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 PROBLEM-SOLVING OR PRACTICE IN THINKING 
 
 By 
 
 SAMUEL CHESTER PARKER 
 
 Professor of Educational Methods 
 The University of Chicago 
 
 Reprinted from the Elementary School Journal 
 
 Yh\. XXI, Nos. I, 2, 3, 4, September, October, 
 
 November, December, 1920 
 
Copyright 1921 By 
 Samtjel Chester Parker 
 
 All Rights Reserved 
 
 Published January 19 21 
 
 M 15/921 
 
 0)CI.A604987 
 
^.oV 
 
 /( 
 
 PROBLEM-SOLVING OR PRACTICE IN THINKING 
 
 SAMUEL CHESTER PARKER 
 School of Education, University of Chicago 
 
 Definite technique established. — During the past twenty-five 
 years a definite technique of giving to pupils practice in problem- 
 solving or thinking has been developed in progressive American 
 elementary schools. It is the purpose of this series of articles to 
 acquaint more teachers with this technique so that any skilled 
 teacher who is a good thinker may give pupils practice in problem- 
 solving and make them aware of the elements of skill in effective 
 thinking. In order to show the importance and vahdity of the 
 practices to be described we shall also discuss the place of problem- 
 solving in everyday life and the ways in which great problem- 
 solvers think. 
 
 Sections of the discussion. — We shall divide our discussion into 
 four sections, as foUows: I. Problems of everyday life. II. Actual 
 lessons illustrating problem-solving in school. III. How skilled 
 problem-solvers think. IV. Rules for training pupils in effective 
 problem-solving. 
 
 I. PROBLEMS OF EVERYDAY LIFE 
 
 A problem is a question involving doubt. "To be or not to be. " — 
 For our purposes a problem may be defined as "a question involv- 
 ing doubt. "^ From this point of view the problem frame of mind 
 is well depicted in Hamlet's famous lines beginning, "To be or 
 not to be, that is the question." Whenever we thoughtfully 
 search for means of dealing with any such doubt or perplexity or 
 uncertainty or difficulty, we are engaged in reflective problem- 
 solving. The problem may arise from some practical difficulty or 
 from mere curious wondering about some unexplained or unusual 
 fact. Such a practical problem as "Where shall I spend my 
 
 ^ This definition is based on Webster's International Dictionary. 
 
2 THE ELEMENTARY SCHOOL JOURNAL [September 
 
 vacation?" often causes the most profound thinking and inquiry. 
 Similar investigation is often entailed in deciding whether to go to 
 college or to enter business. After one has decided upon a certain 
 resort for his vacation or a certain school for his education, the 
 clothes problem or baggage problem may become crucial. You 
 may say to yourself, "To take a suitcase or a trunk, that is now 
 the question." If a suitcase is decided upon, the problems may 
 become very minute, such as, "To take this sweater or not, that 
 is the question. " 
 
 Large and small problems, from large policies to minute issues. — 
 Thus we see that the practical problems of life may vary from 
 momentous decisions, such as deciding upon a college education, 
 down to such minute matters as pondering whether to take or 
 leave a certain garment. In the larger responsible positions of 
 life we find the same contrast between large and small problems. 
 For example, a business executive has large matters of policy to 
 determine, such as how to increase his business, or how to keep his 
 salesmen full of ''pep" and make them skilful in selling, etc. On 
 the other hand, in his correspondence he solves scores of small 
 problems each day, many of which involve merely a moment's 
 glance at a letter and a half-minute's dictation of the answer. 
 In the life of a school superintendent or principal or dean the 
 same extremes occur. For example, at one time when I was 
 "deaning" I had the following large problems: (i) How to dis- 
 cover a talented young man to become my successor as dean. 
 To solve this required three years of exploration. (2) How to 
 improve the annual catalogue, so that it would be more easily 
 read by entering students. This required occasional editorial pon- 
 dering during four years. (3) How to reconstruct certain rooms 
 so as to provide more offices for an increasing faculty. Secur- 
 ing satisfactory plans for remodeling two particular rooms took 
 several months of occasional planning. At the opposite extremes 
 were the small, short problems of advising students who were 
 registering. On registration days from twenty-five to forty 
 students were advised. Each case usually took from one to ten 
 minutes and was determined in the Light of such questions as: 
 (i) What is the student planning to do in life ? (2) What are her 
 
ig20] PROBLEM-SOLVING OR PRACTICE IN TfflNKING 3 
 
 special talents? (3) What has been her previous training? (4) 
 What required courses does she have to take ? (5) What courses 
 are offered that will meet her needs? (6) How can conflicts of 
 hours be avoided ? 
 
 Need of training in both short problem-solving and prolonged 
 patient thinking. — The relative proportion of large and small 
 problems in life will influence our plans for organizing opportunities 
 for problem-solving in school. It is my impression that the small, 
 short problems play such a prominent part in the daily life of 
 most persons that we are justified in organizing in school thousands 
 of such problems, each of which may consume only from one to 
 ten minutes in its solution. At the same time we should provide 
 for solution large problems which may puzzle the students for one 
 hour or many hours, and thus train them to do the prolonged, 
 patient thinking that is required in the larger, longer problems of 
 later life. 
 
 Practical versus speculative problems; *' The Lady or the Tiger. " — 
 Up to this point our examples of problems have all been of a 
 practical nature in the sense that they related to practical plans or 
 actions, usually of the person who was solving them. It is impor- 
 tant to realize, however, that much problem-solving thinking in 
 daily life is concerned with purely theoretical or speculative ques- 
 tions, the answers to which are not needed by the thinker in order 
 to determine some important hne of practical activity. To take an 
 extreme example, some years ago Frank Stockton, the well-known 
 writer, published a puzzling story called "The Lady or the Tiger." 
 This story tells of a lowborn hero who dares to woo a princess. 
 The king opposes the match and casts the hero into the arena, 
 where he must choose between two doors. If he opens one, a 
 tiger will come out and devour him. If he chooses the other, a 
 woman whom he must then marry will appear. The princess, 
 in the balcony, knows the secret of the doors. She gives her hero 
 lover a sign and he opens one of them. The story ends with the 
 question, which comes out — "The Lady or the Tiger ?" 
 
 Girls puzzle over princess' choice. — When this unexpected puz- 
 zling ending to the story appeared, the country got into a turmoil 
 of discussion in an effort to solve the problem. I watched a class 
 
4 THE ELEMENTARY SCHOOL JOURNAL [September 
 
 of high-school Freshmen recently discussing it. One girl said she 
 had read every line about the princess eleven times in an effort to 
 determine whether the princess' love and jealousy would lead her 
 to indicate the door of the lady or the door of the tiger. 
 
 Playful speculation abounds in politics, religion, and science. — 
 Other examples of such unresponsible problem-solving occur in 
 politics, religion, and science. The chief mental recreation of 
 many persons consists in puzzling over the political issues of the day, 
 issues that are often so remote that the thinkers have absolutely 
 no possibility of modifying matters in a practical way. Arguments 
 about the Bible are often of a similar unpractical character. 
 Finally, in the realm of science we find all types of inquiring 
 persons, from the young boy who puzzles over pollywogs and elec- 
 trical bells and flying machines, up to the advanced astronomer who 
 tries to locate a new comet or planet — all concerned merely with 
 *' Why does it do that?" or "How does the thing work?" or 
 "Where is the planet that explains these gaps in our calculations ? " 
 
 'Playful puzzling may train for practical problem-solving. — Often 
 such playful puzzling proves of value to the problem-solver and to 
 society. For example, the adolescent girls who puzzled about love 
 and jealousy as exempHfied in, Stockton's princess probably were 
 acquiring knowledge and skill in judging some of the most 
 crucial issues of Ufe; issues to which we find our greatest novelists 
 and dramatists devoting their best talents. Similarly, the inquiring 
 reader who ponders with interest political issues that do not concern 
 him in a practical way is acquiring knowledge and skill which may 
 help him in arriving at sound decisions upon political issues in 
 which he does have a voice. The way in which playful, theoretical, 
 or speculative problem-solving thus prepares for practical problem- 
 solving is merely one example of the way in which play in general 
 trains for serious activities. Dogs play at running, catching, 
 biting, and fighting and are thus prepared for the real fighting and 
 hunting of life. Men, women, and children play at puzzling out 
 all kinds of interesting problems and may thus be trained and kept 
 in condition for more serious problem-solving when this is required. 
 
 Great variety of problems in social life: mechanical, diplomatic, 
 moral, expressional, aesthetic, scientific, mathematical. — The examples 
 
1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 5 
 
 discussed above have given us some notion of the varieties of prob- 
 lems found in everyday life. In order to extend our impressions 
 of the many types of problems that exist, we may note the following 
 partial classification of them. 
 
 1. Mechanical construction problems, i.e., problems of how to 
 make something. These may vary from the small but very puzzKng 
 problem of how to "make over" an old garment, up to such a 
 complex scientific problem as how to make a flying machine— a 
 problem that puzzled the world for centuries. Many construction 
 problems are now provided in elementary schools. It is important 
 to notice that in the present chapter we are interested in the 
 thoughtful planning and designing that enter into the solution of 
 such problems, rather than in the actual mechanical construction. 
 
