TV, T 315 THIRD REPORT ( g tfj Course of Studies for Elementary Schools. BY JOHN T. PRXNTCE, AGENT OF THE MASSACHUSETTS STATE BOARD OF EDUCATION. BOSTON : WRIGHT & POTTER PRINTING CO., STATE PRINTERS, 18 Post Office Square. 1899. Digitized by the Internet Archive in 2015 https://archive.org/details/thirdreportuponcOOprin REPORT. In previous reports upon a course of studies for elementary schools* I presented some conclusions based upon a careful inquiry respecting the opinions of prominent educators and the practices of types of the best schools in this and other countries. These conclusions relate to (1) the age of admitting pupils, (2) subjects of instruction, (3) the grouping of subjects, (4) the relative amount of time which should be given to each group, (5) correlation of studies, (6) departmental instruction, (7) elective studies, and (8) the grading and promotion of pupils. There remain to be considered four other features of a course, viz., the scope, relations, sequence and limitations of the various subjects. The consideration of these features will be confined mainly to suggestions and recommendations for the making of a course, followed by a brief outline of a general course. The conclu- sions reached are drawn from observation and experience, sup- plemented by a careful study of some of the best courses in the country and of various general and special reports that have been made. Before referring to the special subjects of a course, I desire to direct attention to some general features of existing courses of studies and practices relating to them. My observations of schools, coupled with the present investi- gation of courses of studies, have led me to believe that the plan of putting before teachers a detailed statement of all they are expected to accomplish during fixed periods of time, is wrong in principle, as it is harmful in practice. Some courses even go so far as to point out the exact pages of the text-book which are to be gone over in a given period, the presumption * See reports of Massachusetts Board of Education, 1895-96, pp. 437-480, and 1896- 97, pp. 279-314. These reports are also printed in pamphlet form, and will be referred to in this report as " Preliminary Report " and " Second Report" 4 being that the topics included in those pages constitute the entire work of all the pupils. The leveling system is complete where examinations based upon these requirements are given by some one other than the teacher. Nothing in this inquiry has been more evident than the fact that much more should be done than is now generally done to reach individual pu- pils, by giving them instruction and training suited to them both in kind and amount. The excessive number of pupils to a teacher found in most schools renders it impossible to accomplish this result in any degree satisfactory to the best teachers. The brighter and quicker pupils, as well as the duller and slower ones, are not reached in the way they should be reached. The present generally followed plan of keeping to- gether for long periods all the pupils of a large class upon the same kind of work is harmful alike to the quicker pupils and the slower, — to the former in undue suppression and lack of stimulation to healthful effort, and to the latter in discourage- ment and superficialness. It is well known that the tendency of unwise and unskilled teachers is to emphasize the quantitative rather than the quali- tative side of their work ; to regard the work of teaching mainly as an assistance to the pupils in obtaining a certain amount of knowledge or information, and, as this can be meas- ured best by the pages of the book or the per cent , marks in an examination, these standards are uppermost , in their minds. The method of apportioning the subjects and topics in a course of studies so that the attention is fixed mainly upon the amount to be learned tends to strengthen these convictions of unwise teachers and places unnecessary restraints upon wise ones. It may be said that, whenever a course of studies gives a great degree of freedom to teachers, there is likely to be a neglect of essentials and a weakening of work that may be called consecu- tive. But this can be true only of unwise and unskilled teach- ers. With those teachers who understand what all their pupils most need and who know how they are best to be provided with it, the faults above alluded to are not likely to exist. To them the fixed bounds of non-essentials stand in the way of a proper adjustment of the work to the needs of the pupils. In matters only that are essential or important should limitations be indicated in a course of studies. But even the limits of the 5 essentials of knowledge might well be omitted in a course to be followed by one teacher alone. It is only in a system of schools where two or more teachers are employed that a limited plan or program of studies is needed. The fact that the non-essential subjects are almost limitless in number and kind renders it impossible to make a selection of such subjects which will be suitable alike for all schools and classes or for the pupils of all teachers. For these reasons, a course of studies intended for the schools of a large section, as of a county or State, should first of all be general in character, and be confined largely to the designa- tion of subjects that are essential or important. This course may well be used as a basis of a more detailed course for a comparatively small group of schools. Moreover, the sub- jects assigned to particular times should be so arranged as to permit a division of the school into groups or sections of pupils of different degrees of ability. Further, the subjects should be so arranged as to permit extra work to be done by individual pupils. This feature of a course was mentioned in one of the recommendations contained in the report upon the grading and promotion of pupils. It was as follows : — The course of studies as far as possible should be made so as to assist the teacher in adapting the work assigned and called for to the abilities of all pupils in every class. This can be done by designat- ing important or principal features which must be taken by all for a proper understanding of the subjects, and by suggesting supple- mentary work that may be done profitably by pupils after -they have acquired the necessary portions, and while they are waiting for others who have not acquired them.* One other feature of a general course of studies should ap- pear, — that of giving all subjects such a place as will permit a rational and orderly correlation of the studies not only of a single group but also of all groups so far as it is possible to do this. Upon this and other points the recommendations of the Second Report are as follows : — 1 . The selection of topics should be so made as to be of general use. This general course to serve as a basis for more detailed courses in given localities. * Page 36 of Second Report. 6 2. The selection of topics should be made from all groups, so that at least one subject of every group will be presented for a given time. 3. The selection of topics from each group for a given time should be made with reference to their logical relations to the topics of all other groups, so far as the nature of the subjects and a proper treatment of each will permit. 4. No reference to a centre or to centres of correlation need be made in the general course, it being understood that each subject taught will be the centre, with which all other subjects at the time will be correlated. 5. No reference to the place or time of isolation in teaching need be indicated, since that and all other matters relating to methods of treatment will be left to the teacher.