years, until 100 is reached. 2. It attempts to master each number before taking up the next, as if it were a matter of importance to know the factors of 51 before the child knows anything of 75, or as if it were possible to keep children studying 4 when the majority know something of 8 before they enter school. 3. It attempts to treat the four processes simultane- ously, as if they were of equal importance or of equal difficulty, which they are not. 686. Speer method. — This is an attempt to teach concretely that ratio is number. Judgments of relative magnitude are secured by using the type forms — cubes, prisms, etc. — in getting the concept of number. Criti- cism: Not a direct use of materials in daily life; from complex to simple. It should be noted, however, that this method recognizes the acceptable ratio idea of num- ber and attempts to introduce the ratio idea earlier than has been the case. Smith seems to favor this earlier introduction (page 105). 687. Graphic methods. — Graphic methods include all objective ways of aiding visualization, such as writing, drawing, pictures, cubes, etc. Technically, a graph is a line representing variations of temperature, price, population, class standings, etc. Illustration. Add J and |. ARITHMETIC 351 1^3 2 6 2~^3 6 6* Properties of Number for Primary Grades 688. Extent of work. — Certain properties of number are easily grasped by children of the earlier grades and may be profitably taught to them. The distinctions of odd and even numbers, and of prime and composite numbers, and the tests of divisibility by 2, 3, and 5, are of this class. Also definitions of factor, product, power, root. 689. Odd and even. — Study the numbers / // /// ////, etc. Which of them are capable of being grouped in pairs? Such are even, the rest are odd. What is the appropriateness of the names? 690. Prime and composite. — Represent the several numbers by scoring, as in the preceding section. Some of them, as 1, 2, 3, 5, 7, cannot be divided in any way into equal groups, but 4 (// //) may be divided into two groups of two each, 6 (/// ///) or (// // //) into two groups of three or three groups of two, 9 (/// /// ///) into three groups of three. Those of the first class we call prime, those of the second, composite numbers. What is the appropriateness of the names? 352 METHODS IN EDUCATION 691. Divisibility. — State how to tell without dividing whether 2 will be exactly contained in a number? The answer is contained in the definition of even number as given in section 689. As it happens, these numbers always end in 2, 4, 6, 8, or 0. Study the multiplication table of 5's and, noticing how the numbers all end, frame a statement telling what numbers are divisible by five. Verify. Study the numbers 10, 11, 12, 13, 14, 15, 16, 17, 18. Which are divisible by 3. Is it also true that the sum of the digits of those numbers is divisible by 3? What is true in this respect of the other numbers? Make a general statement summarizing the observations. Verify. Properties of Number for Higher Grades 692. Induction and deduction. — The examples in the preceding section illustrate the application of the induc- tive method to the discovery of the principles of arith- metic, and at the same time show that the formal steps of instruction are simply the steps in inductive reason- ing. It is well established that in the earlier years, at least, the principles of arithmetic should be arrived at inductively. But on the other hand, arithmetic {i.e., the science or theory of number) may be treated as a purely deductive science, and in the later grades it is well to give the children some notion of that truth. Properties of number is a topic well adapted for that purpose. 693. Commutative, associative, and distributive laws. — See section 673. 694. Other general properties. 1. If a number is contained exactly in two numbers, it is contained exactly in their sum or difference. ARITHMETIC 353 This law is probably as nearly axiomatic as any law can be. The following will illustrate the necessary char- acter of its truth: a h c b-\- c If a is exactly contained in h and also in c it is evidently exactly in 5 + c. » 2. If a number is exactly contained in another it is exactly contained in any multiple of that other number. This is a corollary of number 1. 3. If a number exactly contains two numbers, prime to each other, it contains their product. If 24 contains 3 and 4, it contains 12. This rule is a corollary of the associative law of mul- tiplication; because if 24 contains 3 and 4 and some other factor a, then 24 = 3 X 4 X a. Therefore 24 = (3 X 4)a by associative law. These laws are general because they are true of num- bers as such, while the tests of divisibility are true only for our particular system of notation. The whole body of principles of number may, moreover, be derived deductively from these general properties as geometry is derived from a few axioms and definitions. 695. References. — For more exhaustive treatment of the properties of number, see Chrystal's Algebra Part II, Chapter 35; any approved college algebra; Encyclopedia Brit., Theory of Numbers. 696. Application : tests of divisibility. — The tests of divisibility illustrate the application of the laws of properties of number as expressed in our decimal nota- tion. A number is divisible By 2, if it ends in 0, 2, 4, 6, 8. 354 METHODS IN EDUCATION By 3, if the sum of its digits is divisible by 3. By 4, if the number represented by the two digits at the right is divisible by four. By 5, if it ends in or 5. By 6, if divisible by 2 and by 3. By 8, if the number represented by the three digits at the right is divisible by 8. By 9, if the sum of its digits is divisible by 9. By 10, if it ends in 0. By 12, if it divisible by 3 and by 4. By 7 and 11, actual division test. 697. Types of demonstration. — We may, as stated before, satisfy ourselves of the truth of these proposi- tions by inductive study, but deductive demonstration is more satisfactory to the mature mind, because it not only satisfies us of the truth of the proposition but shows that the truth is a necessary logical consequence of more fundamental truths. For example, take tests of divisibihty by 3 and 12. 698. Test by 3. — Let a, h, c, d, and e represent the digits of the number and assume that the sum of the digits a+6+c+ 5 , T- 716. Addition. — Recall that only like numbers can be added. 2 bu. + 8 bu. = 10 bu. To add | and |, change so that pupils will see 4 eights + 6 eights = 10 eights. Thus f + I = V-. Addition is well presented in most of the text-books. For further exercises, con- sult any approved text. 717. Subtraction. — No new operations or principles here. Apply common denominator again. 718. Multiplication : fraction by integer. — This oper- ation appears easy. Take multiplication of fraction by whole number first. Proceed as follows: $7X5= $35. 7 dollars X 5 = 35 dollars 7 tenths X 8 = 56 tenths - ^^ tenths To X 8 = yo Explanation by Bailey This abstract is taken from an address by L. H. Bailey, New York Training School for Teachers, h} N. E. A. Report for 1905, page 383. *' Let us illustrate by teaching the multiplication of a fraction by an integer. Preparation consists of making sure that the learner has in mind the knowledge through which the discovery of the general principle is to be ARITHMETIC 367 made. What does 8 denote? What does the denom- inator denote? What does the numerator denote? Presentation consists in selecting an example and in finding a method of performing the operation. This may be done objectively or abstractly. We will choose the former. Let us take f X 2. We will draw a circle, separate it into eight equal parts, and shade three of them to represent f . Multiplying f by 2 we obtain six of these parts, or |. To multiply | by 2, we multiply the numerator. Comparison consists in showing that every other example in the multiplication of a fraction by an integer is exactly similar to f X 2 in all respects essential to the demonstration. This is true because multiplying the numerator of every fraction by an integer will multiply the number of equal parts that are taken without affecting the size of the parts. Gen- eralization consists in stating the general principle. To multiply a fraction by an integer, multiply the numer- ator. Application consists in following this general principle in the solution of individual examples. Mul- tiply T3 by 9. /s X 9 is an example in the multiplica- tion of a fraction by an integer; to multiply a fraction by an integer, multiply the numerator; to multiply ts by 9, multiply the numerator." 