 2. Transportation problems, i.e., problems of how to take or send 
 something to some place. These may vary from the simple personal 
 problem of how to get a parcel to a friend around the corner up 
 to the enormous transportation problems that confronted the 
 Allies during the war. Such problems occur in aU kinds of situa- 
 tions. For example, in department stores there is the problem of 
 transporting the money from the salesmen to the cashiers. In 
 large libraries enormous problems of human energy and conven- 
 ience are involved in the stacking and arranging of books so as to 
 render their transportation to readers swift and economical. In the 
 courses in history, civics, geography, and science problems of trans- 
 portation are being pondered more and more in progressive schools. 
 
 3. Problems of personal relations, reactions, and influences, e.g., 
 "Would Stockton's princess prefer to see her lover devoured by 
 the tiger or to see him become the husband of another woman?" 
 In daily life we are constantly pondering such human-nature 
 problems. Often they are of a diplomatic character, e.g., how to 
 influence our relatives, friends, and associates. Recently I pon- 
 dered for two days how to present a business proposition to a 
 certain man. At first I decided to write an outline of it, lay it 
 before him, and explain it. On my way to see him, however, I 
 decided that he so disliked Hstening to others that the only thing 
 to do was to let him talk and then gradually insinuate my own 
 proposals piecemeal, as occasion offered, during his conversation. 
 
6 THE ELEMENTARY SCHOOL JOURNAL [September 
 
 This proved successful. In all the social studies — history, civics, 
 biography, literature, etc. — personal relations, reactions, and 
 influences appear which offer opportunities for problematic dis- 
 cussions that train pupils in solving such human-nature problems 
 when they are encountered in daily life. 
 
 4. Problems of social organization, such as "How shall we 
 organize our literary society ? " or "Which is better, for the govern- 
 ment to own and operate the railroads or merely to control and 
 supervise their operation?" From the simple organization of 
 domestic activities up to such international organizations as the 
 League of Nations we find thousands of problems under this 
 heading. In the social studies, when properly taught, pupils are 
 given training in planning, suggesting, criticizing, and evaluating 
 solutions of such problems. 
 
 5. Moral problems, such as "Is it right for me to accept an 
 education and services from my parents without making any 
 immediate return in the form of home service?" Literature, 
 biography, history, civics, and school activities are full of moral 
 problems which especially competent teachers have pupils ponder 
 and solve with benefit to their future powers of moral discrimination. 
 
 6. Expressional problems, e.g., "What is the best way to word 
 my refusal of this invitation ? " or "How shall 1 write this chapter ?" 
 In planning to write the present series of articles I pondered for 
 weeks whether to open it with this section on problems of daily 
 life or to open with actual lessons illustrating problem-solving in 
 school. I finally decided to place the lessons as the second section, 
 but I am not sure that this is the best order. Thus expressional 
 problems vary from the simple choice of a word up to the large 
 outlining and planning of a book or outlining a whole series of 
 addresses. Training in expression in school thus offers one of the 
 best opportunities for training in problem-solving. 
 
 7. Artistic problems, e.g., "What is the most pleasing arrange- 
 ment of the pictures in this room ?" or "What is the most pleasing 
 way of massing the shrubbery in this park?" or "What is the 
 most pleasing color scheme for this window display?" In the art 
 courses reflective thought about such problems is now encouraged 
 in many schools. 
 
igso] PROBLEM-SOLVING OR PRACTICE IN THINKING 7 
 
 8. Pure science problems, e.g., "Why does the mist hang in 
 clouds a short distance up the mountain, but disappear lower 
 down ? " or " Is the interior of the earth a molten mass or is it rigid 
 and solid?" We are all famiHar with such problems from our 
 high-school science courses. In the grades, instruction in geog- 
 raphy and science is being improved so as to offer increasing 
 opportunities for pupils to puzzle out answers to scientific problems 
 instead of merely learning scientific facts. 
 
 9. Purely mathematical problems, e.g., "How do I calculate 
 the amount of income tax that I have to pay?" or "What is the 
 best way of auditing the report of the treasurer of our society in 
 order to verify his accounts ? " Not only in arithmetic, but also in 
 manual training, geography, science, and civics, pupils in pro- 
 gressive schools are being trained in puzzling out problems of 
 arranging quantitative data and determining quantitative relations 
 in order to prepare for the mathematically precise scientific 
 method of problem-solving which is playing an ever-increasing 
 part in solving modern civic, philanthropic, and business problems. 
 
 These examples suggest the large social value of training in prob- 
 lem-solving. — Several other types of problems could be described, 
 but sufl&cient has probably been said to serve the purpose of this 
 introductory article, namely, to give the reader a notion of the 
 importance of the type of learning and training which we have 
 under discussion. In discussions of handwriting and spelling it is 
 possible to present the results of precise investigations showing 
 just what degrees of handwriting skill and what spelling words are 
 important in everyday Hfe. For problem-solving we do not 
 possess similar precise information, but our numerous examples up 
 to this point have probably served to impress the reader with the 
 frequency of the occasions for problem-solving in daily life, and the 
 consequent desirabihty of training pupils to be skilful problem- 
 solvers. 
 
 Origin of problems — in something puzzling, perplexing, confusing, 
 disconcerting, unexpected, queer, strange, or odd.—Beiore proceeding 
 to the discussion of sample lessons which illustrate the organization 
 of such training it is desirable to get in mind the idea with which 
 this article opened, namely, that a problem involves both a certain 
 
8 THE ELEMENTARY SCHOOL JOURNAL [September 
 
 intellectual and a certain emotional mental condition in the thinker ; 
 a problem is a question involving doubt. Consequently, for our 
 purposes, a problem is not merely a topic, as it often appears to be 
 in some courses of study, nor is it merely a question. It is a type of 
 mental condition in the pupil, a condition in which he is possessed 
 of a question plus doubt. The more doubtful, uncertain, and 
 perplexed he is the more intense is his problematic frame of mind. 
 Creating such a state of mind in the pupils, consequently, is the 
 starting-point of problem-solving activity. Several words to 
 describe this initial frame of mind have been brought together by 
 Professor John Dewey, our leading authority on reflective thinking, 
 in his excellent book entitled. How We Think. In one place 
 (p. 12) he says, "The origin of thinking is in some perplexity, 
 confusion or doubt." Again (on p. 74) he speaks of "something 
 unexpected, queer, strange, funny [i.e., odd] or disconcerting" 
 as furnishing the starting-point for reflective inquiry. FinaUy 
 (on page 9) under the heading "the importance of uncertainty," 
 he speaks of a "genuine problem" as existing in "whatever — no 
 matter how slight and commonplace in character — perplexes and 
 challenges the mind so that it makes belief at all uncertain." 
 
 Genuine problem for pupil when mentally challenged by something 
 strange, perplexing, unexpected, or disconcerting. — From these 
 terms we may derive a meaning for the rather ambiguous statement 
 that has been current, namely, that the problem must be a problem 
 for the pupil, not merely for the teacher. In terms of our dis- 
 cussion, this means that the starting-point for the pupil must be 
 something — no matter how slight or commonplace in character — 
 that puzzles or perplexes him; something that appears to him as 
 unexpected, queer, strange, odd, or disconcerting. When his mind 
 is challenged by such matters the pupil has a genuine problem. 
 It may be practical or it may not. It may be merely something 
 "frnmy" in the sense of being unexpected or strange; in fact, much 
 of our most intense problem-solving thinking by adults and 
 children occurs in response to just such "funny" unexplained 
 phenomena. 
 
 Presented problems and discovered problems. — Sometimes prob- 
 lems are "presented" to a person in daily life, and at other times 
 
I920] PROBLEM-SOLVING OR PRACTICE IN THINKING 9 
 
 he seems to "discover" them. The common use of the expression, 
 "the problem then presented itself," suggests the frequency of the 
 first type of appearance of a problem. Many mediocre thinkers 
 never seem to feel a problem at all keenly unless it is vigorously 
 "presented" to them by some obvious difl&culty, such as missing 
 a train or having no money to buy something to eat. They are 
 perfectly complacent mentally except in the face of some such 
 vital emergency. At the opposite extreme we find persons who 
 are of such an inquiring frame of mind that they are continually 
 poking around and turning up doubtful questions or problems in 
 all kinds of unexpected places. 
 
 Presented problems abound in practical afairs. — In practical 
 affairs we meet frequent occasions both for solving "presented" 
 problems and for " discovering " problems. For example, a business 
 executive or manager is "presented" with a batch of problems 
 every time he reads his mail or listens to questions from his 
 subordinates or customers. A busy executive solves scores of 
 problems a day which are presented to him in this manner. One 
 of the greatest elements of skill in executive work is the ability to 
 decide rapidly many such problems as they are presented. Con- 
 sequently, when we present pupils in school with many problems 
 which they did not originate, but which they must solve rapidly, 
 we are paralleling one of the most important t5^es of problem- 
 solving in practical hfe. 
 