* It may be necessary to designate periods of time during which prescribed work must be accomplished, but it should be done in such a way as to permit the elastic system of grading and promotions recommended at the close of the Second Re- port, f This may be done by designating the minimum of work which is to be done within certain periods, and by placing in a parallel column the time at which all that goes before shall be completed. The outline of subjects thus presented will be only the essential or most important work required to be done. Some superintendents follow the plan of placing a general course before their teachers, and of supplementing this course by specific directions in monthly grade meetings. This plan succeeds well where too many details are not given, and where the independence and originality of the teachers are not inter- fered with. It has the advantage of affording opportunity for constant adjustment of work to new and varied conditions, and of assisting untrained or inexperienced teachers in a proper interpretation of directions. This plan is especially advanta- geous for directors of special subjects, like drawing and nature study, inasmuch as it gives opportunity for instructing teachers in technical details which are not well understood by them. The plan of issuing separate pamphlets or slips, containing the prescribed work for each subject in all the grades, has the advantage of bringing before each teacher a statement of what is expected to be done in a given subject in all the grades, thus * Page 13 of Second Report. t Pages 35-37 of Second Report. ? making it easy for every teacher to know what every other teacher is expected to do, — a necessary condition for good work. This practice of teachers is likely to be discouraged and the work narrowed by following the plan adopted by a few superintendents, in presenting the prescribed course of each grade in a single pamphlet. The features of a course of studies which I shall consider briefly in this report are : first, the scope or aim and range of subjects to be presented under each group ; second, the relation which the subjects of a group bear to each other and to the subjects of other groups ; third, the sequence or order in which the various subjects or parts of subjects should be presented ; and, fourth, the limitations both in time and substance which should be made in each branch of study. The aim or purpose of a given subject may be general and remote, or specific and immediate ; a course of studies has to do mainly with the former, the latter aim belonging more to a statement of methods which are supposed to be known by teachers. The range of topics outlined in each branch of study will be determined partly by the aim and partly by the condi- tions under which the school is carried on, — these conditions being the number of pupils, the number of classes, the length of the course, the number and character of the teaching force. It is understood, of course, that, as ''preparation for complete living "is the end of education, so all subjects and parts of subjects that do not contribute to this end are to be excluded from the course. The subjects of study should be so placed in a course as to assist the teacher to correlate them in teaching ; that is, to present them in right relations, by which each fact of knowledge or information acquired shall be fortified and enriched by others, and by which good habits of thinking shall be encouraged. So far as possible, the relation of each subject to its use, and especially to its use in life, should be indicated. The sequence or order in which the various topics should be presented is determined by their relations of dependence one upon another, and by the natural order in which the mind acts. The sequence of subjects in a course should not be so marked or finely drawn as to cause the teacher to think more of the 8 relation or dependence of subjects one with another than of the relation of each subject to the mind and life of the child. The limitations of any branch of study in respect to time and subject-matter will be determined largely by the relative importance of that branch or of the subjects of that branch as a means of accomplishing the ends to be desired. Other limita- tions are those which are determined by the length of the session and school year and by the number of classes and pupils to a teacher. The percentages contained in the tables of the Preliminary Report of this series are intended to show the relative impor- tance of the various subjects, and the time program on page 44 of that report shows the actual time given to each group of subjects, on the supposition that the school day is five and one- half hours long, and that there are five school days in the week. For future reference in the apportionment of time limits to separate subjects, that table is here reproduced, with change of groupings made in Table XV., in which literature is classed with language instead of history. The table is as follows : — Time Program, showing the Number of Minutes a Week spent in Reci- tation by a Pupil or Group of Pupils in Five Groups of Subjects; also the Number of Minutes a Week given to Opening Exercises and Recesses and to Study in School. GROUPS OF STUDIES. Sub- pri- mary.* Grade Grade 2. Grade 3. < trade 4. Grade 5. Grade 6. Grade 7. Grade 8. I. Language and literature, 348 378 378 371 312 320 320 380 380 II. Mathematics, .... 72 108 108 146 156 160 160 184 230 III. Elementary science, 240 108 108 146 195 200 200 184 138 120 90 90 97 117 120 120 172 172 V. Miscellaneous, 420f 216 216 215 195 200 200 230 230 Opening exercises, physical exer- 250 250 225 225 200 200 200 200 500 500 450 450 450 450 300 300 Total school time, . . 1,200 1,650 1,650 1,650 1,650 1,650 1,650 1,650 1,650 * Figures in this column indicate the number of minutes spent in recitation and busy work taken together. t Including physical exercises, games, kindergarten occupations, etc. It should be understood that the figures in the above table represent the amount of time given in recitation only by a pupil or a group of pupils. They do not express, the amount of time given to study, which of course will depend upon the number of sections in a room and upon how much the sections recite together. In considering the five groups, the subjects of scope, rela^ tions, sequence and limitations will be set off by figures in the order named. Group I. — Language. 1. Language is the expression of thought. The term as used in the school curriculum is intended to mean the expression of thought in words. As a subject of instruction, it relates to getting thought by means of the printed or written page, and to expressing thought both by speaking and by writing. Lan- guage, therefore, includes upon the practical side reading and composition. Upon the theoretical side it includes grammar, rhetoric and logic, the elements only of which should be taught in the grammar school, and always in close connection with reading and composition. In some schools a foreign language may be taught during the last years of the grammar school course, the subject being offered as an elective for those who can carry on the regular English branches. The immediate aim in language teaching is the power to gain and communicate ideas through written or spoken words. This will involve (a) power to read intelligently and (b) power to speak and write correctly and effectively. The reading must include, first, a mastery of the symbols, that is, learning to read ; and, second, such companionship with and study of good literature as shall develop power to understand and appreciate the best in literature. The power to speak and write correctly and effectively in- volves, first, the mastery of written and spoken forms in accordance with accepted usage ; second, analysis of language to discover the rules of usage ; and, third, constant practice in speaking and writing, both before and after such analysis. While the elementary course in grammar has for its chief end correctness, it may also include some features of effective- ness, such as clearness, conciseness and force. The most important fact to be kept in mind is that the study of this sub- ject in the grammar school should be elementary and very 10 practical, the aim being to teach principles by which the pupil is enabled, first, to understand the language of literature ; and, second, to express his thoughts in some measure as they should be expressed. An incidental but by no means unimportant end in the study of grammar is mental discipline, — a power of the mind to generalize, to make rules from facts, and to apply principles and rules to practice. 