719. Multiplication : fraction by fraction. — The next work is to multiply a fraction by a fraction. Develop- ment may be as follows: '^Xi= ? )f X 1 = Si '4 /\ J- "«^4 S3 01 4 = S4 2 X } = $1 or $i ans. In the second step we have used 1 as a multipher (process understood from last paragraph). With a mul- 368 METHODS IN EDUCATION tiplier | as large, the product is, J of $f or $J. Using f instead of J as multiplier, the product is twice as large; hence, 2 times $i or $|. The same result may be secured in a shorter process by multiplying the numerators for a new numerator and the denominators for a new denominator. Continued multiphcation is a larger appHcation. Use cancellation to review divisors, and reduction to lower terms. Emphasize cancellation as a short, practical process. ^v/ i5\/ 9 v 35 — 9 ^ /\ 44 /\ To /\ T 8 — • Note. — Concerning multiplication of a fraction by a fraction it might be pointed out that strictly speaking the expression involves contradiction of terms. Multiplication means manifold- ing or repeating. The multiplier specifies the number of times. But when the multiplier is a fraction, the number of times is not all of one time, but only part of a time, and the idea of repetition vanishes. I X f, read | times f, strictly speaking, therefore, is nonsense and it means and can only mean ^ of f . But inasmuch as it is convenient to speak of the process as multiplication and inas- much as in any case the world will continue to speak of it as multiplication, this is the point at which a somewhat broader definition of multiplication should be introduced; namely, finding a number that is related to the multiplicand as the multiplier is related to unity. Graphic Illustration of Multiplication f X f Let rectangle AB represent 1. Then A I \ — AC will represent f . Then, dividing alti- tude into fourths, and drawing lines through points of division parallel to base, the whole unit A B will be divided '^ ^into 20 equal parts and A D, which is f of f , is 2% of the whole unit. The rule for multiplication may now be made by — — D — ARITHMETIC 369 inspecting the terms" of product and factors and noticing their relation to each other. Then verification and application complete the work. This inductive pro- cedure does not answer the question, Why should the numerator of the product be the product of the numer- ators of the factors? But the inductive method never does answer that question (see section 697) and insistence on the question why, with reference to such rules, means insistence that arithmetic must be made a deductive science throughout. 720. Faulty arrangement. Find cost of 3J yards at $2J a yard. This statement of the operation does not give mathe- matical truth. It says $2J = $8J. Economy of time and brevity of form are not advantages here. Arrange the work in steps. 3 J yards = -3^- yards $5. \/ 1 — ©50 — Too? TOO' 100- A caution should be observed against the use of large numbers in complex fractions. Such fractions are use- less if they go beyond the demands of ordinary business hfe. 4. Aliquot parts; as 16? _ 1 334 = 1 ITU 6 J TOO 3- ARITHMETIC 381 A chart showing the equivalent ahquot parts should hang in every class-room. 12i TOO = 1 8 = 100/0 .125 25_ Too = 1 4 = 25 % = .25 37i Too = 3 8 = 37i% = .375 T%% = 1 2 = 50 % = .50 62i TOO = 5 8 = 62J/0 = .625 tVo = 3 4 = 75% = .75 8 7* To5 = 7 8 = 87i% = .875 1 en Too = 1 6 = 161% = .16! 33J 100 = 1 3 = 33|/o ~ .331 66§ TOO = 2 3 = 661% = .661 83^ TOO = 5 6 = 83§% = .83J 20_ TOO = 1 5 = 20% = .20 _4 0_ 100 = 2 5 = 40% = .40 T%% = f = 60% = .60 l%% = 4 5 = 80% = .80 Other ahquot parts may be used and other arrange- ments on the chart may be preferred. The given plan emphasizes the grouping of the aliquot parts as common fractions in their simplest form as given in the second column. Pupils should memorize this chart. 737. Method of decimal fractions. — The table of ahquot parts may be used as a table of equivalents also. Then the apphcations of decimal fractions in percentage are matters of substituting the equivalent decimal for the common fraction. The interpretation of the prob- lem brings nothing new; the operation itself is the same; and the regular principles of decimals are adequate. 738. The method of the equation. 1. This is a vahd use of algebra to simphfy relations and processes in arithmetic. The early work in arith- 382 METHODS IN EDUCATION metic has made pupils familiar with such examples as these: 6 X ? = 48? 7 X ? = 63? 11 X $? = S132? 2. The next step is to see that pupils understand that per cent means hundredths, hundredth, or of a hundredth; as 6 per cent means 6 hundredths. 1 per cent means 1 hundredth. I per cent means | of a hundredth. 3. The third step in teaching the equation is to im- press again the meaning of the symbols yf o, .06, and 6%. The table of equivalents should show that all three forms mean the same. 4. A fourth step is a review of the decimal method in percentage. These preparatory steps are really a review of all the work in percentage. Then the pupils are ready for the equation. 6x?= 30? 6 times what number = 30 ? Qx = 30. By algebra. If Qx = 30, what is the value of x? If ^x = 30, what is the value of re? If Jx = 30, what is the value of x? If j^x = 30, what is the value of x? If .5a; = 30, what is the value of x? If 0.05x = 30, what is the value of x? If 0.005a; = 30, what is the value of x? 5. Application. $12 is 4% of how many dollars? $13 is 4^% of how many dollars? 20 miles is 5% of how many miles? ARITHMETIC 383 6. Form. 0.04a: = $12 0.04ir = $13 0.05a; = 20 miles. 7. An example solved. // an automobile is sold for $1025 at a profit of 25%, how much did it cost? Let X = cost .25a: or \x = gain X + .25a; = $1025, selling price. 1.25a; = $1025 X = $820, cost. Siriiple Interest 739. Terms used. 1. The sum of money on which interest is paid is the principal. 2. The per cent, of the principal paid for the use of the principal for one year is the rate. 3. The money paid for the use of the principal for the entire time is the interest. 4. The interest added to the principal is the amount. 740. Methods. 1. When the time is an exact number of years and months, find interest for one year and multiply this by the number of years. 2. Six per cent method. 3. Exact interest is interest obtained by considering 365 days as one year. 741. Faulty Arrangement. Avoid untrue statements like the following solution in finding the interest on $500 for four years at T^oo X $500 = $30 X 4 = $120. 384 METHODS IN EDUCATION Arrange the work in two steps. $500 X xf = $30 $30 X 4 = $120 ans. Miscellaneous Topics 742. Algebra used in arithmetic. — The close relation between arithmetic and algebra is no longer a matter of doubt. Nearly all the modern text-books on arith- metic have introduced the elements of algebra. The rule and its hmitations may be stated thus: Use algebra wherever its use will make the processes in arithmetic easier or clearer. 743. Ratio. — Relation in arithmetic is ratio. In- stead of waiting to reach this topic in the last part of arithmetic, it is advisable to use it all through arith- metic. Every analysis that directs attention to com- parative quantity uses ratio. Hence, the importance attached to unitary analysis, variable unit, common fractions, and equations. 744. Short processes and business methods. — Mod- ern usage favors the introduction of short processes whenever they are of such a nature that the child can readily comprehend their practical value. For instance, in multiplying by 10 or any multiple of 10 the addition of the number of ciphers found in the multipher is a direct way to the product; in dividing by 10 or any multiple of 10 pointing off to the left as many places as there are ciphers in the divisor; cancellation, factoring by inspection, the use of aliquot parts in common frac- tions and percentage and the contracted methods in interest and the other applications of percentage. Dr. Smith says that the teacher who fails to keep in touch with the demands and methods of modern business is not ARITHMETIC 385 doing her duty toward herself or the class. In regard to business methods considerable discussion has arisen about how much commercial arithmetic should be introduced in the regular courses. This question brings in the phases of commercial discussion which cannot be treated fully here but suffice it to say that the text-book in use in the school may serve as a guide in the limitations in this matter. The following footnote, page 218 of the Young's The Tsacliing of Mathematics, is a good presentation of the demands of business. " An excellent idea of what the business world believes it has the right to expect from schools is given in Still's report to the N. E. A. 1900, digested from six hundred replies representing fifty-seven different occupations and lines of business. *' Mechanical Aids: — 1. Importance of decimal point in business. 2. Necessity for legible figures. 3. Accuracy and speed. 4. Use of interest and discount tables and graded schedules. 5. Use of cash registers and arithmometers. 6. Fractions hke f , it, il, etc., should receive scant attention. 7. Importance of ''short cuts." 8. Value of teaching multiplication table through 20 X 20. 9. Importance of familiarity with English money. 10. Business forms, such as checks, notes, receipts, statements, and price lists should be understood by all pupils of the seventh year and upward. 11. Constant repetition and drill in the use of the four fundamental processes. 386 METHODS IN EDUCATION 12. Processes of Solution. (In reply to question as to differences between processes of school work and outside world.) On the whole, no great differences. (In interest, the only case, find interest and amount: facility in the four fundamental processes and approx- imate estimates important.) " 745. Unitary analysis. — This kind of analysis goes back to one common unit of measure. The fixed unit one is the basis. Illustration. Six books cost S9; find cost of eleven books at the same rate. $9 = cost of 6 books $9-^6= Hi, cost of one book. Hi X 11 = $16.50, cost of 11 books. The other important method of solving problems is the equation. 