 Discovering problems, illustrated by inquiring experts. — -On the 
 other hand, the discovering of problems is constantly illustrated in 
 practical affairs when an expert examines a situation with a view 
 to improving it. For example, a friend of mine has just taken 
 over the management of a large business and one of the first ques- 
 tions he asked was, " When do you have your salesmen's meetings ? " 
 The old manager said they did not have any meetings, and was 
 surprised when my friend pointed out that this was a serious defect 
 in the organization. It is becoming more and more common to 
 employ consulting experts (for example, in making school surveys) 
 who visit a situation and by prying here and there with their ques- 
 tions uncover many problems which the "home folks" never 
 
lo THE ELEMENTARY SCHOOL JOURNAL 
 
 realized were there. The importance of organized training for 
 this type of activity is stated by Judd when he says: 
 
 Not merely the solution of problems suggested by one's own experiences, 
 then, constitutes the end and aim of school training, but the discovery of new 
 problems is an important part of education. Youth is a period of learning to 
 see problems as well as learning to solve problems.' 
 
 Group discussions and individual solution. — Sometimes the 
 problems which are thus presented or discovered are solved by an 
 individual working alone, but frequently group discussion plays a 
 very large part in the solution. Even where one individual does 
 most of the thinking which attains the solution, he is often greatly 
 aided by a few moments of discussion with someone else. In 
 organized business and social Hfe many of the crucial decisions, 
 such as occur in undertaking new business ventures or passing new 
 laws or trying cases in court, are reached only after many hours of 
 problem-solving discussions by groups of persons. Hence, while 
 it is important to train individual pupils in school in the solving of 
 problems, it is equally important that they be given practice in 
 problem-solving discussions so as to give them skill in this important 
 social art. 
 
 Reflective problem-solvers to be trained, not impulsive ones. — • 
 Finally, before turning to the sample lessons which will illustrate 
 how pupils are actually given practice in the art of problem- 
 solving, we may note that we desire to produce reflective problem- 
 solvers, not impulsive ones. To reflect means to turn the matter 
 over in the mind, to view it from various angles, to consider carefully 
 the various possibiHties of solution. To develop skill in securing 
 the true solution of problems by such reflective study is the topic 
 of these articles. In the next instalment we shall describe sample 
 lessons which show just how skilled teachers give such training. 
 
 ^ C. H. Judd, "Initiative or the Discovery of Problems," Elementary School 
 Teacher, XHI (1912), 153. 
 
PART II 
 
 Synopsis of preceding article. — The preceding article was concerned with 
 "problems of everyday life," and brought out the following points: i. Such 
 problems vary from very large questions of policy to minute issues requiring 
 only a moment's thought for their solution. 2. Consequently, in school we 
 need many small problems as weU as larger ones. 3. Both practical problem- 
 solving and speculative problem-solving prevail in daily life. 4. Playful, 
 speculative problem-solving, "just for fun," is a very characteristic human 
 activity and has large social value. 5. The great variety of problems found in 
 daily life appears when we try to classify them as mechanical, diplomatic, 
 moral, expressional, aesthetic, scientific, mathematical, etc. 6. Consequently, 
 training in problem-solving may be provided in many subjects in the school 
 7. In order to start problems for pupils, we must know what a problem is 
 psychologically and how it originates. 8. For our purposes, a problem may be 
 defined as a question involving doubt. 9. Problems originate in something 
 puzzling, perplexing, confusing, disconcerting, unexpected, queer, strange, or 
 "fimny." 10. When a pupil's mind is challenged by something of this nature, 
 he has a genuine problem. 11. Both "presented" problems and "discovered" 
 problems abound in daily life. 12. Sometimes everyday problems are solved 
 by an individual working alone, but many are solved by problem-solving group 
 discussions. 13. Hence, practice in the solution of group problems through 
 group discussion trains pupils in a very useful social art. With this social 
 setting of problem-solving in mind we shall turn our attention to a number of 
 actual lessons which will illustrate how training in problem-solving has been 
 organized by progressive teachers. 
 
 II. ACTUAL LESSONS ILLUSTRATING PROBLEM-SOLVING IN SCHOOL 
 
 A. Seventh Grade: Should the United States Produce Its 
 Own Sugar ? 
 
 Illustrates results of preceding training in problem-solving. — The 
 first lesson which we shall describe is taken from an upper-grade 
 class in order to illustrate what large issues may be considered 
 reflectively by pupils who are about to graduate from an elementary 
 
12 THE ELEMENTARY SCHOOL JOURNAL [October 
 
 school in which training in problem-solving is provided from the 
 kindergarten up. After presenting this upper-grade example, we 
 shall describe lessons from the kindergarten and the second and 
 fifth grades, in order to illustrate the gradual progress in the pupils' 
 reflective abilities as they advance through the grades. All the 
 lessons are from the Elementary School of the University of Chicago, 
 but similar instruction may be found in hundreds of progressive 
 schools throughout the country. The seventh-grade geography 
 lesson which we shall present first was taught by Miss Edith Parker.^ 
 Relation to preceding lessons. Pupils reviewing various factors 
 in America's progress. — The class was reviewing the geography of 
 the United States, following a previous study of it in the fourth 
 grade some years before. As the University Elementary School 
 completed its work in seven years, the culmination of the geography 
 training was so organized at the end of the seventh grade that it 
 gave the pupils an opportimity to use their geographic knowledge 
 in considering certain large geographic problems of their native 
 country .2 As this class was studying the country in 191 9, shortly 
 after the close of the war, they had been especially impressed with 
 the marvelous achievements of the United States and had become 
 interested in the following large question as the basis of the review: 
 "What are the factors that make the United States such a great 
 nation ?" In discussing the matter, they had brought forward a 
 number of geographic factors such as the location and size of the 
 country, its varied topography and natural resources, the char- 
 acter and amount of immigration, etc. For a few days they had 
 concerned themselves with ascertaining the relative achievements 
 of the United States and other countries in crop production. They 
 had studied the cotton and corn crops, and had waxed enthusiastic 
 
 ' To satisfy the curiosity of the reader, I may say that Miss Parker and the author 
 of these articles are not related. Hence it is not inappropriate for me to remark that 
 Miss Parker's technique in conducting problem-solving lessons is a model of artistic 
 teaching of this type. We shall describe some of her fifth-grade geography lessons 
 later in these articles. 
 
 ^ For a description of the course in geography in this grade, see the Elementary 
 School Journal, XVIH (December, 1917), 271-79. For an article illustrating Miss 
 Edith Parker's general procedure in organizing a large project problem in geography, 
 see her paper entitled "The Partition of Africa— A Seventh-Grade Geography Unit," 
 Elementary School Journal, XX (November, 1919), 188-202. 
 
1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 13 
 
 over our production of these staples. They next turned their 
 attention to sugar production, and it was at this stage that the 
 lesson which I shall describe occurred. 
 
 Pupils disconcerted by small sugar production. Problem keenly 
 felt. — After some preliminary discussion, Miss Parker raised the 
 chief problem for the day by pointing to a graph which she had 
 drawn on the blackboard. The pupils examined it and found that 
 the United States produced in a given year only one-fifteenth of the 
 world's supply of sugar, but consumed one-fifth. After their earlier 
 findings of the enormous production of cotton and corn in America, 
 and their general contention that a great nation should try to be 
 self-sufficient in its production of the necessities of life, many of 
 the pupils were nonplused at this revelation of the sugar situation. 
 Many of them were greatly disconcerted, perplexed, and puzzled 
 by this unexpected shock to their enthusiastic national complacency. 
 A psychological problem situation had been skilfully and easily 
 created by the teacher. The current shortage of sugar served to 
 make the problem felt even more intensely. 
 
 Problem clearly defined. Proposition to increase production 
 written on the board. — The problem was then clearly presented for 
 solution. "If we produce only one-fifteenth and use one-fifth of 
 the world's supply of sugar, what should we do about it?" Some 
 pupils suggested that we use less; others that we grow more. One 
 pupil finally presented a clear proposition that we produce as much 
 more sugar as possible in order to try to meet our domestic needs. 
 Miss Parker deliberately wrote this on the board and then asked 
 all the pupils to decide if they agreed with it. They all did. 
 
 Search for solution. Geographies consulted to determine possi- 
 bility of raising more. — The question then arose, why, if this 
 was advisable, hadn't the country done it before ? In answering 
 this question, attention became centered on the word "possible" in 
 their proposition to produce more, and the teacher asked the pupils 
 how they could find out whether it would be possible for us to 
 raise more sugar. The pupils suggested looking up in their geog- 
 raphies the maps and other data showing the areas of possible 
 sugar production and the conditions governing it. They decided 
 to deal with cane sugar first. 
 
14 THE ELEMENTARY SCHOOL JOURNAL {Octoher 
 
 Pupils suggest conditions; get data from maps; decide greater 
 production is possible. — In reply to Miss Parker's question concern- 
 ing the conditions which they would have to ascertain, the pupils 
 replied "number of growing days," "suitable soil," and "amount 
 of rainfall." She wrote these items on the board, as she had done 
 with a number of other crucial points in the discussion. Following 
 their suggestion to ascertain the number of growing days needed, 
 she directed the pupils to turn to their geographies where they 
 found a map of the United States with a line showing how far north 
 cane could be grown. They then compared this map with one 
 showing actual cane production, and decided that as far as number 
 of growing days was concerned, much more cane could be grown. 
 Similarly they took up suitable soil conditions and rainfall and 
 arrived at similar conclusions. 
 