2. It is plain to see that all forms of language as branches of study are closely related to one another and to nearly all other branches. The forms of expression in the reading books become models for imitation and practice in all departments of composition work, which serves both as a means and as an end of grammar and rhetoric. The relation of the theoretical side of language to practice both in reading and in writing should be indicated by prescribing practice in analysis of sentences and in constant application of the rules of syntax most fre- quently violated. The work in composition should be closely related to the pupils' thinking; and, as the regular subjects of study are supposed to occasion thought, they therefore constitute a good basis for language in the recitation. Moreover, the regular studies, especially geography, history, science and reading, should furnish topics constantly for composition. Some of the most obvious relations which the branches of this group have with one another and with other subjects of study are matters of apperceptive teaching, which every good teacher understands, and which therefore need not be indicated in a course of studies. 3. In securing a mastery of forms in language, a certain definite order should be followed. In learning to read, that order is governed by a well-known principle of proceeding from a vague knowledge of the whole through analysis and synthesis to a clear knowledge of the whole. While a course of studies may not give the steps by which this principle is observed, it may properly state that the teaching should begin either with words alone or with words in sentences, and that analysis and synthesis of words follow in natural order. It may also state that the first words and sentences should be read from the blackboard, and afterwards from the chart and from the first readers. The order to be followed at this stage in the 11 selection of reading material is sufficiently indicated by the ordinary first and second readers. The order of selection after the pupils have acquired skill in reading should be determined by the tastes and abilities of the children, the selection to be made from given lists of books. The sequence to be followed in the technique of writing may be sufficiently indicated by stating that during the first two years much copying of good texts should be done, beginning with words whose letters are easily made, as man and cow, and proceeding by degrees to Avords more difficult to write. Some courses prescribe much practice with single letters to be taken up in a given order. In spelling, it appears to be the custom in the best courses to prescribe some oral spelling for the lower grades, the main attention, however, to be given to writing words in sentences. The words selected for drill in these grades are to be found in the regular reading books. Beyond the third grade, in addi- tion to the words used in the composition exercises, lists of words such as are found in a good spelling book may be used with profit for dictation, the words to be written both singly and in sentences. English grammar may be regarded as one of the few strictly sequential subjects of the elementary course. Each topic should lead up to the next, and all should have distinct reference to the ends already pointed out. The following general outline shows the order which may be pursued in an elementary study in this subject : — (1) The sentence and kinds of sentences defined. (2) Subject and predicate, simple and complete. (3) Parts of speech. (4) Limiting phrases and clauses. (5) Nouns, — kinds and forms. (6) Pronouns, — kinds and forms. (7) Eules of syntax, respecting case of pronouns. (8) Verbs, — kinds and forms. (9) Rule of syntax, respecting the form of the verb. (10) Adjectives, — kinds, forms and uses. (11) Adverbs, — kinds, forms and uses. (12) Prepositions, — uses. (13) Conjunctions, —kinds and uses. 12 4. The amount that can be done in the various language subjects will depend largely upon the grade and natural abili- ties of the pupils. The exact amount to be done in some sub- jects should not be prescribed, while in others the amount prescribed will indicate the least that should be done in a given period, with a provision for sufficient time to permit classes or individual pupils to do as much as they are able to do. At the end of the second year the pupils should have so far mastered the symbols of reading as to read easily at sight any ordinary second reader. To accomplish this, several first read- ers and several second readers should have been read through during the two years. After the second year the reading should be carried on in the two lines already indicated, an average of ten pages a week of each kind being required in all grades. It should be remembered that this is the minimum required, and does not include the amount of reading done at home or the extra reading by individual pupils. In most schools probably the limit set is no more than half of what can be well done. Except in special instances, no set exercises in writing should be given after the fifth year. Whatever is needed to secure legibility and rapidity of writing after this time should be done in connection with the composition and dictation work. Most of the special instruction in spelling should be given during the first six years. With the exception of occasional reviews, the work in this branch during the last two years of the course should be confined to the correction of words mis- spelled in the composition and other written exercises. The limits in written language are difficult to define. It is understood that more depends upon the quality of work done than upon the quantity ; and yet it is manifestly the latter feature only that can be presented in a course of studies. An average of ten lines a day of carefully written original work during the entire course beyond the second grade, and an equal amount of dictation for instruction in punctuation, spelling, etc., from the third to the sixth grades inclusive, should be the minimum of written work required, it being understood that monthly compositions should be required of all pupils in the three high- est grades. In designating the subjects of this group, no mention was 13 made of memorizing choice selections of poetry and prose. While such an exercise may be brought into close connection with the reading and dictation, particular mention of it should be made in the course. An average of at least ten lines a week should be required to be memorized by pupils of all grades, it being understood that the selections memorized shall be of a high order of literary merit, and adapted to the capacity of the children. The necessity of limiting the study of grammar in the gram- mar school to the elements of the study and to its use in analy- sis and syntax has been referred to. Only those properties of the parts of speech should be required to be learned that are needed for analysis of sentences and for a proper understand- ing of the rules of syntax. These rules should be limited to rules which are most commonly violated. Not more than ten rules should be made and learned, but they should form the basis of constant practice in the construction of sentences. These and other limitations of the subject appear in what has been said upon the sequence of topics to be studied. Where there are so many branches in a group as are included in this group, it may be well to designate approximately the amount of time to which the recitation in each branch should be limited. For example, if the recitation time for the lan- guage studies should be as given on a previous page of this report, the allotment for each branch may be based upon that time, as shown in the following : — Time Program, shoiving the Number of Minutes a Week spent in Recitation by a Pupil or Group of Pupils in Heading, Writing, Spelling, Composition and Grammar. SUBJECT. Sub- pri- mary. Grade Grade 2. Grade 3. Grade 4. Grade 5. Grade 6. Grade 7. Grade 198* 190 190 150 120 120 120 120 120 50 50 50 50 50 ] 1 H 60 60 75 60 60 >200 160 160 50 78 78 96 82 90 1 J 100 100 348 378 378 371 312 320 320 380 380 * Including story-telling. It should be understood that the above figures are only ten- tative and approximate, and are given merely to show how an apportionment may be made under given conditions. It should be understood also that the time given is the recitation time only of a pupil or group of pupils. The time for writing at the seat outside of recitation in copying or composing is not counted. One advantage as a saving of time which composi- tion, spelling and writing have over some other subjects should be taken into account, and that is the practicability of having all the pupils of a school recite together. Group II . — Mathematics . 