746. Variable unit. — In contrast to the fixed unit one, we have the variable unit. When a convenient ratio exists between the two quantities in the problem, it is convenient to use that ratio instead of going back to the cost of one. Illustration. Six books cost $9; find cost of thirty- six books. $9 = cost of 6 books. Ratio of 6 books to 36 books is 6. Hence, $54 = cost of 36 books. The unit of comparison happens to be 6, but it might be any other number. Note that this device does not apply to the problem in 745; there is no integral ratio between 6 and 11. 747. Series. — Grube and others have used the series of combinations for abstract and concrete drill. Illus- tration of series in building number 7: ARITHMETIC 387 6+1=7 1+6=7 2+2+2+1=7 5+2=7 2+5=7 3+3+1=7 4+3=7 3+4=7 748. Arithmetical complement. — The difference be- tween any number and the next higher power of 10 is the arithmetical complement of that number. 3 is the complement of 7, since 7 + 3 = 10. 32 is the complement of 68, since 68 + 32 = 100. 135 is the complement of 865, since 865 + 135 = 1000. 0.26 is the complement of 0.74, since 0.74 + 0.26 = 1. 749. Problems. — " Problems include all the examples in arithmetic in which the operations are not directly stated. They are divided into simple, involving only one operation, and complex, involving more than one operation. The solution of these problems is always made through a form of reasoning called traduction." 750. Proof, verification, or checking. — The proof of correct solution may be answers in the book, the teacher's decision, a second solution in the same way or in another way. Verification of a few problems is worth more than the solution of many additional problems without veri- fication or proof. Some kinds of proof have been men- tioned. Here we add that of casting out 9's. This is useful but it fails to detect such errors as the addition of 9, the interchange of digits, and all errors not affecting the sum of the digits. Casting out 9's to Check Addition 751. Rule. — The excess of any number over a mul- tiple of 9 is equal to the excess of the sum of its digits over a multiple of 9. 745 = 9(82) + 7 Excess 7. 7+4+5=9X1+7 Excess 7. 388 METHODS IN EDUCATION The proof is practically identical with that given for test of divisibility by 3. a+ 6+ c-\- d-{- e = sum of digits, a + 10 6 + 100 c + 1000 d + etc .= the number. 9 6+ 99 c + 999 d + etc.=^ multiple of 9. a+ 6+ c+ d-\- etc. by subtracting. This signifies that a number is equal to the sum of its digits plus a multiple of 9. Hence throw out all the 9's from the sum of the digits and the remainder is the same as though the 9's were thrown out from the number itself. Now take the several examples, throw out the 9's from the sum of the digits, and according to the rule we infer that 56342 = a multiple of 9+2. 64723 = another multiple of 9+4. 57849 = a third multiple of 9+6. 23454= a fourth multiple of 9+0. 202368 = a fifth multiple of 9 + 12. The sum of several multiples of 9 must itself be a mul- tiple of 9. If a number is contained in each of several numbers it is contained in their sum. If equals are added to equals, the sums are equal. But a fifth multiple of 9 + 12 = a sixth multiple of 9 + 3, and we perceive (casting out 9's from sum of digits) that 202368 = a multiple of 9+3. But it is impossible that the same number shall at same time be equal to two different multiples of 9+3. Therefore the work is probably correct. Text- Books in Arithmetic 752. Guiding principles. — Arithmetic is no excep- tion to the two pedagogical principles governing the ARITHMETIC 389 selection and use of subject-matter. The sociological principle requires matter to be such as will appeal to present and future interests of the community; and the psychological principle requires adaptation to the spiritual capacities. The former determines the nature of the problems; the latter decides arrangement of book and method of teaching. 753. Elimination of subject-matter. — The modern text-books are leaving out a large number of the topics treated in the older books. This view is looking to the practical value of what is learned in mathematics rather than to the disciplinary value of the study. Young argues for simphfication and suggests, on page 220, the elimination of the following: 1. G. C. D. or L. C. M. of large numbers otherwise than by factoring. 2. Fractions with large or unusual denominators. 3. Compound or complex fractions. 4. All measures not actually in use in the community at large. 5. Reductions of decimals to common fractions and decimals beyond thousandths. 6. Circulating decimals. 7. Square root and cube root except by factoring. 8. Profit and loss as a separate subject. 9. True discount. 10. Partial payments. 11. Equation of payments. 12. Partnership. 13. Compound proportion. 14. Compound interest. 15. Business forms which do not conform to the usage of the day. 390 METHODS IN EDUCATION 16. Large numbers and exercises involving many numbers. 17. The premature introduction of difficult matter. 754. Content of the problems. — The elimination of matter implies a very close observance of child psychol- ogy and business demands. What, then, should be the bearing or nature of the problems? The answer is that the problems should conform to the spirit and content of American life. It is argued that the content taken from geography, history, science, and industrial life is likely to divert attention from the process, but this argument falsely assumes that the teacher is only a passive agent. Such content is a basis for interest that readily permits transition to drill that assures mastery of the processes. '' Every usable arithmetic has always been an encyclopedia," says Smith; ''what we have to determine is whether it shall now be an encyclopedia of vital, modern facts, or one of obsolete, dull, useless information." (Monograph, 1909, page 16.) Young takes a similar view as he discusses the source of problems in the quantitative side of nature, pages 209 to 214. Compare sections 649, 749, and 763. 755. Types of books. — The arrangement of material is the second characteristic of modern books, the first characteristic being the nature of the problems. The old books treated each topic exhaustively, and the com- pletion of the book implied the mastery of the subject. The other extreme is a different book for every grade, the eight books constituting an elementary series. Be- tween these extremes, we find several three-book series. The lack of uniformity in grading and courses of study does not encourage the effort to produce one series of arithmetics to satisfy American schools. ARITHMETIC 391 Three types of books may be mentioned. 1. Topical. This arrangement is the old type modi- fied by ehmination or other means of adjustment. In presenting a complete treatment of common fractions, for instance, the teacher can use her judgment about the quantity of material to be used, the order, the assign- ment to groups, the drill, etc. The ambitious pupils can go on by themselves, irrespective of class or grade limitations, because they and the teacher feel the stimu- lus of definite, unified, and complete presentation of the work. The topical arrangement is a compliment to the tactful judgment of the teacher and a source of joyous, invigorating responsibility to the child. 2. Concessive or Adapted. This type of book em- bodies the best according to writers of books, and at the same time arranges the matter to suit the average demands of several leading courses of study. It is eclectic in trying to choose desirable material, con- cessive in trying to suit those who make courses of study, praiseworthy in trying to bring about uni- formity, and hopeful in contributing to an American ideal. It may be largely topical, largely spiral, or sanely composite. 3. Spiral. This type is the extreme reaction against the old topical books. It is based upon that view of psychology which figuratively uses concentric circles to represent the child's thought from year to year. ''It consists," says Smith on page 119, ''in taking the class around a circle, say with the topics of common fractions, decimal fractions, greatest common divisor, and square root; then swinging around again on a broader spiral, taking the same topics, but with more difficult problems; then again, and so on until the subjects are sufficiently 392 METHODS IN EDUCATION mastered." But it is a mistake to assume that the nor- mal child's progress can be arbitrarily limited in that way. The same mistake is observed in the Grube method. There is a deadening effect on the pupils on account of the fragmentary treatment, rigid gradation, and the inhibition of initiative that would otherwise take certain pupils far ahead of their less industrious companions. It is encouraging to know that this type of book is passing into the second type. New York City Point of View 756. Suggestions. — The sections 757 to 766 inclusive are from the Course of Study, and the subsequent sec- tions are based upon the course of study. While this information is helpful for all students, it is used here especially for those who are required to know it. 757. General directions. 