 Teacher verifies pupils' conclusion by reference to a special 
 treatise. — In order to verify their conclusion. Miss Parker read 
 from a special book on sugar a statement to the effect that there 
 were thousands of acres in the country in which conditions were 
 favorable for raising sugar cane that were not being used for this 
 purpose. 
 
 Teacher held discussion to " possibility '^ before considering 
 "profit." — As all these data were being produced and were gradually 
 bringing out the possibility of easily producing more sugar in the 
 United States, one boy kept suggesting that it might not be profitable 
 to do so. Miss Parker made a memorandum of his suggestion on 
 the board for later discussion, but suggested that they finish the 
 investigation of the crop possibilities before they took up questions 
 of profit, since the fundamental proposition to which they had all 
 agreed and which was written on the board stated that more should 
 be grown if possible. Some difficulty was experienced in getting 
 the boy to give up his idea of considering profitability before 
 determining possibility. 
 
 PupiVs suggestion of lack of profit examined. Uncertainty about 
 original proposition. — However, after the possibility had been 
 definitely proved, Miss Parker turned to the issue of profit. The 
 pupils readily saw that what is possible is not necessarily profitable, 
 and began to think that maybe their proposition to which they 
 
ipso] PROBLEM-SOLVING OR PRACTICE IN THINKING 15 
 
 had all assented at the beginning, namely, to produce enough sugar 
 to meet our needs, might not be sound. In considering why the 
 South had not raised more sugar cane, since it is quite possible, 
 they suggested two important factors, namely (to use their own 
 language), "competing crops" and "cost of labor." They stated 
 that probably portions of the South found cotton and other crops 
 more satisfactory than cane, and that labor in Cuba was probably 
 cheaper than in the southern states. 
 
 Pupil suggested tariff. Teacher left it an open question. — Thus 
 they concluded that the United States did not produce enough sugar 
 to meet its own needs because it could be imported so cheaply 
 that the farmers found it more profitable to raise other crops. 
 The period was almost ended. Hence, in order to relate the day's 
 problem concerning sugar to the larger issue concerning the great- 
 ness of the United States and its self-sufl&ciency in producing the 
 necessities of life. Miss Parker again raised the question of what 
 we should do about the sugar problem. One boy suggested that 
 we place a tariff on sugar. Miss Parker asked, "Who would pay 
 the tariff ?" The pupils said, "The people of the United States." 
 "Who are the people of the United States?" she then asked. 
 "We are," they said. She then asked if it seemed wise to make 
 every family in the United States pay more for its sugar by means 
 of a tariff in order that the coimtry might produce enough sugar 
 to meet its own needs. Without waiting for an answer, she con- 
 cluded the hour by saying, "This is a problem upon which the 
 greatest American statesmen disagree, and to which Congress 
 devotes long discussions." 
 
 PRINCIPLES ILLUSTRATED BY SEVENTH-GRADE PROBLEM-SOLVING LESSON 
 
 Broad flexible grasp of subject-matter needed by teacher in such 
 lessons. — This type of geography teaching is becoming common 
 in schools where a special departmental teacher is employed to 
 teach the subject in the middle and upper grades. It is obvious 
 that the teacher needs a thorough mastery of the subject-matter 
 of geography if the discussions of the pupils are to be as flexible and 
 broad as in the foregoing lesson. The teacher in such a case has 
 to be familiar not only with such large issues as the question of 
 
1 6 THE ELEMENTARY SCHOOL JOURNAL [October 
 
 protecting native sugar production by means of a tariff but also 
 with such details as the number of growing days required to mature 
 sugar cane. 
 
 Broad knowledge anticipates issues and prepares scientific data. — 
 It is important to note, however, that when a teacher is thoroughly 
 informed concerning the problem imder discussion, as Miss Parker 
 was in this case, she can anticipate the various issues that will 
 arise, have ready the necessary scientific treatises and references, 
 and guide the discussion so that it follows important scientific lines 
 instead of being sidetracked on minor or irrelevant issues. Thus 
 Miss Parker realized in advance that the pupils would need to use 
 the map showing sugar-cane production, and to save time had a 
 memorandum prepared of the page on which it was to be found. 
 She knew that the pupils would reach certain conclusions that 
 needed verification, and she had on hand a special treatise on 
 sugar and a certain report of the Department of Agriculture, 
 with memoranda of the pages upon which the verifications could 
 be based. 
 
 Pupils suggest and evaluate data and procedures. — Yet, with all 
 this definite anticipation, planning, and direction by the teacher, 
 the pupils carried the main burden of solving the problem — they 
 made all the important suggestions and evaluated most of them. 
 Their suggestions included not only matters of fact, such as the 
 necessity of enough growing days and of suitable soil, but also 
 methods of procedure, for example, suggestions that they examine 
 certain maps in their geographies to find certain data. These 
 suggestions of procedure went even farther and included decisions 
 concerning how the question should be subdivided and which phase 
 should be taken up first, etc. For example, early in the hour the 
 question arose whether to consider the possibilities of increased 
 production of cane sugar or of beet sugar. Miss Parker had the 
 pupils decide which of these should be investigated first. They 
 chose cane sugar and held to it. 
 
 Points of technique in problem-solving lesson. Rapid view. — 
 Before turning to other lessons which will further illustrate the 
 special technique to be used by a teacher in guiding problem- 
 solving by pupils, we may note briefly some points of such technique 
 
1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 17 
 
 as is illustrated in this lesson. It is not necessary to study these 
 carefully at this point, as most of them will be illustrated repeatedly 
 in the later lessons and will be summarized in Section IV of the dis- 
 cussion. However, the cumulative effect of frequent reference to 
 them will be helpful. Miss Parker's lesson, then, had the following 
 general characteristics found in the artistic direction of problem- 
 solving discussions. 
 
 1. She created an intense problem frame of mind by discon- 
 certing the pupils with a graphic representation of the contrast 
 between our large consumption and relatively small production of 
 sugar. 
 
 2. She had the problem for discussion clearly formulated and 
 wrote it on the board. 
 
 3. She kept the problem clearly before the pupils by frequent 
 reference to it as written. 
 
 4. She encouraged suggestions from the pupils not only in mat- 
 ters of fact or data but also in the matters of procedure, i.e., in 
 regard to such questions as "What shall we do next?" or "How 
 can we find out about that?" 
 
 5. She encouraged careful evaluation and criticism by the 
 pupils of the various suggestions. 
 
 6. She gave practice in the use of scientific treatises as the 
 source of data and as a means of verification. 
 
 7. She encouraged the attitude of desiring verification of 
 suggestions by reference to standard authorities. 
 
 8. She conducted the lesson at a deliberate pace, so that pupils 
 were required to think before answering. As a special device in this 
 connection, she occasionally said, "When you have your mind 
 made up, you may rise," and then waited until most of the pupils 
 had risen. 
 
 9. She kept the discussion organized along definite lines by out- 
 lining on the blackboard the various important suggestions that 
 were made, and then holding to the order in which they had decided 
 to pursue the discussion. In this way the main problem became 
 analyzed into a number of subordinate problems which were 
 disposed of in an orderly manner. 
 
 Small subordinate problems that arise give dull pupils a chance. — 
 These subordinate problems included some very large ones and 
 
1 8 THE ELEMENTARY SCHOOL JOURNAL [October 
 
 some small ones. Perhaps the largest that arose was the final one, 
 namely, "Should a tariff be placed on sugar ?" This seems almost 
 as large as the original dilemma, namely, ''Should the United States 
 produce all the sugar it needs?" Somewhat smaller were these 
 problems : "What factors make it improfitable to grow more cane ?" 
 and "What conditions are necessary to produce sugar cane?" 
 Still smaller were these problems: "How shall we find out how far 
 north sugar cane can be matured ?" and "How can we find out what 
 states produce sugar cane?" The breaking up of the large issue 
 into these smaller ones results m the lesson providing trainmg in 
 the solution of both large and small problems. Some of the duller 
 pupils, who might not be able to wrestle with the larger issues 
 involved, might readily suggest looking up a sugar-production 
 map and be able to read from it the data needed. 
 
 In the next lesson to be presented, namely, one from the kinder- 
 garten, we shall find such small, simple problems presented that 
 even five-year-old children can easily solve them. By reading 
 through the other lessons which are to follow, we can see how 
 children are gradually trained up to the point where they carry 
 on the high-grade type of reflective problem-solving illustrated in 
 Miss Parker's seventh-grade lesson on sugar. 
 