1. Mathematics, or the knowledge of quantity and space relations, is taught both for its practical and for its disciplinary value. In the elementary schools it is taught mainly as an art, although the foundations of mathematical science are laid throughout the grammar school course, and in the upper grades something of the science itself is taught. The department chiefly pursued in the elementary schools is that of arithmetic, the elements of geometry and algebra being taught in the upper grades. To these is added a simple form of book-keeping, which may be regarded as an extension of the practical side of arithmetic. Arithmetic is a knowledge of numbers, their expression, relations and operations. The numbers to be learned are in- tegral and fractional, simple and denominate. So much of this knowledge should be acquired as will help the pupils to solve all the ordinary problems of daily life, and at the same time to serve as a means of mental discipline. The scope of arithmetic in successive grades will be determined largely by the power of the pupils to grasp new relations and conditions. In recent courses a broad basis of subjects has been prescribed in the lower grades, including fractions (both common and decimal), percentage and measurements. The two kinds of work, com- putations with abstract numbers and work in practical prob- lems, should be presented in all grades, the amount of the former decreasing and of the latter increasing in successive grades. 15 The aim of geometry in the grammar school is chiefly to sup- plement the course in arithmetic, and to furnish a good basis for instruction in mechanical drawing and manual training. The work required should be both constructive and inventional, supplemented by as many simple demonstrations as circum- stances will permit, the aim being to make the work as prac- tical as possible. The design of algebra in the grammar school is to give pupils a general idea of numerical relations and operations. Besides furnishing short and easy solutions of problems which are in arithmetic quite difficult, algebra gives pupils the power to state in general terms the conditions of a problem and the process of its solution, and thereby to deal with formulae and rules more easily than by arithmetic. Moreover, the elementary work in algebra may be so arranged as to give support to the higher form of the study in the high school . Bookkeeping may be regarded as only one of the many practical applications of arithmetic. Its end in the grammar school is ability to keep accounts which would be ordinarily needed by a farmer, mechanic or small retail shopkeeper. In- cidentally there will be acquired in the study some knowledge useful in higher forms of bookkeeping. 2. The close relations of the various departments of mathe- matics to one another are apparent. So close are these rela- tions in the early stages of algebra and geometry that the subjects may be said to be continuous rather than discrete. This is especially true in many kinds of practical work in which arithmetical processes are shortened by the use of algebraic symbols, and are practically applied in geometrical measure- ments. The relation of the subjects of this group to other subjects of study is not so close as to make it necessary to bring them together constantly. Yet the facts of geography, history and elementary science may be sometimes employed in arithmetical operations, to the advantage of all the subjects involved. 3. While it is true, as has been said, that there should be a broad basis of subjects in the lower grades, there is a pro- gressive order in the operations to be performed with numbers which should be prescribed in a course of studies. This order 1G has to do with the relative complexity of processes and also with the size of the numbers. In integral numbers, the work prescribed should be in successive steps, as follows: (a) from 1 to 10, (b) from 1 to 20, (c) from 1 to 100, (d) from 1 to 1,000, (e) from 1 to 1,000,000, (/) unlimited. In fractional numbers the fractional parts of numbers should first be taught almost from the beginning, and proceed in the third grade with fractional units, using in succession halves, fourths, eighths, thirds, sixths, twelfths, ninths, fifths, tenths, sevenths and elevenths. Decimals begun as early as the fourth grade should be taught by steps from tenths, hundredths and thousandths, which are the only decimals used for one year, to decimals of a lower denomination. Denominate numbers should be taught from the very beginning, the order of instruction being gen- erally from measures most familiar to those that are less so. The order of teaching numbers of all kinds should be first with objects and afterward without objects, and also first with- out figures and afterward with figures ; the warning being expressed that too much dependence should not be had either by using the objects too long or by employing figures unneces- sarily in the solution of problems. The sequence of steps in algebra and geometry will be indi- cated later, when their limitations are treated. 4. The time allotted to arithmetic should be given mainly to what may be called the essentials of the subject, or to such work as w T ill be found useful in everyday life. The following topics will indicate the degree of restriction that may be made : (1) Correctness and rapidity in adding, subtracting, multi- plying and dividing. (2) Ability to work without the aid of figures in all operations, to 100 in whole numbers, to twolfths in common fractions and to thousandths in decimals. (3) Knowledge and skill in the use of such denominate numbers as are used ordinarily in buying and selling and in keeping ac- counts. (4) Knowledge of percentage and of the simple appli- cations of percentage, such as are needed in ordinary business affairs. (5) Knowledge of geometrical measurements, so far as to perform problems involved in the ordinary affairs of life. It should be understood that, if more is done than is comprised in the above outline, it should not be at the expense of thor- 17 oughness in these subjects. It is believed that a large part of this work can be done in the first six grades. During the last two grades one or two lessons a week might be given to the more difficult problems involved. The geometrical exercises of the grammar school should be limited to work in mensuration carried on in connection with arithmetic, and to exercises of a concrete and experimental kind. The following outline in mensuration, followed in the Springfield, Mass., course, sufficiently indicates the needed limitations of this part of the subject : — A. Surfaces. — (1) Parts, (a) number of sides, (b) rela- tive direction of sides (whether parallel, perpendicular, etc.), (c) angles. (2) Comparison with other surfaces as to (a), (b) and (c). (3) Length of perimeter or circumference. (4) Area. B. Solids. — (1) Parts, (a) number of faces, (b) kinds of faces (plane or curved), (c) number of edges, (c7) relative direction of faces (whether parallel, perpendicular, etc.). (2) Comparison with other solids as to (a), (6), (c) and (d). (3) Length of all the edges. (4) Surface area. (5) Volume or solid contents. The limitations of work prescribed in experimental and con- structive geometry should not be too strictly drawn. The better way will be to present an outline from which teachers may select work adapted to the ability of their pupils. Such an outline may include : (1) Definition of volume, surface, line, angle. (2) Definitions of various kinds of lines. (3) Defini- tions of various kinds of angles. (4) Division of line into any number of equal parts. (5) Construction of angles of various magnitudes. (6) Definitions of various kinds of triangles, parts, etc. (7) Problems relating to angles and sides of tri- angles. (8) Definitions of quadrilateral and kinds of quadrilat- erals. (9) Problems relating to angles and sides of parallelo- grams. (10) Definitions of pentagon, hexagon, heptagon, etc. (11) Problems relating to the construction of polygons. (12) Problems relating to the division of polygons. (13) Problems relating to the construction of similar polygons. (14) Defini- -tions of circle and parts of circle. (15) Problems relating to diameter, circumference, arc, chord, secant and tangent. (16) Definitions of various kinds of volumes. (17) Problems in relation to the surfaces of volumes. (18) Problems in relation to the solid contents of volumes. The problems indicated in the above outline may be either concrete and constructive, or demonstrative, depending upon the ability of a class or of the individual pupils of a class. If the purpose of algebra in the grammar school is as indi- cated in a previous paragraph, its limitations might be somewhat as follows: (1) Algebraic notation. (2) Simple arithmetical problems, solved by algebra. (3) Addition, subtraction, mul- tiplication and division. (4) Factoring of simple algebraic quantities. (5) Reduction of fractions. (6) Resolving of equations containing one and two unknown quantities. (7) Practical problems involving the foregoing. Group III. — Elementary Science. 1. The immediate* end of all the studies of this group is a knowledge of nature, including man and all that is below man. The term nature study in recent years has been made to cover the study of plants, animals and minerals, and the elementary work done in physics and chemistry. This group also includes physiology and hygiene and geography. While it may be necessary in nature study to lead the pupils to learn through observation the facts of nature, they will learn them not for their own sake, nor mainly for the use they will make of them later in the study of science, but for the habits of observation which the lessons will help to form and for the abiding love of nature which they will help to arouse. These two ends, therefore, — the formation of habits of observation and the arousing of a love for nature, — will determine largely the character and extent of the study. It will include in their appropriate season the observation of minerals, plants and ani- mals, and some of the more apparent physical forces. These observation lessons will fail to produce the desired ends if they stop with a knowledge merely of what is observed. The inter- pretation of phenomena is of more value than the mere obser- vation of them as facts. The adaptation of parts of animals and plants to the uses they perform will early become an object of inquiry. It should be observed that, while a love for nature 19 is the primary end of nature study, it cannot be reached by simply talking about the objects observed. Such lessons may drift into mere sentimental reflections of little value. The facts must be learned not by reading or hearing, but by observing, and those facts should be reviewed frequently enough to be readily brought to mind. The study of physiology and hygiene includes in its scope such knowledge of the anatomy of the body, and the uses of the various parts as will help the pupils to have respect for the body and to keep it in health and strength. The study should be especially helpful in guarding against the dangers of the use of stimulants and narcotics. Through the study of geography the pupils acquire a knowl- edge of the earth as the home of man. There are two elements, therefore, of this branch of study ; first, nature, in making the earth suitable for human habitation ; and, second, the people, in making it a place in which all the activities of life are carried on. So far as possible, the pupils' knowledge of the earth should be interpreting knowledge, or knowledge by which they may understand the relations to human life of its various feat- ures, such as climate, surface, soil, etc. 2. The facts acquired in nature study are closely related to the primary facts of geography ; indeed, many of the facts of nature study and geography are identical. The subjects of study in these two branches should therefore be arranged in the course with reference to purposes of correlation ; and where it is possible the relations should be made to appear, as, for ex- ample, the effects of running water as a topic of nature study, and the study of relief forms as a topic of geography. The relations also of one or both of these branches to arith- metic and history should be indicated. Probably no subjects in the course will be found to be more serviceable for compo- sition and for drawing than these. If these relations are not indicated in the course, opportunity at least should be afforded for abundant practice in expressing in writing or in drawing the facts acquired. In the lower grades resemblances and differences of the human structure and that of the lower animals should be objects of study, and in the higher grades the connection of 20 the facts of anatomy and physiology with those of chemistry and physics should be made to appear. In all grades the rela- tion of parts of the body to uses and of uses to health and strength should be shown. 3. The allotment of work in nature study to be done in a given time, whether it be for a year or a day, should be deter- mined by the pupils' natural powers, both of observation and of interpretation. With young children, little is gained by establishing a fixed order of presentation. In general, it may be said that the observations should be made first 4 1 in the large " and afterward more minutely ; but, if children are inter- ested in the parts of an object very early in their observations, attention should be given to them, especially if the interest centres in the uses of the parts. It is always a safe rule to teach those things which will best serve as interpreters of other things of value for the child to know. On the same principle, a clear and definite knowledge of home surroundings is neces- sary to a proper knowledge of distant features and conditions. A knowledge by observation of a hill range will be the means of interpreting the distant mountain range described in the book. As far as possible also the logical order should be fol- lowed in teaching the various topics. The situation and sur- face of a continent or country may determine to some extent the climate and rainfall, — a knowledge of which helps the pupils to infer what the productions and the occupations of the people are. In anatomy and physiology, the practice in the best schools of deferring the teaching of the internal structure of the body until the later years of the grammar school seems wise. 4. The two chief ends of nature study should be kept in mind in determining the amount to be done. To form good habits of observation and to acquire a love of nature, there should be no forcing of acquisition. In no study will it be found more necessary to be led by the natural aptitudes and desires of the children than in the study of plants, animals and minerals. While it may be well to set before the teachers a wide field for observation, it should be understood that such selection of the work assigned may be made as will be best suited to given conditions. Again, a broad range of topics will furnish the needed extra and optional work for some pupils already spoken of. 21 While it is true, as shown in a previous report,* that nearly all the best schools are giving attention to nature study or ele- mentary science, there is a great difference in the amount and kind of work attempted. In some places, largely through the efforts of a superintendent of schools, especially interested in the subject, and a special teacher, the amount of ground cov- ered is ten times that covered in other places. One superin- tendent reports recently that his schools even in the higher grades do but little more than give the pupils a knowledge of the common flowers and trees. But it should be remembered that the highest ends of the study do not depend upon the number of facts acquired. Here is an additional reason for making the requirements elastic. Group IV. — History. 