1. Much oral drill and blackboard work should be given. 2. Answers should be tested approximately to ascer- tain whether they are probably correct. 3. The results of addition, subtraction, multiplica- tion, and division should be proved before they are declared. 4. Excessive repetitions of forms of analysis and elab- orate written explanations should not be required. 5. Definitions should not be required until the mean- ings of the terms to be defined are fully understood. 758. The combinations. — Special importance is at- tached to the thorough mastery of the combinations in addition, subtraction, multiplication, and division. The following are the steps which should be followed in learning the combinations of each table: ARITHMETIC 393 759. Addition and multiplication. 1. Care should be taken that the pupils apprehend the nature of the required operations. 2. The combinations that have been taught in the preceding grade should be reviewed frequently. 3. The results of the new combinations should be determined in addition by counting objects, and in multiplication by adding the multiplicand as many timgs as there are units in the multiplier. 4. The entire table should be repeated with the objects in view in addition, and with the addends in view in multiplication. 5. The entire table should be repeated without the objects or addends in view. 6. The results of combinations, miscellaneously pre- sented, should be given without the aid of any form of mnemonics or external devices. If a pupil misses a combination, there are two methods of correction: in addition he may be told to count objects, and in mul- tiplication to add numbers; or he may be required to deduce the result of the combination in question from the nearest combination whose result he knows. (Thus he may ascertain that 6 X 7 = 42 from 5 X 7 = 35, since 6 sevens are one seven more than 5 sevens.) The former method is objectionable for two reasons: the performance of an isolated example will be of little value to aid association the next time the combination occurs; and the pupil is in danger of forming the habit of using his fingers as counters. The value of the refer- ence to the nearest known combination consists in the association of the combination in its proper relations with the other terms of a series. 7. Exercises in finding the parts which constitute a 394 METHODS IN EDUCATION number either as addends or as factors should follow the drills on tables. 8. The combinations should be applied in the solu- tion of simple problems. 760. Subtraction and division. 1. Each combination in subtraction and in division should be related to its corresponding combination in addition or in multiplication. In subtraction the minu- end is the sum and the subtrahend is one of the terms of a combination in addition; in division the dividend is the product and the divisor is one of the terms of a combination in multiplication. 2. The results should be stated without the relation, in order that they may be given instantly. An error should be corrected by reference to the primary com- bination. 3. The combinations should be applied in the solu- tion of simple problems, in order that their mastery may be seen to be a means to an end. 761. Constructive and inventional exercises. — Aside from the consideration of their educational value, the constructive and inventional exercises of the seventh year have been selected with a twofold purpose in view : 1. To furnish pupils with a knowledge of the essential elementary principles involved in the work in mensura- tion in grade 8A. 2, To furnish pupils with a knowledge of the con- structive principles employed in mechanical drawing and construction and in shop work. The method of teaching these exercises should be suggestive in form and spirit. Formal demonstrations should never be required. ARITHMETIC 395 762. Problems. — Numerical relations may be found wherever the mind seeks them; hence problems may be derived and should be derived from the life of the home, the school, the farm, the laboratory, the factory, and the railroad, as well as from the shop and the bank. The limitation of problems to transactions in dollars and cents tends to give practical arithmetic a purely formal and disciplinary character; on the other hand, excursions inta other fields of human activity, while sacrificing nothing of the disciplinary value of the subject, give it a varied and interesting content. Problems may be classified as simple, or those involving only one opera- tion, and as complex, or those involving more than one operation. 763. What to look for in the solution of problems. — The solution of problems should be effected by the dis- covery of what is given, what is required, and what is the relation between these terms. If difficulty is experi- enced in the determination of the relations between large numbers, small numbers should be substituted. 764. Analysis in solution. — A brief and well expressed form of analysis should be employed in the solution of problems to find a part of a number, to find a number when a part is given, to find what part one number is of another, and to find a number when the number plus or minus a part is given, whether common fractions, decimals, or per cent expressions are involved. 765. Rote work criticised. — The mere manipulation of numbers in a set order, which the pupils accept on authority as the means to a correct answer without comprehending the reason therefor, is a form of rote work that ought not to be tolerated except in the teach- ing of involved and difficult processes to young children 396 METHODS IN EDUCATION as, for example, the process of long division, or the Euclid- ean process of finding the greatest common divisor. 766. Progressive advance in difficulties by grades. — The following tabulation shows the progressive ad- vance in the complexity of problems through the grades: lA. — Simple problems solved without formal ex- planations. The children represent the terms by objects and find the results by counting; no term is greater than 10. These involve: 1. Addition and subtraction. 2. Multiplication and division. IB and 2 A. — Simple problems solved without formal explanations. The children apply the combinations in addition and subtraction as soon as they have mastered them; no term greater than 20. These involve: 1. Addition and subtraction. The problems are similar to those in 1 A, but the results are found from a knowledge of the combinations involved. 2. Multiplication and division. The problems are similar to those in lA. Problems in multiplication are solved by writing the multiplicand as many times as there are units in the multipher, and by adding. Problems in division are solved as in lA by counting. 2B and 3A. — Simple problems solved without formal explanations. The children apply the combinations in multiplication and division as soon as they have mastered them. These involve : 1. Addition and subtraction. The problems involve larger terms than in the pre- ARITHMETIC 397 ceding grades, and the results are invariably found by aid of the combinations. 2. Multiplication and division. The problems are similar to those in 1 A, but the results are found from a knowledge of the combinations involved. 3B. — Complex problems solved without formal ex- planations. These involve: 1. Finding a fractional part of a number. 2.» Two operations — relations direct. 4A. — Complex problems solved by analysis. These involve : 1. Finding a number when a fractional part of it is given. 2. More than one operation — relations direct. The problems are similar to those in 3B, but are explained formally by analysis. 4B. — Complex problems solved by analysis. These involve : 1. Finding what fractional part one number is of another. 2. More than one operation — relations indirect. 5A. — Complex problems solved by analysis. These involve : 1. Finding a fractional part of a number. 2. Finding a number when a fractional part is given. 3. Finding what fractional part one number is of another. 4. Other problems usually given under the head of common fractions. 5B. — Complex problems solved by analysis. These involve : 1. Finding a decimal part of a number. 2. Finding a number when a decimal part is given. 398 METHODS IN EDUCATION 3. Finding what decimal part one number is of another. 4. Finding a number when the number plus or minus a fractional or a decimal part is given. 5. Other problems usually given under the head of decimals. 6 A and 6B. — Complex problems solved by analysis. These involve in 6A: 1. Finding a per cent part of a number. 2. Finding a number when a per cent part is given. 3. Finding what per cent part one number is of another. 4. Finding a number when the number plus or minus a per cent part is given. 5. The problems usually given under the head of denominate numbers. These involve in 6B: 1. The first four subdivisions of 6 A as appHed in business. Each should be related to the corresponding problem in which a common fraction instead of a per cent expression is involved. 