 B. Kindergarten Problem: How to Make the Front of 
 Cardboard Store 
 
 Contrast old-fashioned dictated constructions with new problem 
 type. — In the kindergarten and primary grades many of the prob- 
 lems which pupils solve concern how to make something. In the 
 old-fashioned kindergartens, it was customary to dictate to pupils 
 just what steps to take in constructing each object. There was 
 little room for reflective thinking by the pupils. In a modern 
 progressive kindergarten, on the other hand, large opportunities 
 are given to pupils to experiment in their constructions, and the 
 experimentation is made of a reflective thoughtful type through 
 class discussions which the teacher organizes. In order to bring 
 out the contrast between the old dictated type of constructive 
 activity and the newer experimental type, we shall present first a 
 lesson from an old kindergarten manual published in London in 
 1874, a.nd then follow with a modem problem-solving lesson in 
 
1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 19 
 
 making the front of a cardboard store. In the old manual the 
 "fifth gift" is described as consisting of twenty-seven small cubes 
 piled together to make one large cube. Some of the small cubes 
 were further subdivided into triangular prisms. Each child had 
 this material before him and, in the dictated exercises, all per- 
 formed the same operations as illustrated in the following quotation 
 in which the teacher addresses the children thus: 
 
 "Show me the top three cubes in front. Place them on the back three 
 cubes. What has our large cube become ? A flight of steps or a flower stand . ' ' 
 Then talk with the chfld about these objects. "Divide the flower stand into 
 three parts in length— what does it become?" "Three narrow flights of 
 steps." "Place the three together again. I take the middle step away, and 
 place the three cubes upon the top step— what have we now ?" etc. 
 
 While the pupils may be gaining in motor control and in ability 
 to follow directions in such a lesson as that quoted above, and may 
 even be quite happy in the process, it is obvious that they are not 
 being trained in thinking and are not acquiring much skill in 
 solving construction problems. 
 
 Problem lesson: How to make a suitable front for a cardboard 
 store. — In striking contrast with such mechanical dictated activity, 
 we find the following description of a lesson in the kindergarten 
 of the University of Chicago Elementary School in 191 8. The 
 problem which engaged the attention of each pupil was the making 
 of a suitable front for a small cardboard grocery store. The teacher 
 was Miss Olive Paine. 
 
 Relation to course of study in community life. — According to the 
 course in Community Life, History, and Civics in this elementary 
 school," the children in the kindergarten study the family in its 
 relation to the community. Needs of the family and the com- 
 munity as supplied by grocery stores furnish many problems. 
 The pupils engaged in the lesson to be described were almost ready 
 for the first grade. 
 
 Previous work. Trip to a grocery store. — The children had been 
 taken to a grocery store some days before, where they observed 
 the arrangement of the windows, doors, front of the store, shelves 
 inside of the store, articles on the shelves and in the windows, etc. 
 
 'See the Elementary School Journal, XVII (February, 1917), 397-404. 
 
20 THE ELEMENTARY SCHOOL JOURNAL [October 
 
 A store of large blocks previously constructed. — A store of some 
 considerable size had been constructed of large blocks and was 
 still standing in the recitation room. 
 
 Individual stores started. — The day before the lesson each child 
 had almost completed a small store made from heavy construction 
 paper or from a cardboard box. The new lesson centered in the 
 completion of a suitable front for each store. For this purpose 
 each child had been given a piece of construction paper somewhat 
 larger than the front of his store. Some children had already cut 
 out windows and doors in these sheets. 
 
 Problem for the day. Making suitable fronts. — The stores and 
 fronts were brought out. The fronts were to be criticized and 
 remade, if necessary. In short, the problem was the making of 
 suitable fronts for the stores. 
 
 WORKING OUT OF THE PROBLEM 
 
 1. Criticism of previous work. — ^As the teacher handed a child 
 his store and his front, she asked him to place the front in position 
 and see if he thought it was just as he wanted it to be. Sometimes 
 the windows extended out beyond the outside walls of the store. 
 Sometimes the doors and windows were higher than the store. 
 
 2. Children suggest modifications; finding how to fit the fronts. — 
 One child was asked how his front could have been made to fit the 
 store. He held the sheet of pasteboard in front of the store, and 
 folded it around the side. Miss Paine asked what that was for. 
 The child replied: "You could paste it tight to the store to hold 
 the front on." One child suggested folding the sheet over. The 
 teacher asked how. Various children made suggestions, and they 
 finally concluded the sheet might have been held up in front of 
 the store before the windows and door had been cut out. The 
 place at which to fold might have been marked with lines drawn 
 with a pencil. Miss Paine asked how they would have marked 
 straight lines. Finally, it was brought out that the sheet might 
 be laid on the floor and folded over in a straight line by placing the 
 edges of the top nicely together. Some of the children who needed 
 new sheets of paper received them.^ Each child was led to hold 
 
 ' An interesting dilemma arises in deciding how much to let children experiment in 
 such construction work. On the one hand it might be said that such experimentation 
 
i92o] PROBLEM-SOLVING OR PRACTICE IN THINKING 21 
 
 the sheet up in front and mark a place with the pencil; then to lay 
 the sheet on the floor and fold it over at one side; then to hold the 
 sheet up again and find the other side. 
 
 3. Deciding how to make doors and windows; crude idea by one 
 child. — Then the children were led to see that the doors and windows 
 must come in between the two folds thus made at the side. Some 
 wanted two windows and one door. This time one little girl (the 
 least able of the class, it seemed) cut a very narrow door about 
 twice as high as her store. She was asked why so high a door. 
 She said she wanted it that way. The other children said it was too 
 high. The girl then said it was for an upstairs. The teacher asked 
 if stores and houses had a high door that was for both the lower 
 floor and the upstairs. The child held out that hers was all right. 
 Finally the teacher gave her a new sheet and pretty closely directed 
 her work and tried to get the child to see proper proportions for 
 windows, door, etc.^ 
 
 4. Informal but directed designing and making: what next and 
 how. — The children worked on the floor in a perfectly informal 
 way. They were led to see what the next thing was and to want 
 to do that thing. How it could be done was discussed and worked 
 out very skilfully. Some of the children left the part cut out for a 
 window uncut at one end of the window. Some wanted to use this 
 to raise up for an awning, and some wanted it for a shelf under the 
 window. Evidently something of this kind had been done at some 
 
 with its erroneous results is necessary for children of kindergarten age in order to get 
 them to feel the need for the thoughtful planning which prevails in the lesson which 
 we are describing. On the other hand, some educators would favor more direction 
 by the teacher in order to avoid the waste of material incurred in this lesson. In the 
 steel industry, Carnegie would tear down and throw in the scrap heap an expensive 
 plant which had been in use only a short time in order to make way for another which 
 afterthought had shown to be better. How much should kindergarten children be 
 permitted similar waste in solving construction problems? A later article on the 
 nature of problem-solving will throw some light on the dilemma. 
 
 ^ Children with low-grade intellects are often unable to plan intelligently but can 
 acquire skill in motor arts, e.g., Goddard indicates that a certain type of moron can 
 learn to use machinery and care for animals and needs no supervision for routine 
 work, but cannot plan. It is a waste of time to try to train such pupils to be skilled 
 thinkers, but it is profitable to teach them practical motor arts by careful supervision. 
 For Goddard's convenient table showing some of the possibilities of the feeble-minded 
 see the author's General Methods of Teaching in Elementary Schools, p. 304. 
 
22 THE ELEMENTARY SCHOOL JOURNAL [October 
 
 other time. The observer doubted if that came out accidentally 
 on the part of so many without having been brought out at a 
 previous lesson. However, it was quite skilfully used by many 
 of the children. 
 
 5. Teacher suggests standards for comparison. — Miss Paine kept 
 bringing out the idea of size by comparison of the relative heights 
 of doors, windows, shelves, men, women, etc., in the store they 
 had seen and also in the store made of blocks. 
 
 6. Children vary ideas of hinges. — The number of hinges needed 
 for the door was discussed. One child had just one hinge and 
 seemed happy. She was sent to examine a door to find out how 
 many hinges other doors had. Different children decided that 
 two or three hinges would be best. One boy said four would be 
 best. He wanted that number. 
 
 7. Intercomparison and exchange of judgments by children. — • 
 The children were led to judge of the quality of their own work and 
 to supplement the judgment of others concerning their work and 
 to supplement the judgment of the teacher. 
 
 8. Fast children plan further work. — Two children were much 
 quicker and showed more ability in motor co-ordination than the 
 rest. They completed their windows and doors and were ready to 
 go on. They were asked what they wanted to do next. They 
 said, "Make a shelf." They were asked what they wanted to 
 make it out of . "Pieces of cardboard." The teacher handed one 
 a piece and asked if that would do. " It is too little," he said. The 
 teacher said they would make the shelves the next day, as the end 
 of the period had arrived. 
 
 9. Articles put away until next day. — The children were asked 
 to get their stores and fronts ready to put up. "How will you 
 know them?" asked Miss Paine. "Mark letters on them," they 
 said. Then they made their initials on the inside of the stores and 
 the fronts. Quite naturally they gathered up their scraps and put 
 them into the waste basket. 
 
 Evaluation of kindergarten problem-solving lesson. Remarks by 
 trained observer. — ^The foregoing account of the observed lesson, 
 except the paragraph headlines, was written by an experienced 
 teacher of high-school mathematics, Miss Mildred Harris, who 
 
1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 23 
 
 had become interested in problem-solving in general. She was in 
 the process of organizing her ideas of the technique of such teaching 
 while attending a class for supervisors of teaching. Consequently 
 the following comments which she made as a high-school mathe- 
 matics teacher observing a kindergarten construction lesson are 
 suggestive concerning the general matter of problem-solving. 
 