1 . The place and scope of history as a branch of study have materially changed in recent years. Instead of occupying, as it once did, a small part of the last year or two of the grammar school course, it is now in the best schools begun in the first year and carried on throughout the course ; and, instead of being a dry and profitless study of wars and dates, it has come to be regarded as a study both pleasureable and useful as a means of culture. According to this later view of the subject, its purpose from the first should be to inspire the pupils with high ideals of life, both as citizens and as members of society. Moreover, to lead the pupils to acquire a taste for history, the subject should be made interesting from the first. Myths, fairy stories and stories of semicivilized and colonial life should be told to and read by the children in the lower grades, to be continued each year by the reading of stories of biogra- phy and of American history in chronological order in the middle grades, and by the study of English and American history in the higher. All phases of social, civil and institu- tional life are to be presented to the children in forms suited to their interest and capacity. Thus we see that history, which is a record of the growth of a people from their earliest state to the present, includes biography and civil government as well as history proper. * Preliminary Report, pp. 7, 8. 22 2. As history teaches all sides of life, it stands in close relation to all the other studies of the school which are supposed to be a preparation for life : to arithmetic, in furnishing mate- rial for computations ; to science, in showing the analogies of the evolution of the race and that of the individual ; to geogra- phy, in the use of charts and maps, and in furnishing a basis of comparison whereby the present conditions of social and civil life are better known ; to literature, in providing the basis of much of the finest forms of the oration, and the ballad, the drama and the epic ; and to drawing and language, in awaken- ing thoughts that deserve the pupils' best efforts of expression. While most of these relations cannot appear in a course of studies, they must be considered in giving history its proper place. In literature especially should the close relation of history be recognized in the course of studies. There are phases of history that can best be known through literature, as there are forms of literature that can be fully interpreted only by a knowledge of history. 3. While the order of topics will depend somewhat upon the interest and capacity of the pupils, there is now a generally recognized order of presentation which should be embodied in a course. The first year or two may be given to the telling and reading of folk and fairy stories, myths and fables. These should be followed by reading stories of Indian and early settle- ment life, supplemented by biographical stories. As soon as the pupils are ready for it, and before the consecutive reading and study of American history are begun, attention should be given to interesting facts of local history, such as scenes of celebrated events, early settlers and well-known traditions. Consecutive topical study in connection with the reading of both American and English history should be prescribed for the last years of the course. 4. The limitations of subject-matter in history should be determined largely by the limitations of time and by the de- mands of other subjects. Not even a minimum of requirements should be prescribed, so far at least as such requirments are made a basis for marking or examinations. In this, as in no other subject, may the amount read and studied be adapted to the abilities of each individual pupil. If the work required to 23 be done be given out and recited by subjects or topics, each pupil may learn as much of each subject or topic as time and ability will permit. The course therefore should be so ar- ranged as to permit the greatest degree of freedom in teaching the subject. If this is done, and examinations have their proper place, the teachers alone will be responsible if the pupils have not a loving interest in the subject, — not only while they are being taught, but also after they have left school. Group V. — Miscellaneous. 1. In no branch of instruction has there been a greater change of place and scope than in drawing. Twenty-five years ago the number of public schools in which drawing was system- atically taught was very small. Now the schools in which it is not taught are as rare to find as were the schools formerly where it was taught. At first the cultivation of the aesthetic sense was considered the only end to be sought, and it was in some way thought to be reached through drawing endless castles and rustic mills from flat copies. Later, the dominant purpose seemed to be to make the subject as practical as pos- sible. This was carried out by the introduction of mechanical drawing, which had little relation to practical mechanics, and which was generally a laborious and tedious process to all con- cerned. Gradually these two ideas of the purpose of drawing as a branch of study have been supplemented by a third, which is that drawing is educational, and serves to train all the powers of the mind. As such the subject has its strongest claim for a place in the program. With this later idea of the function of drawing have come improved methods of teaching the subject, which serve to accomplish in good ways the ends that were formerly sought, — of aesthetics, by leading the pupils to draw and to use colors in imitation of nature and to appreciate by observation and study the most beautiful works of art ; and of practicalness, by drawing free-hand from objects and by con- necting closely the mechanical part of the subject with the work of manual training and with the every-day uses of life. The growth of manual training as a branch of study in the schools has been somewhat like that of drawing. At first it was sought as an accomplishment, afterwards as a trade, now 24 as a means of mental discipline in furnishing a good foundation for practical life. Its claims to a place in the course of studies are: that (1) it teaches dexterity of hand; (2) it trains to habits of order and neatness ; (3) it cultivates a sense of truth and right by demanding exactness of details ; (4) it cultivates the will in its requirements of persistence until an object is completed; (5) it serves as a valuable aid to drawing and art studies ; (6) it cultivates the ethical sense in enabling pupils to make useful objects ; (7) it serves to offset the strain of intel- lectual work ; and (8) it gives respect for manual labor. The reasons for making singing a regular and systematic subject of instruction are that it affords rest and recreation, is a means of healthy exercise and cultivates the aesthetic, ethical and religious sense. Governed by these ends, the aim and scope of singing as a subject of instruction are clearly (1) to train the ear so as to appreciate and enjoy good music that is felt and (2) to understand and be able to sing at sight any ordinary secular or sacred piece of music. 