7A. — Complex problems solved by analysis. These involve : 1. Simple interest — direct case. 2. Metric system. 3. Foreign money. 4. Longitude and time. 5. Common relations. 7B. — Complex problems solved both by analysis and by algebra. These involve: 1. Simple interest — indirect cases. 2. Simple interest — applications. ARITHMETIC 399 3. Percentage — indirect cases. 4. Problems solved by proportion. 5. Common relations. 8A. — Complex problems solved by analysis or by algebra. These involve: 1. Mensuration. 2. Business relations. 3. Common relations easily expressed by two un- known quantities. 767. Problems illustrating progressive order of diffi- culties. — This section gives illustrative examples and problems that may be used to overcome difficulties in the order in which those difficulties arise. Suhtradion 1. 8—5. Inverse of addition. 2. 14 — 9. Inverse of addition; borrowing. 3. 24 — 9. Borrowing units. 4. 213 — 38. Borrowing units and tens. 5. 304 — 126. Zero and borrowing hundreds. Multiplication 1. 297 X 135. No zero used. 2. 297 X 130. Zero in the units column. 3. 297 X 103. Zero in the tens column. Division 1. 786 -^ 265. No zero in divisor. 2. 786 -^ 205. Zero in tens column, 3. 780 -V- 250. Zero in units column. 400 METHODS IN EDUCATION 1. f + 1 + 2 6 2 7 7 Addition and Subtraction of Fractions Denominators the same. -7 n- T 3. i+f+^ 4. *-'• 8 n^ 3 T^ 5 7 __ 3 '8 ^ 4 18 12 3 1 "8 4 One denominator is common denom- inator. ^ , ^ J Miscellaneous denominators. D. 7. Bought 3| lbs. Ceylon tea, 2f lbs. of Japan tea, and 5f lbs. Canton tea. How many lbs. in all? 8. A merchant bought 28| bu. potatoes. He bought 7| bu. from A, 13f bu. from B, and the remainder from C. How many bu. did C sell? 9. Fred walked 121 miles, Luke 13i^o miles, and Walter 4f miles. How far did the three boys walk? Subtraction of Mixed Numbers 1. 12| — 5f . Same denominators. 2. 12| — 5f . 8 = common denominator. 3. 12f — 5|. Same denominators; borrowing. 4. 12| — 5f. Different denominators; borrowing. 5. 12^1 "~ 5xT. Denominators difficult. Multiplication of Fractions 1. f of $16. Familiar operation. 2. f X 12. Fraction by integer. 3. 12 X f. Integer by fraction. 4. f X |. Fraction by fraction. 5. At $f a yard, what is cost of 75 yds.? 6. Find cost of 10 tons of coal at $6f a ton. 7. Find cost of f can of molasses at $| a can. 8. If land is worth $40J an acre, what is the value of a farm of 12i acres? ARITHMETIC 401 Division of Fractions 1. f -i- 3. Numerator divided. 2. f -i- 3. Denominator multiplied. 3. 12 ^ I See section 724. 4 3 _:_ 1 5. 6J ^ 2. 6. 6i ^ 2i. 7. A woman exchanged 30 lbs. of butter at $.25 per lb. -for cloth costing $.37§ a yard. How many yards did she get? Division of Decimals Addition, subtraction, and multiphcation of decimals do not involve many difficulties. Following is an order for division: 1. 638.724 -^ 12. 2. 63872^ .12. 3. 638.72 ^ .012. 4. At 5J cents per lb., how much sugar can be bought for $4.40? 768. Methods applied in New York City. — This sug- gestive work is more specific than what precedes in the chapter on arithmetic. Addition 769. Grade lA. — Combinations of numbers of one order with 1 and 2. 1 2 9 1 1 1 1 1 1 to 1; also 2 3 4 to 9 2 3 10 3 4 5 10 234 9 222 2 2 2 2 to ^ also 3 4 5 to 9 456 IT 567 11 402 METHODS IN EDUCATION These combinations are taught by counting objects; later the value of each is recognized at sight, without counting, and memorized. No written addition in this grade. 770. Grade IB. — New combinations. 3 4 9 3 3 3 3 3 3 to _3| also 4 5 6 to _9 6 7 12^ 7 8 9 12 4 5 6 9 4 4 4 4 4 4 4 to 4; also 5 6 7 to 9 8 9 10 13 9 10 11 13 Written addition: numbers of one order, numbers of two orders, within the tables, with no carrying. Use lA combinations at first. (1) (2) (3) 2 1 1 1 3 5 1 2 1 3 1 2 2 2 1 1 1 1 1 5 1 1 11 12 11 11 10 12 11 12 11 11 10 12 11 11 11 When teaching addition of two orders, designate units and tens columns. ARITHMETIC 403 Now use examples with IB combinations, no carrying. 13 43 31 23 11 11 3_ 2? 12 34 10 In column addition, not more than five numbers to be used, and no addend greater than four to be used. In this grade the signs + and = are used in tables. 771. Grade 2A. — The tables through 9's completed. 5 6 to 7 5 5 to 5 5 5 5 6 7 9 6 7 to 9 6 6 6 6 6 6 7 8 9 7 8 9 7 7 7 7 7 8 9 8 9 8 8 8 9 9 9 Written addition: numbers of two and three orders; in column addition, not more than five addends; addi- tion with carrying. Numbers of two orders. Here it is necessary to reach the fundamental fact that ten units make 1 ten. 26 34 13 33 26 7 1 31 76 404 METHODS IN EDUCATION \ Numbers of three orders; carrying units only. 231 713 416 134 j 138 149 etc. j ■j Numbers of three orders; carrying units and tens. i 314 347 I 486 ' 266 ' 121 143 etc. I 141 382 624 463 110 40 123 235 103 146 117 71 J 31 110 76 i Teach fact that ten tens make one hundred. In the 2B, the column addition is limited to 6 addends. 772. Grade 3 A. — Numbers of four orders; carrying into the thousands column. Special attention given to accuracy and rapidity. Subtraction 773. Grade lA. — Subtraction in this grade is taught objectively, and as the inverse of addition. 6+2=8 carries with it 6 +? = 8, and ? + 6 = 8 or 8 less 6 = ? 8 less 2 = ? 774. Grade IB. — Subtraction within the tables. 1-0=1 2-2=0 1-1=0 3-3 2-1=1 4-4 to 9-9 3-1=2 4-1=3 to 9-1=8 ARITHMETIC 405 Minus sign (— ) taught; vertical form taught. (1) 1 2 3 to 9 - 1 - 1 - 1 - 1 (2) 15 26 36 - 1 - 1 - 1 (3) 26 36 45 78 - 11 - 11 - 11 - 11 (4) 42 58 63 - 12 - 22 - 21 (5) 46 79 87 - 34 - 43 - 40 etc. 775. Grade 2A. — Subtraction within the tables. Written subtraction, without borrowing; numbers of two and three orders. 99 87 -78.-62 899 413 - 678 - 202 776. Grade 2B. — Subtraction with borrowing; two or three orders. Special attention given to proofs and accuracy. (1) 426 368 borrowing tens only. - 117 - 249 (2) 426 368 borrowing hundreds and - 137 — 276 tens. 406 METHODS IN EDUCATION (3) Use of zero and borrowing. 804 790 506 300 — 322 - 648 - 268 — 124 Methods used in subtraction: borrowing. 425 - 186 6 from 5 I cannot take; borrow 1 ten from the 2 tens, add to the 5 units, making 15 units. 8 tens from 1 ten I cannot take, so I borrow one 100 (or 10 tens) from 4 hundreds. 10 tens and 1 ten =11 tens 8 from 11 leaves 3 1 from 3 leaves 2 239 ans. Explanation by decomposition: 425= 4h. + 2t. + 5u. = 400+ 20+ 5 = 3 h. + 11 t. + 15 u. = 300 +110+15 _ 186 = - Ih. + 8t.+ 6u . = 100+ 80+6 1 h. + 3 t. + 9 u. = 200 + 30 + 9 Methods in subtraction: the tens method. 425 - 186 6 from 5 I cannot take, so I add 10. 6 from 15 = 9. When I add 10 to the minuend, I must add 10 to the subtrahend. (Principle of subtraction: If both minuend and subtrahend be equally increased, the difference will not be changed.) 9 from 2 I cannot take, so I add 100 to the minuend. 100 = 10 tens 9 from 12 = 3. ARITHMETIC 407 According to principle, add 100 to subtrahend. , 2 from 4=2 239 ans. Explanation by decomposition: 425 + 10 + 100 = 4 h. + 12 t. + 15 u. - 186 + 10 + 100 = 2h. + 9t. + 6u. 2 h. + 3 t. + 9 u. = 239 Methods in subtraction: German or complementary. 425 - 186 I cannot take 6 from 5, so I take 6 from 10 = 4. 5+4=9 When you say " from ten " in the units column, add 1 to the next subtrahend. (No reason given.) 9 from 2 I cannot take; 9 from 10 = 1; 2 and 1 are 3. Add 1 to next subtrahend; 2 from 4=2. Ans. 239. The advantage of this method is that subtraction facts through 10 only need to be learned. Methods in subtraction : Austrian or additive. — The process of finding what must be added to the subtrahend to produce the minuend. 425 - 186 6 and 9 are 15 " 8 ''3 'Ml first way. 1 '^ 2 '' 3 . Explanation : 425 = 400 + 20 + 5 = 300 + 110 + 15 186 = 100 + 80 + 6 = 100+ 80+6 200+ 30+9 408 METHODS IN EDUCATION and are 6+9 = 15' 9+3=12 second way. 2+2= 4 J Explanation. Add 10 to each, then 100. 425 = 400 + 20 + 5 = 400 + 120 + 186 = 100 + 80 + 6 = 200 + 90 + 15 6 200+ 30+ 9 Advantages. No subtraction tables need be learned. Addition facts being used so much more frequently than those of subtraction, there is an increase of speed and certainty. To prove subtraction, add subtrahend and remainder to produce minuend. 777. Grade 3A. — Numbers of four orders. 7314 8420 - 3247 - 6548 etc. 778. Grade 2B. tipliers 2, 3, 4, 5. Preparation. Presentation. lowing way: Multiplication — Multiplicands of two orders; mul- Counting by 2's, 3's, 4's, 5's (review). Develop multiphcation tables in fol- 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 etc. How many times have I written 1? Write 1 times 2=2. What is the symbol for times? X . 1 time. ARITHMETIC 409 Write it on board. How many times have I written 2? 2 times. 2X2=4 etc. When you have developed tables, ask children to write the work in vertical form. 2 2 2 2 2 2 0< 22< 3X fX _5_X 6X etc. After tables have been developed and written in ver- tieal form, write : 173 TO -u *11 Children say 2 X 11 = 22. 2X 22 Here is another way of doing it : II 11 2X1 unit = 2 units. 2 X Put 2 in units place. 22 2X1 ten= 2 tens. Put 2 in tens place. Have children notice that product is same. Order of difficulties: 24 23 30 52 2X 2X 2X 2X Multiplication involving carrying. Multipliers 2, 3, 4, 5. Preparation. Drill on multiplication tables. II 26 2X6 units = 12 units. 2X Put down 12. 12 2X2 tens = 4 tens. 4 Put 4 in tens place. 