 1. Definite aims. — The object of the lesson was clear to both 
 teacher and children and was kept before the minds of the children 
 all the time. Suitable fronts for the stores were to be made. This 
 was the object in the minds of the children. In the mind of the teacher, 
 many purposes were in view. Each thing done was a preparation 
 for the next higher-level thing. Progressive development was 
 aimed at. This was evident in her questions, suggestions, etc. 
 
 2. Self-criticism by pupils. — Progress was made in the children's 
 criticism of their own work. Each child, as he worked on his own 
 front, was led to judge his own work from time to time as it was 
 completed at that stage. They were led to find out how they could 
 determine if it was just what they wanted it to be. This was one 
 of the parts of the recitation in which the teacher showed skill 
 above the ordinary. 
 
 3. Co-operative suggestion and evaluation. — The matter of 
 co-operative work, suggestions, etc., was brought out in supple- 
 menting criticisms of each other and of the teacher. The teacher 
 worked with the pupils and they worked together and yet each 
 child was busy with his own store front. 
 
 4. Encouraging pupils to make suggestions. — Independence on 
 the part of pupils was encouraged by such questions as "What 
 would you do?" "How might you do this time?" "Could you 
 do it this way ?" "If that is not just as you want it, how can you 
 make it as you want it to be?" 
 
 5. Responsibility for planning. — Each child was led to feel his 
 own responsibility for the making of his front, planning, etc. He 
 was first led to see what he wanted, and then he tried to find out 
 how he could make what he wanted. 
 
 6. Pupils interested. — The children were interested in their 
 own work. This was shown in the fact that they wanted to go on 
 even after the end of the period. 
 
24 THE ELEMENTARY SCHOOL JOURNAL 
 
 7, Teacher anticipated pupils' difficulties. — A child's probable 
 difficulty was anticipated. The teacher really kept a sharp lookout 
 on each child's work, although she seemed to be leaving the child 
 to do as he pleased. If she saw a child marking a place that would 
 result in the same error he was trying to avoid, she would ask him 
 questions and get him to try to find out if that mark was just right. 
 Sometimes she would ask a child who was about to get into trouble 
 to look at the work of another who was succeeding and see what he 
 thought of that. The child, without any suggestion, often got a 
 clue for his own work and proceeded. If not, the teacher suggested 
 something, etc. 
 
 8. Left a problem for next day. — The teacher left a problem in the 
 minds of the children to be worked out for the next day — how to 
 make the shelves on which to put the things they wanted in their 
 stores. 
 
 Note. — In the next article we shall describe sample lessons from the second and 
 fifth grades which will illustrate the practice in thinking that the pupils are given as 
 they progress from the simple construction problems of the primary grades up to the 
 ability demonstrated m the seventh-grade sugar-production lesson with which the 
 present article began. 
 
PART III 
 
 Synopsis of preceding articles. — ^The preceding discussion consisted of two 
 parts, (I) An account of the place of problem-solving in everyday life, and 
 (II) two sample lessons from the University of Chicago Elementary School. 
 These depicted (o) pupils in the seventh grade debating the possibility and 
 desirability of increasing America's sugar production, and (b) kindergarten 
 pupils engaged in designing and constructing cardboard grocery stores. The 
 present article will continue the sample lessons constituting section II of the 
 discussion and then introduce section III on "how great problem-solvers 
 think." 
 
 C. SECOND grade: how to dress an ARAB doll 
 
 Relation to course in community life. — The study of the pupils' 
 immediate enviromnent which we found illustrated in the kinder- 
 garten lesson on grocery stores is followed in the first grade by a 
 study of farm life and Indian life. These social types enrich the 
 pupils' ideas of human wants and needs and of means of meeting 
 these. In the second grade another strategic type of civilization 
 is encountered in the study of primitive shepherd life.^ Here the 
 Arabs of the desert were being studied when the lesson which we 
 shall describe was observed. The lesson occurred after the class 
 had been studying Arabs for some time. On the sand table the 
 children had made a desert, sand hills, and camel tracks, and had 
 planted some miniature palm trees. On the blackboard along one 
 side of the room were pictures of deserts, sand hills, and several 
 camels. The teacher was Miss Mary Cameron. 
 
 Conversation reported to illustrate details of technique. — In describ- 
 ing this lesson we shall report more of the language used by the 
 teacher and pupils in order to give a more detailed impression of 
 the mental activities of the class, and of certain details of the 
 
 ' For a full description of the study of shepherd life in this grade, see the Ele- 
 mentary School Journal, XVII (February, 1917), 411-16. 
 
26 " THE ELEMENTARY SCHOOL JOURNAL [November 
 
 teacher's technique. Only a part of the total conversation of the 
 pupils and teacher is reproduced, but enough is given to illustrate 
 the conversational method of teaching. To assist the reader 
 in following the conversation, the teacher's part is printed in 
 italics.^ 
 
 Problem for the day. — In the teacher's mind, the problem for the 
 day was a study of the dress of the Arabs. The fundamental aim 
 was to clarify and enlarge the ideas of the children concerning 
 costumes. In the minds of the children, it was dressing dolls to 
 people their desert. 
 
 Procedure: (i) Children suggested several things that needed to 
 be done. — "We have finished our oasis and desert. What shall we 
 do today?" asked Miss Cameron. The children replied, "Make 
 some camels." "Make some Arabs." "What Arabs would you like 
 to make?" "Some traveling Arabs." "We can make some tents, 
 too," said one child. "How many Arabs shall we make?" 
 "Twelve." "But," said the teacher, "our sand table is not very 
 large." "Let's make two tents and two families," came from a 
 little girl. "How many do you want in your family?" "The 
 father, the mother, and a little boy or a little girl." "All right," 
 said Miss Cameron, "or there might be both a little boy and a little 
 girl. Now, here are the dolls you brought me. Which shall we 
 choose for the father?" One doll was chosen. "What shall we do 
 next?" "Make his clothes?" "Yes, but what must we do before 
 we actually make the clothes ? What does your mother do before she 
 makes you a dress?" "She cuts a pattern." "Yes, and what 
 else ?" " She measures me." " Yes, and what else ?" It was then 
 decided that the clothing must be plaimed before it could be made. 
 The planning followed. 
 
 2. Teacher focused attention on planning clothes for father doll. — 
 "What clothes shall we need to make for the father?" asked Miss 
 Cameron. "A turban." "A robe." "A sash." "Weapons." 
 Then someone else suggested sandals. "How can we make 
 sandals?" came from a little girl. "We will leave that for another 
 time," replied the teacher. "What else shall we need for the father ? " 
 
 » Again I am indebted to Miss Mildred Harris, who took shorthand notes, for 
 a description of this lesson. I have inserted the paragraph headlines. 
 
1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 27 
 
 "A shawl." "Why does an Arab wear a shawl?'' "It is so cold 
 at night." 
 
 3. Summary of suggestions by children.— "Who can tell me every- 
 thing that we shall need to make for the father T' A child volunteered, 
 "A sash, a robe, a turban, sandals, and a shawl." "Let's look at 
 some pictures'' said the teacher. "Notice carefully what these 
 Arabs have on. Think about how we can make the clothes for the 
 father." The children then all looked at the pictures. 
 
 4. Attacked problem of making a robe. — One little girl exclaimed, 
 "We will have to have a robe." "What will you need to make a 
 robe ? " Then, from various children came " Scissors." "Thread." 
 "Red cloth." "A ruler." "Needles." "White cloth." "All 
 right, ' ' said Miss Cameron, ' 'here is some cloth. Who has a suggestion 
 for making the robe?" 
 
 5. Boy experimented on robe.— A boy went up to the table and 
 taking a small piece of white cloth, cut a hole in it, and slipped it 
 over the head of the doll. The teacher asked him to hold it up 
 so that the others might see it. 
 
 6. Criticisms and alternative suggestions by other children. — A 
 couple of the children objected to the looks, saying, "It is too 
 short." "How long should it be?" "It should come below the 
 knees." "Oh, it should come clear to the heels," from another 
 pupil, "What else can you suggest about this robe?" "Robes are 
 loose over the shoulder." "How could we make a robe that way?" 
 One boy said he would have a piece hang over each shoulder. 
 Another wanted it to come to a point in the back. Another 
 wanted it fastened in some way. One said the hole for the neck 
 was too large. "Why is it too large?" asked Miss Cameron. 
 "It won't stay on the shoulder." "You could button it on," said 
 one girl. "Who thinks he can make a better robe?" A girl tried. 
 She held the doll up and said, "I would hold it together, this way, 
 with a sash." "Is it all right ? " asked the teacher. "No, it is not 
 full enough." 
 