2. The relation of drawing to manual training is so close that each may be said to be incomplete as a subject of instruc- tion without the other. Both subjects also are closely con- nected with geometrical measurements. Drawing as a form of expression is closely related to every other subject of study, — to literature in illustrated sketches, to arithmetic in plans and working drawings, and to history and geography in diagrams and maps. In fact, it may be used as other forms of expres- sion are used, and in some cases it may be used profitably when other means fail to express the thought or feeling. In the lower grades the placing of singing in close relation to the reading and nature exercises and to the morning talk is made very effective. In the lower grades also singing in con- nection with some of the physical exercises is found beneficial. The use of singing tones has come to be recognized as a valu- able means of securing good speaking tones, just as the phonic exercises in spoken tones have been found helpful in developing a good singing tone. 3. Skill in the subjects of this group, as in all technical subjects, will depend upon the fidelity with which the successive steps are taken. Nowhere is a close application of the maxims 25 6 6 from the known to the related unknown " and ' ' from the simple to the complex " more necessary than in connection with these subjects. In the early stages of drawing as at present pursued there is a free expression of ideas through illustrative sketching without reference to principles. Attention is then given to form with special reference to correct proportion and outline, succeeded by exercises which give skill in rendering characteristic detail. Finally, there is sought to be secured a full and free expression of grace of form and harmony of color. In the mechanical side of drawing the successive steps are : first, exercises in precision, as paper folding and cutting ; second, exercises in accurate measurement ; third, accurate drawing of surfaces of given dimensions ; fourth, conventional grouping of figures to ex- press solidity ; and, fifth, drawing to scale. So far as the occupations of the kindergarten are educative, they are but the beginning of a series of manual exercises which should have no break throughout the elementary school course. In the earlier stages of the course, paper and cardboard should be extensively used, and always in close connection Avith draw- ing, for the purpose mainly of developing manual dexterity. In the later stages exercises to teach the use of tools should be given, and applications of what has been learned should be made in the manufacture of useful objects. In the last two years the course may, if thought desirable, be divided into two departments, — one for wood working and the other for sewing. In singing, care should be observed that the steps of tech- nique be taken in a natural order, and that the demands upon the children keep pace with their vocal powers and musical appreciation. 4. Within the scope and time already laid down, there need be given no limitations in drawing and manual training be- yond what is necessary under a class system of instruction. Here, as in other branches, the minimum of what is expected to be done may be prescribed, together with extra or extended work to suit the circumstances. Limitations in singing should be made in two directions : first, in respect to the time of learning the language of music ; and, second, in respect to reach of tones. The child needs to 26 acquire a musical sense, — that is, a love for and appreciation of music, — before the language of music is learned. For this reason two or three years of careful practice in simple phonic exercises and rote songs should be spent before sign reading is begun. Such exercises are also needed for a proper develop- ment of strength and sweetness of tone. The danger of over- straining young children's voices is avoided by confining the exercises during the first year to the lower tones. A Foreign Language. It will be observed that no reference has been made to a foreign language in the preceding discussion, although that subject was recommended in previous reports.* In my second report I referred to the desirability of making it a part of the elementary course, but of offering it as an elective, " either by making it an extra study or by permitting it to be taken in place of some part of the work in English grammar." If it is taken as a separate and extra study, of course only those pupils should take it who have time and strength for it in addition to the required work of the school. If the new language is begun in the fifth or sixth year of the course, and if but two recita- tions a week are given to the study, little extra time need be given to it to acquire a fair degree of facility in reading and some knowledge of the grammar of the language. The question of what foreign language shall be selected for study in the elementary schools has been discussed by educa- tional leaders. No agreement has been reached, and perhaps none should be expected or desired. The preponderance of practice seems to be in favor of Latin. The arguments in favor of Latin are : (1 ) the desirability of giving pupils who do not go to the high school an opportunity of acquiring some knowl- edge of a language from which a large percentage of English words are derived; (2) the advantage of a good start in the study before the high school is reached, so that the increased requirements for entrance to college may be met easily in four years ; and (3) the comparative ease of getting good teachers of the subject. * See Preliminary Report, p. 45, and Second Report, p. 15. 27 Weighty as the above reasons are for choosing Latin as the foreign language to be offered in the grammar school, they seem to be outweighed by considerations in favor of a modern lan- guage, French or German. In the first place, in making the choice there should be primarily regarded the interests of those pupils who are not to continue their studies beyond the grammar school, on account of their limited means of culture. For such pupils a slight knowledge of French or German would be- quite as disciplinary as Latin, and far more useful. In four years, with the limited time indicated, — two lessons a week, — a pupil should be able to read easy French or German at sight, and to talk somewhat in the language studied, — acquisitions which would be much more useful in a living than in a dead language. Again, if French is selected, the comparative ease of acquisition should be considered, not merely for the acquisi- tion itself, but for the use that may be made of it in learning Latin. Many teachers advise the study of French two years before Latin is begun, for the help which it gives in the latter study. If French or German is taken as an optional study, there should be no more than two lessons a week, involving comparatively little of outside study. Easy reading should be put into the hands of the pupils after a few weeks of oral lessons. Attention should be confined to reading and talking during the first two years, or grades five and six. During the last two years these exercises should be supplemented by simple gram- mar lessons and writing, all pointing to the practical ends of correctness and facility in reading and talking. Sub-primary Class. Before giving an outline of prescribed work for the sub- primary class, I desire to give the reasons for recommending the formation of such a class, and to explain more fully than I have done the character of the exercises proposed for it. In the first report of this series the following statements are made with reference to the need of a special class for children under six years of age : — It is possible that the differences in this country in the earliest age of admission to the elementary schools and in the length of the course of such schools will disappear when the kindergarten becomes uni- 28 versally a part of the public school system. It may be fairly ques- tioned, however, in any event, whether much of the formal intellectual work now carried on in many first-year primary classes should be demanded of children before the age of six. If, where children are permitted to enter school at five, a sub-primary course could be pur- sued, consisting largely of manual and observational work, advance- ment in subsequent work required would be likely to be quite as rapid as it is at present, where pupils are required to read and write much during the first year. In case there is a kindergarten course which children can begin at three or four years of age, the work of this sub-primary class could be supplementary to the work of the kinder- garten and preparatory for the more formal work of the primary school. According to many of our best kindergartners and primary school teachers, this connection between the two schools is very much to be desired.