52 Add: 4 tens + 1 ten = 5 tens. 410 METHODS IN EDUCATION Shorter way: m 26 2X6 units = 12 units. 2 X 12 units = 1 ten and 2 units. 52 Put 2 in units place. 2X2 tens = 4 tens. 4 tens + 1. ten = 5 tens. Order of difficulty. Multipliers 2, 4, 5, 3. 779. Grade 3A. — Multiplication of numbers of three orders by numbers of one order. Order of difficulty: 113 124 345 6X 6X 6X 104 340 142 6X 6X 10 X 780. Grade 3B. — Multiplication of numbers of three orders by numbers of two orders. Preparation. 27 27 3X 10 X Review. Presentation. 13 is the same as 1 ten and 3 units. g'3 27 What shall we multiply by first? 13 X By 3. 81 3 what? 270 3 units. 351 Multiply. Now what is the next figure? 1. 1 what? 1 ten. ARITHMETIC 411 Multiply by 10 units. 270 units. What shall I do to get the product? Add. Why? Because we multiplied by 10 and 3, and that is the same as multiplying by 13. Let us take an easier way. Multiply by 3 units. fl g fl 27 Now- what is the next figure? 13 X 1. 81 1 what? 27 Iten. 351 1 ten X 7 = 7 tens. Where shall I put it? In the tens place. 1 ten X 2 tens (or 20) = 20 tens. 20 tens = 2 hundreds. Put 2 in hundreds place. Add. Have children notice that we omitted in units place. 127 107 470 13 X 13 X 26 X 381 321 2820 127 107 940 1651 1391 13220 412 METHODS IN EDUCATION Division 781. Grade 2B. — Short division , without remainders. Preparation. 2 2 2 ■ 2 2 2 2 2 2 2 etc. How many 2's in 2? 1. How many 2's in 4? 2. How many 2's in 6? 3. How many 2's in 8? 4. What is addition sign? +. What is subtraction sign? — . What is multipUcation sign? X. What is division sign? -i- . (If they do not know, tell it.) Presentation. Read from board, 2-^2. W^hat does this mean? It means to separate the first number (dividend) into groups of 2's, and tell how many there are. It means how many 2's in 2? 4 -v- 2 = ? What does this mean? It means to separate 4 into groups of 2's, and tell how many 2's in 4, etc., etc. I shall show another way to write a division example. 2J2~ 2)T~ 2JQ~~ Read: What does it mean? 10 12 2)'20" 2)24 Then teach inexact division. What does this mean? 2)5 It means separate 5 into groups of 2's. // // / How many 2's? 2 2's and 1 remaining. ARITHMETIC 413 2)7 2)9 2)11 2)13. etc. 782. Grade 3A. — Short division with remainders. 1 6 How many 2's in 3 tens? 2) tens units 1 and 1 remaining. 3 2 1 what? 1 ten. 1 ten = 10 units; 10 u. + 2 u. = 12 u.; how many 2's in 12? 6 2's in 12. Order of difficulty: 2)452 2)728 2)1608 2)1430 Divide by 3, 4, 5, 6, 7, 8, 9. 783. Grade 3B. — Long division. 1. How many 2's in 4? 2. 20)40 2. Then how many 20's in 40? 2. 3. Which number did you try first? 2. 1. How many 3's in 12? 4. 4 2. Then how many 30's in 120? 4. 30)120 3. Which number did you try first? 3. 1. How many 2's in 17? 8. 8 2. How many 20's in 170? 8. 20)170 3. Which number did you try first? 2. We call the number we try first the trial divisor. Presentation. I shall show you another way of writing this example. How many 2's in 17? 1. How many 20's in 170? 8. 20)170 2. Multiply 8 X 20 = 160. 160 = 8X 20 3. How much left? 10 4. Say nothing about remainder. 414 METHODS IN EDUCATION 21 1. Which number do we try first? 21)441 42 = 2 X 21 2. How many 2's in 4? 2. 21 3. How many 21's in 44 tens? 21 = 1 X 21 tens. 4. 5. Multiply. Left? 2 tens. 6. 2 tens = 20 u. 20 u. + 1 u. = 21 u. 7. How many 2's in 2 . 8. How many 21 s in 21? 9. Multiply. Class tell steps. 31 1. Try. 31)961 2. Divide. 93 3. Multiply. 31 4. Compare. 31 . 5. Subtract. First Step. 6. Compare. 7. Bring down. Second Step. When the divisor is contained in one or more of partial dividends fewer times than the trial divisor is contained in trial dividend. 43 35)1505 140 105 105 Third Step. When the divisor is contained in one < or more of partial dividends a greater number of times than trial divisor is contained in trial dividend. ARITHMETIC 415 93 19)1767 171 57 57 Fourth Step. When a zero occurs in quotient. 27 205 32)6587 64 187 160 27 References on this Chapter Smith, The Teaching of Mathematics, 1909, Teachers College Monograph. Smith, The Teaching of Elementary Mathematics, 1900, Macmillan. Young, The Teaching of Mathematics, 1907, Longmans. McLellan and Dewey, The Psychology of Number, 1908, Applet on. McMurry, Special Method in Arithmetic, 1908, Mac- millan. Jackson, The Educational Significance of Sixteenth Century Arithmetic, 1906. Conant, The Number Concept, 1896. Brooks, Philosophy of Arithmetic, 1902. Mary Louise Eastman, The Teaching of Primary Arithmetic, in McEvoy Magazine, May, June, Novem- ber, and December, 1910, and January, 1911. 416 METHODS IN EDUCATION Annie B. Conselyea, Devices in Arithmetic for Elemen- tary Grades, in McEvoy Magazine, December, 1910. McNair, Division of Decimals, in McEvoY Magazine, January and February, 1911. W. A. Cornish, Department of Mathematics, State Normal School, Cortland, N. Y., who personally directed the revision of the chapter on arithmetic for this edition. CHAPTER XVI QUESTIONS ON THE TEXT I. Comment on the meaning of education as defined by Butler. ' 2. Mention six subjects in an elementary course of study and classify each under the intellectual inheritances discussed by Butler. 3. Define and illustrate correlation, co-ordination, concentration, and enrichment as applied to a cur- riculum. 4. Explain and apply the culture epoch theory. 5. Define apperception. Illustrate its application in (a) first-year reading, (b) eighth-year arithmetic. 6. What is meant by a principle of education? Dis- tinguish principles of education and maxims of teaching. 7. Define habit. What are the three fundamental laws of habit? 8. What do you understand by interest in the educa- tional use? Show relation of attention and interest. 9. What is meant by a mental faculty? Mention the faculties in their natural order of development. 10. Show that habit includes all the aims of education. II. What are the advantages of opening exercises? Prove your answer by showing relation to habit. 12. What is implied in the term ''group teaching"? Advantages? 13. Outline affirmative and negative arguments on home study. 417 418 METHODS IN EDUCATION 14. Discuss examinations in regard to (a) purposes, (b) kinds, (c) marking. 15. Mention five suggestions to guide the moral instruction of pupils. 16. What is punishment? Classify kinds as approved and disapproved. 17. Give three objections to corporal punishment. Show bearing of inhibition by repression. 18. Give favorable and adverse criticisms of the Socratic method. Briefly discuss three other methods. 19. It is said that the inductive process of reasoning leads to the general notion. Explain meaning and formation of a general notion. In your answer show that the general notion utilizes sensation, perception, imagination, memory, judgment, and reasoning. 20. Explain and illustrate (a) apperceiving mass or group, (6) reaction in psychology, (c) artificial incentives. 21. Name five school virtues that should be substi- tuted respectively for five school vices, and explain your method of inhibiting by substitution. 22. What is your interpretation of the term general method? Show how it embodies the inductive-deductive method, method-whole, from particular to general, and from concrete to abstract. What is its relation to the apperceptive process? 23. State three causes of inaccuracy in spelling. 24. Make a list of ten words frequently misspelled, give reasons for difficulty in each word, and state specifi- cally how to teach pupils to observe and overcome such difficulties. * 25. How should homonyms be taught? 26. What uses of the dictionary can be taught in (a) primary grades, (6) grammar grades? QUESTIONS ON THE TEXT 419 27. Illustrate a practical way of teaching word- analysis by applying it to five words. 28. Outline five other ways of teaching the meaning of words. 29. (a) What is the meaning of dictation exercises? (6) What is the aim or purpose? (c) Describe faulty dictation exercises, (d) Illustrate appropriate dictation work for an intermediate grade. Make it correlate at least four subjects of instruction. 30. Types are bases of apperception. Explain; illus- trate a type in grammar, spelling, geography. 31. What are three uses of a model in composition? 32. What is the difference between criticism and correction of compositions, from the teacher's point of view? 33. Outline five plans of criticism, and then defend a composite plan. 34. Present a commendable plan of correcting com- positions after criticism. 35. What fundamental facts in grammar may be used in helping pupils acquire useful habits of mental activity? 36. What is the critical distinction between an attri- bute adjective and an adverb modifier? 37. Outline a lesson on adverb modifiers according to the Herbartian steps. 38. Cite the rules governing the use of shall and will. 39. Classify participles according to use. 40. Illustrate ten uses of infinitives. 41. What are the essential facts in a lesson on concord of relative pronoun and antecedent? 42. Justify the statement that the development lesson uniting words, phrases, and clauses is in accordance with the requirements of apperception. 420 METHODS IN EDUCATION 43. Select a definition of geography and defend your selection. 