 7.. Subordinate problems arose: sleeves and sash. — "Where are 
 the sleeves?" asked a child. "Will someone show us how the 
 sleeves might be fixed so that they will be right?" added the teacher. 
 A girl pinned the sleeves. "Do you think that is better?" "No," 
 
28 THE ELEMENTARY SCHOOL JOURNAL [November 
 
 came from several. Finally, the children got the sleeves pinned 
 a little more to their taste. "What could we use for a girdle?'' 
 queried Miss Cameron. "A piece of cloth." "A piece of tape." 
 "Paper." "/ am thinking of something that your mothers are using 
 a great deal these days," said she. "Yarn!" A piece of yam was 
 selected and wound around the doll. "Do you like the side of this 
 robe? Shall we tomorrow make the side this way?" "No," said a 
 child, "we must sew it." The'teacher then had them examine a 
 seam of a little child's dress. They decided the edge of the seam 
 must be straight and not left rough. "We can tuck it in," said 
 a child, meaning French-seamed. 
 
 8. Devising a turban. — "What else can we make for the father?" 
 "A turban." "All right." A girl then took a piece of white cloth 
 and tried to make a turban. She made it look about like a veil, 
 hanging down the back. "Do you think it looks like a turban?" 
 "No, it should not hang down," said a boy. "You try it," said 
 the teacher. The boy got up and tore a very narrow strip off and 
 wound it around the head of the doll. The result was a pretty 
 good turban. "Looks like the father had a sore head," said one 
 child. 
 
 9. Standard for comparison presented by teacher. — "Compare it 
 with a picture of a turban," said the teacher, producing a picture 
 of a man with a turban. "Pretty good," was the general verdict. 
 But some were not satisfied with the sore-head appearance. 
 "See if you can improve upon it," to a little girl. The latter tried 
 to make a turban by first winding it around her finger. She failed, 
 and then wound the strip around the doll's head as the boy had 
 done. However, she took a broader strip. Some liked it better. 
 "Why do you think it is better?" "It covers the head better." 
 "It is more the shape." "Is the turban finished?" "No, a cord 
 should be around it." "You come and put a cord on." A boy put 
 a bit of yarn around the turban for a cord. " It should be the same 
 color as the sash," came from a girl. "That might look better," 
 said the teacher. 
 
 10. Problem for next day. — "Tomorrow we shall make a shawl. 
 If any of you have anything at home that you think you would like to 
 use to make your shawl, it would be nice to bring it to school." Then 
 
1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 29 
 
 different children told of what they could bring. "We must make 
 a collar. Men wear collars," came from one child. "Do Arabs 
 wear collars?" They decided not. 
 
 II. Child off the track. — One girl arose and very earnestly began 
 telHng how a doll she had was dressed. It was brought from 
 abroad. It was a French doll. The teacher listened a moment 
 and then asked, "But what kind of people are we talking about?" 
 "Arabs " came in a chorus. "Bring your things for a shawl tomorrow, 
 and we shall finish dressing the Arab father." Thus ended the lesson. 
 
 Conversational method prevails in problem-solving discussions. — 
 As indicated above, the conversational form in which this second- 
 grade lesson is described helps us to get a clearer idea of the con- 
 versational spirit that prevails in a problem-solving discussion 
 lesson than we derived from the seventh-grade lesson on sugar 
 production or the kindergarten construction lesson. It is important 
 to realize, however, that in both these lessons the same informal 
 conversational give-and-take between teacher and pupils prevailed. 
 At the same time, in all the lessons, we feel that the teacher is 
 a very definite, stimulating, and guiding force. She keeps the 
 pupils' minds actively directed along educative lines so that they 
 are acquiring important ideas at the same time that they are 
 acquiring training in the reflective solution of problems. 
 
 D. Fifth Grade: Standardized Short Geography Problems on 
 THE British Isles 
 
 Transition from simple primary construction problems to technical 
 scientific problems of higher grades.— As a final example of problem- 
 solving lessons in the elementary school, we shall present one from 
 a fifth-grade class in geography. This lesson will show the transi- 
 tion from (a) the simple construction problems arising out of social 
 needs which we have illustrated from the kindergarten and second 
 grade to (b) the more complicated, technical problems of the upper 
 grades which we illustrated by the problem of the United States 
 increasing its sugar production, and which brought in such technical 
 issues as the number of growing days required by sugar cane, the 
 cost of labor, competing crops, and the question of a tariff on 
 sugar. In this fifth-grade lesson we shall find the children dealing 
 with certain simple technical matters such as the tides in navigable 
 
30 THE ELEMENTARY SCHOOL JOURNAL [November 
 
 rivers and the use of a scale of miles and of the directions, east, 
 west, north, and south, in reading a map. 
 
 London problems. How is London influenced by the Thames? 
 Dialogue. — Under the direction of Miss Edith Parker, the children 
 in the fifth grade had taken up the study of the British Isles. They 
 had begun the study of London shortly before the lesson which we 
 shall describe. In order to give the reader further notions of the 
 conversational technique of problem-solving discussion lessons, we 
 shall present most of this lesson in dialogue form as reconstructed 
 from rapid memoranda which I made during my observation. 
 We shall use capital "T" to designate the teacher's remarks, 
 which are printed in italics, and capital "P" to designate the 
 pupils' remarks. Occasionally, where I caught the name of the 
 pupil, I have used it. Much of the dialogue is omitted, but enough 
 is given to illustrate the procedure. The teacher's remarks are 
 numbered in order to faciHtate discussions of the lesson. 
 
 The lesson. — After the children were seated and quiet reigned, 
 the lesson proceeded as follows: 
 
 Introductory. — (i) T: ''How many can now see London on the 
 map without looking at the latter?" (The pupils held up their 
 hands as Miss Parker waited a moment.) ''About how far from 
 the mouth of the river is it? Look at your maps and, using your 
 scale of miles, work it out." 
 
 P: "I say it is exactly forty miles, because it is double the 
 distance across the Strait." 
 
 Another P: "I say it is just thirty-five by the scale." 
 
 (2) T: "Your differences may be due to your choosing different 
 places as marking the mouth of the river. Measure clear out to the 
 place marked North Foreland." (The children then discussed and 
 decided upon the distance.) 
 
 (3) T: "How could such a large seaport as London develop so 
 far up the Thames River ? Put up your hands when you are ready. 
 I want to see many of you ready before I call on anybody." (She 
 then waited about one-half minute.) Martha: "Because of the 
 tides." 
 
 (4) T: "How do the tides help?" Martha: "I don't know 
 how." JuHan: "The tides help to make it a great port. They 
 let the boats come in." 
 
ig2o] PROBLEM-SOLVING OR PRACTICE IN THINKING 31 
 
 (5) T: "How many agree with Julian? " .... (A brief discussion 
 followed which brought out the fact that the high tides make the 
 river deep enough to let the big boats come up. The teacher told 
 of large vessels waiting at Gravesend for high tide to ascend the 
 river and of "locked" docks being used to keep these vessels 
 afloat during low tide.) 
 
 Written questions presented. — T: "We have here (indicating the 
 blackboard) some questions for you. Some you can answer easily 
 and others you will have to think out. Will you read the first question 
 and answer it, Ellwood?'' (The full list of questions is printed in 
 the footnote below.^) 
 
 First written question. — Ellwood read, "How is the city situated 
 with regard to the Thames ? See map on page — ." (The pupils 
 turned to a small map of London. Ellwood's answer was vague.) 
 
 Another P: "The map shows the river running right through 
 London. They have a Hyde Park!" (These children lived in 
 Hyde Park of Chicago.) Another P: "The river looks awfully 
 twisty here — not straight." 
 
 (6) T: "What other points about London and the Thames do 
 you find from this map ? ' ' Various P : " Many parks . " " Victory 
 roads." (Other irrelevant answers.) 
 
 (7) T: "Do those have anything to do with the Thames? It is 
 not a good answer unless it shows how London is related to the 
 Thames." (The pupils now held better to the question.) P: "It 
 has many bridges." Another P: "The city extends far along the 
 river, both north and south of it." 
 
 ' The questions for Miss Parker's lesson on London were written on the black- 
 board as follows: 
 
 LONDON 
 
 1 . How is the city situated with regard to the Thames ? See map on page — . 
 
 2. What determined the location of London Bridge ? 
 
 3. In which direction are the docks from the bridge and why? 
 
 4. How does the location of the docks affect the location of the factories in 
 London ? 
 
 5. How does the location of the factories affect the location of the living quarters 
 for workers ? 
 
 6. Where would you expect the business section to be ? 
 
 7. Where would you expect the wealthy residence section to be ? 
 
 8. Why has London become such a great city? 
 
2,2 THE ELEMENTARY SCHOOL JOURNAL [November 
 
 (8) T: "How long is London?'^ P: "About eighteen miles." 
 (Various other answers to the first question were developed.) 
 
 Summing up first question. — (9) T: "Now let us sum up what 
 we have found in answer to the first question." (As the pupils 
 enumerated their points, the teacher wrote them on the board in 
 outline form, thus : 
 
 1. On both sides 
 
 2. Winding 
 
 3. 20 miles 
 
 4. Bridges 
 
 Second question. — P (reads from blackboard): "What deter- 
 mined the location of London Bridge?" 
 
 (10) T: "// you had visited the Thames River and the site of 
 London before the city was built, you would have seen something like 
 this." (Then she drew on the board a diagram of the river and 
 described the location of the highlands and the low marshes and 
 swamps.) "When the people wanted to build a bridge over the 
 Thames, where would you say it would be, judging from this diagram ? " 
 (The children were very quiet and considerably puzzled.) P: 
 "Right here where it was narrowest." (Pointing at a certain 
 point on the diagram.) 
 