* Again, in a later part of the same report I said : — In many schools where children are permitted to enter at five, as much is attempted and frequently as much is done in reading, writing and number as is done in schools whose minimum age of admission is six years. That this gain is only an apparent one is obvious to all who are able to compare results at the end of the course. The plan that I would recommend is, that in all places where children are per- mitted to enter school at five years of age, sub-primary classes be established, whose work shall consist largely of an extension or modi- fication of the manual and observational work of the kindergarten, supplemented by some of the nature work and drawing now pursued in our best primary schools, and by a little reading, writing and num- ber work. If sub-primary classes are formed for children under six years of age, the nine years' course for children who enter school at five will be reduced to an eight years' primary and grammar school course, thus agreeing in age of admission, grades and age of graduation with our present eight years' course for children who are admitted at six years of age-t In view of all that has been said by experienced teachers regarding the advisability of supplementing the work of the kindergarten by less formal work than is usually required in a primary school, it would seem unnecessary to plead for the introduction of the proposed class. Every primary school * Preliminary Report, p. 6. t Preliminary Report, p. 38. 29 teacher realizes that the change is very great from the com- paratively unrestrained freedom of the kindergarten, with its dozen or fifteen children, to the school where restrictions are made necessary by the large number of children and by the character of the work required. 4 ' Connecting classes " between the kindergarten and the primary school have been formed in several places, and they have invariably been found to be of great use in wisely leading the children into good school habits. Frequently the class exercises have been such as to permit pupils to omit a portion of the first-grade primary work. But, if the sub-primary class is needed for those children who have had the benefits of the kindergarten, much more is such a class needed for children who have not had the advantage of the better training. The change from the home to the school is even greater than that from the kindergarten to the school, and therefore needs the bridge that the proposed class offers. Most people can recall the ordeal through which they passed during the first few weeks of school life. Perhaps the modern school has made the ordeal less trying than it used to be ; but we can scarcely realize how great, under the best conditions, the gap is between the freedom of the home and the constraints of the schoolroom, where forty or fifty children have to be controlled by a single teacher. To those parents who believe in the usefulness of the kinder- garten and have not the opportunity to send their children to one, the proposition to establish sub-primary classes ought to be very welcome ; for certainly more of the spirit of the kin- dergarten can be infused where there is large opportunity given for the gifts, occupations and games than in the ordinary pri- mary school, where so much formal work is required. In places where the kindergarten is forbidden through ignorance of its benefits, or where it does not exist through lack of means, the establishment of the proposed grade will not be difficult to bring about. Indeed, in places where the age of admission is five years, it lies wholly in the hands of the school authorities to carry the plan into effect, inasmuch as it would simply take the place of the first-grade primary. There is another, and, I believe even stronger, argument for the formation of the proposed class ; and that is, the claim that 30 too much formal and too little observational work is now done in the first year of school. Children five years of age can no doubt do a prodigious amount of formal work. They can read through a dozen first readers, write a good hand, go to a hun- dred or a thousand in numbers, and perhaps read music in three keys, — all during the first year. But the question is, Ought they to do it? Ought they to do half or quarter as much? A fair answer to this question will, I am sure, lead us to revise the primary course, as now generally pursued, in the direction of the plan proposed. The course to be pursued in the sub-primary class will de- pend somewhat upon the previous training of the children ; but in any case the program will consist of an extension of the work of the kindergarten, especially along observational and manual training lines, with a comparatively small amount of reading, writing and arithmetic. The following general out- line may suggest the character of the exercises most desired for the proposed class. The grouping and limitations of time are those given in the time program on a previous page of this report. Groups I. and IV. — (Time spent daily in recitation and busy work for a single group of pupils, about 90 minutes.) Story telling, — selections from kindergarten stories, myths and fairy tales. Reading of words in sentences on blackboard and chart and on picture slips. Reading sentences from black- board and chart. Phonic drill. Some analysis and synthesis by sounds. Writing on tracing slips, blackboard and paper. Large movements. Group II. — (Time spent daily, about 15 minutes.) Fourth and fifth kindergarten gifts for counting and combining. Group III. — (Time spent daily, about 45 minutes.) Recog- nition of common plants and trees, and their principal parts. Observation of and talks about familiar domestic animals and birds. Some resemblances and differences noted. Adaptation of parts to uses observed. Group V., — including physical exercises, singing, games, drawing and hand work. (Time spent daily, about 90 min- utes,) Construction and design, with tablets, sticks and blocks. Moulding in clay. Painting in color with brush. Paper fold- 31 ing and parquetry. Free illustrative sketching from memory and imagination. For physical exercises and singing, make selections from kindergarten songs and games. Outline of a Course of Studies for Primary and Grammar Schools. The following outline suggests a possible adjustment of primary and grammar school work to the conditions indicated in this and in previous reports. While it is probably insuffi- cient to meet fully the needs of any system of schools, it is hoped that it will fulfil in some degree the requirements of a general course, upon which more detailed courses may be constructed suited to various localities and conditions. The absence of repeated directions to review previous work and to follow proper lines of teaching indicates the presumption of professional ability on the part of teachers. A course of studies is not a manual of methods and theories of teaching, however important such a statement of methods and theories may be in some places. Happy is it for those schools whose courses of studies may presuppose the employment of teachers whose knowledge of the principles of teaching is undoubted, and whose judgment is fully trusted in the selection of mate- rials within the bounds of an outline not greatly extended. It should be understood that this course is intended for pupils who enter school at six years of age, and who come either from the kindergarten or sub-primary class. Some pupils who have taken the course outlined for the sub-primary class may be able to take the work outlined for the first grade in less than a year. The figures in the left-hand column indicate the year and quarter during which the work in parallel columns is supposed to be done. For example, 2 3 means the third quarter of the second year. The figures in decimals above each year's out- line of work denote the approximate percentage of recitation time which a pupil or a group of pupils should give to the allotted group of subjects. 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