44. Using your home city as a type, you prepare a lesson-plan for a primary class. What topical headings do you use in your plan? 45. Outline a lesson on Alaska. What elements of prior knowledge can you utilize? Under habituation to formal outlines, what topics will a child expect to find in your outline? Quote section as authority. 46. Comparison in geography is a guaranty of mental economy. Explain, defend, or disprove. 47. Select three important subjects for lessons in geography, give reasons for your selections, and mention points of strength and weakness in the lessons as pre- sented in this book. 48. Express your approval or disapproval, with reasons on (a) the suggested way of studying a map, (6) the suggested way of studying the text. 49. State specifically how the teaching of geography helps in forming desirable habits for life. 50. How does instinctive imitation tend to strengthen character in primary history work? 51. Show that history and civics stimulate the spirit of patriotism in grammar grades. 52. Outhne a lesson in history to illustrate cause and effect. 53. Refer to five sections that suggest ways of making history real to elementary pupils. 54. Comment on (a) the use of note books, (b) the source method, (d) the means of correlation in teaching history and civics. 55. What conditions determine the selection of read- ing-matter in the first year? QUESTIONS ON THE TEXT 421 56. Contrast the old and the new types of books in reading. 57. (a) What four methods are combined in the Mc- Closkey method in reading? (b) Do you approve a combination method? Why? Is this method analytic- synthetic? Why? 58. Briefly characterize the Aldine method. 59. What physical and mental difficulties may be encountered in teaching reading? 60. Classify the difficulties found in ordinary selec- tions for reading, and tell how each difficulty should be removed. 61. Justify your way of helping pupils memorize a selection. 62. Select five important topics in reading, aside from the topics in the seven preceding sections, and give reason why each selection is important. 63. Prove that the habit of intelligent interpretation in reading is a source of success in all the other work in school. 64. Tell specifically what you do in teaching counting in the first grade. Show application of measuring. What would you measure and with what would you measure? 65. Explain the procedure in teaching division of decimals. What rule or principle results? 66. Give, in the order of difficulty, five examples you would use in teaching short division. 67. What is meant by a type in arithmetic? Name the five type examples in common fractions and per- centage. Give graphic illustration of one of the types in fractions; and make a practical, concrete problem to illustrate one of the types in percentage. 422 METHODS IN EDUCATION 68. Tell how you teach longitude and time in arith- metic. Show three direct correlations with life. 69. Illustrate and explain borrowing and carrying in arithmetic. 70. Enumerate three methods of teaching percentage. Make a practical problem and solve it to illustrate the three ways just mentioned. 71. Write analysis of the problem given in answer to 70. 72. What is meant by business applications of per- centage? Illustrate three such applications by making three concrete problems. 73. Explain and illustrate graphic methods in arith- metic. Why do such illustrations help apperception? 74. Briefly describe five devices in teaching arithmetic. 75. Define number. Give psychological justifica- tion of your definition. 76. Defend two conceptions of common fractions. 77. Solve a problem by unitary analysis; explain; contrast variable unit process applied to the same problem. 78. Induction, deduction, and analogy are mentioned under kinds of reasoning. Illustrate induction by out- lining a lesson on division of a common fraction by an integer; deduction in division of decimals; analogy in history. 79. Describe three ways of performing subtraction. Quote page in this book. Advocate, giving authority, your choice of the three ways 80. Accuracy is a habit classified as a school virtue. This habit depends upon knowing how to study. Tell explicitly how you teach pupils to acquire accuracy in studying (a) spelling, (6) model in composition, (c) a QUESTIONS ON THE TEXT 423 problem in reduction of denominate numbers, {d) a selection for memorizing. 81. Consult section 70 for discussion of reaction. There are motor reactions in speaking, singing, writing, drawing, dancing, etc. Show how five kinds of motor reaction help in fixing impressions. Be specific in your answer, e.g., how written expression tends to mastery of thought in arithmetic, history, and other subjects. 82. You aim to develop the critical habit of detection and correction of errors, (a) What is your procedure in written compositions? (6) Apply to map-sketching in history and geography, (c) What plan of checking (verifying or proving) do you teach for each of the four fundamental operations in arithmetic? 83. The law of self-activity of the pupil applies at all times. State briefly and explicitly how you employ this instinct in five different educative ways. 84. Evils and virtues are treated in sections 166 and 167. Those virtues become a part of character by a process of gradual habituation. For each of those virtues, show one way in which your teaching strengthens character. 85. Three laws underlying habit are plasticity, motive, regular repetition. Show bearing of these laws on teaching primary arithmetic. Mention five kinds of drill to secure accuracy and rapidity. 86. In speaking of training the memory, we have the terms apprehension, retention, and reproduction; associa- tion by similarity and contiguity. Illustrate the first three in teaching The Children's Hour; apply sim- ilarity and contiguity in geography, using New York City as an illustrative type. 87. What contemporary events in English history 424 METHODS IN EDUCATION should be studied in connection with the American Revolution? Justify your answer by principles of edu- cation. 88. Mention five ways in which methodical daily teaching tends to strengthen the power of attention of pupils. 89. Alertness, persistent thinking, and co-operative activity are three desirable indications of effectual teaching. Discuss questioning, under a limit of two hundred words, in relation to these ends. 90. ''Turn to use " is a maxim in education. Apply this maxim by outlining ten ways of enlarging pupils' vocabularies in the elementary schools. 91. What is the connotation of the words originality and spontaneity (a) from the teacher's viewpoint in management, (b) from the pupil's viewpoint in composi- tion? 92. What is the value of drill in education? Briefly present your methods and devices in two subjects. 93. What is meant by a good school spirit? How is it secured? 94. Education implies mental, moral, and physical development. Show how the work of one day in school may exemplify the truth of this statement. 95. Every element in school organization carries an opportunity in education. Enumerate ten such oppor- tunities, aside from assigned subject-matter. (Think of marching, singing, cleaning boards, arranging books in desks, etc.) 96. Mention ten of the teacher's methodical ways that are worthy bases for pupils' habits. To what extent is imitation operative? Apply suggestion also. 97. If you are asked to outline a discussion of topics QUESTIONS ON THE TEXT 425 I and II, what other points do you desire to add? If no others, state tersely why you think the points given are adequate. Would such school habits be good hfe habits? I. Securing and retaining attention. 1. Comfortable environment. 2. Personality of teacher: attractive appearance, in- viting manner, persuasive voice. 3. Habit of expectancy in pupils in relation to board, charts, presentation of lesson, drill, and assignment; i.e., variety. 4. Interest through play-impulse. 5. Orderly, progressive questions; get pupil to ask himself questions. II. How to interest pupils. 1. Teach them how to work: consciousness of power to accomplish something. 2. Sympathy, leadership, recognition of meritorious results. 3. Adaptation through proper grading and grouping; discouragement obviated. 4. Useful methods in teaching: graphic, varied; processes worthy of imitation when pupil is studying alone. 98. Define reasoning. Can you prove that pupils are learning to reason when they are seeking reasons for each of the school virtues? Does the will enter this process? 99. Comment on this conclusion by Rousseau: " Edu- cation is certainly nothing but a formation of habits." 100. Define method. INDEX 146 74 18 74 46 93 85 36 40 43 101 References are to Pages. For Consecutive Topics, see Table of Contents. divisors 356 elimination of matter . . 389 factors 357 fractions, common .... 362 fractions, decimal 372 graphic method 350 Grube method 349 habits, automatic 336 history 323 interest, simple 383 marking papers 332 measurement 320, 347 method 325 methods in primary- number 401-417 modern view 316 multiples 360 multiphcation 342, 408 multiplication tables, order 345 New York City view ... 392 number defined 318 partition 347 percentage 380 problems 333, 387, 390 properties of number . . 351 quantity 316 ratio 384 scoring 327 series 386 short processes 384 Speer method 350 subtraction 339, 404 subtraction, four ways . 341 teaching concept of number 327 text-books 388 Abstract in composition . Adolescence .Esthetic inheritance .... Affiliated interests Air shafts Analytic method Answers desired Apperception defined law principle Application, formal step . Arithmetic 316-417 addition 335, 401 aim 321 algorism 338 arithmetical comple- ment 387 association, law 344 Austrian method of di- vision 377 book, early use 330 casting out nines 387 combinations 336 commutation, law .... 344 correlation 30 counting and measuring 320 decomposition . .337, 339, 342 denominate numbers . . 379 devices for drill 330 difficulties graded . . 396, 399 distribution, law 344 divisibility, tests 353 division 347, 412 427 428 INDEX Arithmetic (Continued) type examples in frac- tions and percentage . 397 unitary analysis 386 utility 322 variable unit 386 Assimilation 20 Association, formal step . . . 101 Attention defined 37 law 40 principle 43 Attribute complement, lesson 105 Authority in moral educa- tion 70 B Bailey 366 Batavia plan 62 Boyer 39 Butler 6 C Civics 257-279 Committee of Fifteen .11, 14, 16 Committee of Ten 214 Comparison formal step 101 geography 224 spelling 119, 134 Composition 140-159 aims 140 classification 143 criticism 151 culture 140 miodel, uses of 148-151 motives for pupils 141 pertinent questions an- swered 153 principles 322 problems 146 structural errors 152 subjects 146 utility 140 Concentration 13, 14 Concepts 39 Conception 39 Consciousness 36 Co-operation 70, 138 Co-ordination 14 Correlation Committee of Fifteen quoted 11 illustrated 10 in course of study 10-13, 22, 26 Course of study 5-15 and pupils 5 and teacher 5 assimilation 20 Butler 6 concentration 13, 14 continuity 22 co-ordination 14 correlation. .10, 14, 22, 26-32 culture epochs 9 curriculum distin- guished 5 eclectic 7 enrichment 8 formal vs. content studies 32 Maxwell quoted . , .7, 15-35 objectivity 21 old and new 7 principles 6, 15 variety 20 Curriculum 5 D Decoration of rooms 47 Deductive method 92 Demerit marks 72 Device arithmetic 330 geography 229 management 75 meaning 98 word-building 133 Dexter and Garlick .... 36, 37, 39 Dictation abuse in spelling 114 composition 145 spelling 135 Discipline 70 Discussion 95 class 95 school management ... 50 INDEX 429 Doors and windows 46 Drawing sesthetic 18 correlation 31 Drill, formal step 101 Dutton 46, 47 E Education affiliated interests .... 74 and environment 16 habit a result 40 inheritances 6 ^oral 65 object 16 principles 35-45 purpose 3 Elaboration in composition . 146 Enrichment 8 Evils, school 74 Examinations 128 Expulsion 72 F Faculties defined 36 object or action 36 training 40 Fatigue 75 Feeling defined .' 36 habit 40 Fireplace in ventilation .... 47 Formal instruction 32 Formal steps of instruction . 100 G Garlick 48 General method 98-101 aim 102 formal steps 100 Herbartian view 99 Hervey cited 103 illustration 105 method- whole 108 Generalization, formal step . 101 Geography 201-257 causal relations and series 219 climate 235 commercial trips 231 Committee of Ten quoted 214 comparison 224 compass, points of .... 209 concentric circles 217 correlation 30 debates 231 definitions 202 devices 229 early lessons 208 excursions 213 glaciers 240 globe 232 home geography 208 how to study 225 how to study map 252 how to study text 254 icebergs 242 international date line . 247 latitude and longitude . 245 man and nature 219 maps 209, 229 methods 211 models 219 moisture, forms of .... 237 new way 202 New York City view . . 203 old way 201 pictures 227 rain 238 recitation 226 seasons 242 shape of earth 233 standard time 248 text-books, character- istics 256 volcanoes 248 winds 250 Gordy 37, 109 Grading 58 Grammar 159-201 adjective and adverb distinguished 171 adjective clauses 189 analysis 165 attribute complement, lesson on 105 430 INDEX Grammar (Continued) connectives 194 diagrams 165 drill 166 false syntax 168, 198 fundamental facts .... 161 habit 160 infinitives 178, 186 mode 176 noun, lesson on 176 noun clause, lesson on . 191 parsing literature .... 167 participles 178 parts of speech 169 personal and relative pronouns 173 shall and will 174 syllogism 161 value 159 words, phrases, clauses 188 Grounds, uses of 48 Group teaching 60 H Habit and program 54 defined 39 habituation 40 result in education .... 40 Halleck 36,38 Harmony with environment 16 Harris 322, 323, 325, 334 Heeter 220 Hervey on formal steps .... 103 Hill 323, 325 History 257-279 cause and effect 269 collateral reading 268 correlation 30, 271 definition 260 institutional 19, 257 interest 276 maps 273 means of enlivening . . . 274 memorizing 270 method 263 mistakes in teaching . . 277 New York City view . 257-260 note books 273 outlines 273 reviews 271 source method 267 teacher's preparation . . 264 text-book method 267 topical method 266 value 261 Home lessons 64 Home 37, 39 How to study geography 228, 252, 255 grammar 160 opening exercises 54 selection for memoriz- ing 208 spelling 112 value of program 54 I Imagination constructive in geog- raphy 211 defined 39 in moral education .... 69 Incentives 73 Inductive method 91 Institutional inheritance ... 19 Intellectual inheritances ... 18 Interest defined 36 law 40 principle 43 J James on reaction 43 Judgment defined 39 faculty 40 training 40 K Knowing defined 36 L Language work correlated . . 31 Light 45 Literary inheritance 18 Logical unity 23 INDEX 431 M Maxwell courses of study. . . .7, 15-35 geography 228 group teaching 60 oral composition 143 principles of manage- ment 50 McLellan and Dewey 318, 319, 321, 348, 350, 365 McMurry arithmetic 322 ^ geography 214, 221 Memory defined 39 Memory gems correlation 32 for opening exercises . . 55 our platform 57 reading 311 Method defined 76 general 98-110 Methods of teaching 76-98 analytic 93 analytic and synthetic distinguished 94 concrete to abstract ... 88 conversational 77 deductive 92 development 77 heuristic 90 inductive 91 inductive-deductive ... 92 known to related un- known 88 lecture 78 observation before rea- soning 89 particular to general ... 86 Prussian 91 questioning 78 simple to complex 87 Socratic 82 synthetic 93 text-book 96 topical 95 Method-whole 108 Mind defined 36 faculties 40 training 40 Monroe , 76 Moral education 65 Multiple sense instruction . 245 O Object teaching 35 Observation defined 38 Opening exercises 54 Our platform 57 Outlines composition 150 geography 228 history 273 P Paraphrase in composition . 145 Parker 207 Pedagogics 4 Penalties 72 Percept 38 Personality 53, 65 Preparation, formal step ... 100 Presentation, formal step . . 100 Principles character 66 composition 141 course of study 21 education 41 management 50 mind training 40 moral education 69 reading 281 Principles of education . . . .35-45 Program, value of 53 Promotion 58 Prussian method 91 Punishment 71 Q Questions 78 answers desired 85 consecutive 79 development 80 negative rules 81 positive rules 80 promiscuous 79 Socratic 82 432 INDEX R Reaction meaning 42 motor 42 principle 42 Reading 279-316 accent 301 Aldine method 290 analytic methods 282 analytic-synthetic methods 284 appreciative 299 articulation 301 biography 308 complete works 280 defined 296 difficulties, mental and physical 296 difficulties remedied . . . 298 dramatization 285 eclectic tendency 294 emphasis 301 extensive and intensive 305 former books 279 home 307 inflection 302 interest aroused 297 interpretative 299 literature 307 McCloskey method ... 287 memorizing . . . .300, 308, 311 memory gems 311 modulation 303 pauses 305 pitch 303 principle 281 reading to pupils 297 silent 300 synthetic methods .... 283 tone, quantity, and quality 303 types, modern 281 value 279 Ward method 289 Reasoning defined 39 faculty 40 Rein on aim 102 Religious inheritance 19 Reproduction in composi- tion 145 Reverence 17, 65 Roark 9, 38 S School economy 44-50 School management 50-76 Scientific inheritance 19 Seating 47 Self-activity defined 39 law 40 principle 44 Self-government 67, 73 Sensation defined 38 Sense-perception defined 38 principle 42 Smith, D. E. . .319, 322, 324, 325 334, 341, 350, 374, 377, 391 Socratic method 82 Space for each child 45 SpelUng 110 books vs. lists 116 classification of words . 123 correlation through dic- tation . 135 devices in word-build- ing 133 dictionary, use of 133 difficulties Ill experiments 120 grouping 134 how to study 118 how to teach meaning of words 130 how to teach synonyms . 124 psychology HO rules 122 three ways of teaching . 117 value 110 Spirit of school 66, 74 Studies, moral values 67 Substitution 33 Synonyms, lesson on 124 Synthetic method 93 INDEX 433 T Teacher ability to teach 52 control of class 53 free discussion 50 Maxwell on estimating . 52 . originality 51 personality 53 qualifications 52 responsibility 5Q spontaneity 51 using suggestion 54 Teaching Batavia plan 62 class , 59 examinations 62 group 59 home lessons 64 individual 59, 61 moral 65 Topical method 95 Transcription 144 Type examples 397 course of study 15 geography 221 grammar 164, 169 reading 281 V Variety 20, 22, 33, 136 Ventilation 47 fireplace 47 indirect method 46 Virtues, school 74 W Welch 37, 38, 39 Will defined 36 Willing defined 36 Words classified 123 Y Young 322,385 LIBRARY OF CONGRESS 019 809 886 3