 (11) T: "My diagram is not exactly right if the river seems nar- 
 rower to you at this point. I will change it because the river is not 
 really narrower there. What do you think, Frank?" Frank: "I 
 should say right here, near the highland; one could easily get at it." 
 (The pupils now became quite active in agreeing or disagreeing 
 with Frank.) 
 
 P: "I agree with Frank, but I want to ask a question first. 
 (He then went to the board and asked something about the depth 
 of the river. He quickly decided his own idea was not a good one 
 and retired to his seat. After the hour, Miss Parker said this boy 
 was an impulsive thinker, and that his self-checking in this case 
 really represented growth on his part. As a rule the class or 
 teacher had to check him.) 
 
 (12) T: "Now let's finish the discussion of Frank's plan before 
 we take up another." (Several pupils talked, largely in terms of 
 carrying timbers, easy access to one bank or the other, etc.) 
 
1920] PROBLEM-SOLVING OR PRACTICE IN TfflNKING 33 
 
 (13) T: ^^How many are pretty well convinced now that this 
 would be the best place for the bridge?^' (Many hands were held 
 up.) "Do you have something new to offer, Oliver?'' Ohver started 
 to talk along the same line. 
 
 (14) T: "Yours is just a part of the same general argument. . . . 
 Are you ready to know what really happened? .... This is the place 
 (pointing at the diagram) that the bridge was built. Here the river 
 swings in against the clijff. It was the first place as they came up 
 
 the river, where they could find a good place to build a bridge " 
 
 (She then sketched in the bridge on the diagram.) 
 
 Third question. — (15) T: "Our next question, Jack.''- Jack read: 
 *'In which direction are the docks from the bridge, and why?" 
 P : "That's the easiest question yet. Seaward." 
 
 (16) T: "Yes, that's a good answer, but I mean what cardinal 
 direction, north, east, south, or west." Various P: "North." 
 "West." "East." 
 
 (17) T: "Isn't it strange that you can't tell tne from this small 
 map whether the docks are east, west, north, or south of the bridge. . . . 
 What is the difficulty?'"- (The period was now at an end, so this 
 problem, together with questions 4, 5, 6, and 7, which dealt with 
 the location of factories and residence sections and the reasons for 
 the greatness of London, were left for the next lesson.) 
 
 Growth of diagram summarizes results of thinking. — At the end 
 of the discussion of all the questions, the simple diagram of the 
 bends in the river with which they began had been supplemented 
 with answers from the later questions until it showed the docks 
 for various kinds of merchandise, factories of various kinds, 
 residence districts for poor and rich, etc. 
 
 Points of technique briefly noted. — As in the case of the first 
 two lessons which we described, it will be helpful to note certain 
 general characteristics of this London lesson preliminary to our 
 organized discussion of technique which is to follow in section IV. 
 Briefly stated these characteristics are the following: 
 
 I. A deliberate pace prevailed. For example, in the paragraph 
 numbered 3 in the dialogue, Miss Parker waited about one-half 
 
 ^ Miss Parker explained to me later that while the children had attained fair 
 skill in reading directions on large colored maps, they needed more drill in applying 
 the same principles to small city maps. 
 
34 THE ELEMENTARY SCHOOL JOURNAL [November 
 
 minute after saying, "Put up your hands when you are ready. I 
 want to see many of you ready before I call on anybody." 
 
 2. Evaluation by the pupils was encouraged. Among Miss 
 Parker's favorite remarks are, "Do you think that is a good point ? '' 
 "Do you agree with that?" "Is that a good argument?" 
 
 3. Standards of good thinking were taught the pupils. Examples 
 occur in paragraph 7, where she emphasized holding to the question 
 by saying, "It is not a good answer unless it shows how London 
 is related to the Thames," and in paragraph 12, "Now let's finish 
 the discussion of Frank's plan before we take up another," and in 
 paragraph 14, "Yours is just a part of the same general argument." 
 
 4. Summing up the discussion was periodically attended to. 
 The best example given above is in paragraph 9, where the answers 
 to the first problem were reviewed by a pupil and written on the 
 board by the teacher as a few concise nimibered points. 
 
 5. The thinking was kept organized by four devices, namely (a) 
 writing the principal questions on the board; (b) holding to the 
 main point of each discussion as described above under 3; (c) 
 summing up periodically, as described under 4; and {d) by building 
 upon a diagram the important data, suggestions, and conclusions 
 as they came along. 
 
 Experimentation in grading problems and technical data and activi- 
 ties for fifth-grade geography. — Finally, before turning to section III 
 of the discussion, in which we shall inquire how skilled problem- 
 solvers think, we may, as a further preliminary to our general 
 conclusions about technique in section IV, present Miss Parker's 
 own memorandum concerning experimental work in organizing 
 problem -solving lessons in the middle grades. These points she 
 gave me for presentation to my class of teachers before we 
 observed one of her fifth-grade lessons. She wrote as follows : 
 
 Experimental work in teaching geography in this fifth grade is being done 
 in order 
 
 1. To determine what problems are of the right difl&culty for children of 
 this age; in other words, to grade problems. 
 
 2. To determine the degree of subdivision of problems necessary and the 
 definite steps in solution that need to be indicated for children of this age. 
 
 3. To grade the map reading, text reading, picture reading, and statistics 
 reading that is motivated by these problems. 
 
1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 35 
 
 4. To devise means of establishing thoroughly those principles of interpre- 
 tation of maps, pictures, statements, and statistics that can be established in 
 this grade. 
 
 5. To devise means of helping children of this age to work independently 
 and to check their own inferences. (Written directions are being used at 
 present in an efifort to lessen dependence on the teacher.) 
 
 6. To devise means of getting reactions at each step from each individual 
 rather than from one or two. This is a vital matter in the fifth grade where 
 basic interpretation habits are being formed. It is a matter that is often 
 neglected where the problem-solving method is dominant. 
 
 Conclusion of discussion of actual lessons of section II. Transition 
 to section III. — This will conclude our long section II, in which we 
 have presented, in considerable detail, four problem-solving lessons 
 in order to give the beginning teacher a vivid idea of this type of 
 teaching as it is actually carried on in a progressive elementary 
 school. The seventh-grade lesson on sugar and the kindergarten 
 cardboard construction lesson gave us general notions of the organi- 
 zation of such lessons. The conversational data given in the 
 second-grade Arab lesson and the dialogue of the fifth-grade 
 London lesson brought us more intimately into the conversational 
 give-and-take between teacher and pupils that characterizes 
 problem-solving discussions. In all the lessons, we found the 
 teacher aiding the pupils to get the problem clearly in mind, to make 
 and evaluate suggestions, and to keep their thoughts moving 
 actively along some particular educative line. We found many of 
 the pupils alert and active in suggestion, sometimes keenly critical, 
 and gradually developing in ability from the kindergarten, where 
 they decided how many hinges a door needed, to the seventh grade, 
 where they were ready to consider whether a tariff should be placed 
 on sugar in order to encourage home production. In Miss Parker's 
 final memorandum we found a skilled teacher especially concerned 
 about the issue of grading problems in the middle grades so as to 
 adapt them in general to this grade of pupils, and to give even the 
 slow pupils practice in thoughtfully using the technical tools of 
 problem-solving that are used by scientific specialists in geography. 
 We shall now turn to a description of how problem-solving thinking 
 is done by skilled thinkers, notably great scientists, such as great 
 geographers, astronomers, etc. 
 
36 THE ELEMENTARY SCHOOL JOURNAL [November 
 
 III, HOW SKILFUL PROBLEM-SOLVERS THINK 
 
 Need to analyze skills to determine methods. — In discussions of 
 the teaching of any form of skill such as handwriting or reading, 
 we find it necessary to determine how skilful performers behave, 
 e.g., how skilful handwriters and readers perform, in order to 
 determine how to give pupils similar skill. In the case of hand- 
 writing, for example, we find that careful laboratory experiments 
 have been necessary in order to prove that in much expert hand- 
 writing the letters are made predominantly with finger movements 
 instead of arm movements. In the case of reading, we find that 
 a variety of types of reading skill can be distinguished, and that 
 many tests and laboratory experiments have helped us considerably 
 in understanding how skilled reading is done and how to train 
 children to be skilful, resourceful readers. 
 
 Need similar analysis of skill in problem-solving. — Similarly, 
 in the case of problem-solving, we need a clear understanding 
 of how skilful problem-solvers think in order to practice pupils 
 in doing the same type of thinking. As in the case of handwriting 
 and reading, so in the case of thinking, a number of erroneous ideas 
 have prevailed concerning the nature of the processes of skilled 
 performers. We shall not have time or space, however, to discuss 
 these mistaken notions here, but shall turn our attention im- 
 mediately to an account of the methods of thinking and inquiry 
 used by some of the greatest thinkers, namely, by great scientists 
 as these are described by W. Whewell in his History of the Inductive 
 Sciences.^ 
 
 Biographies of certain great scientists reveal methods of thinking. — 
 Whewell had made a profound study of the methods and results 
 of most of the great scientists up to his time. In connection with 
 his account of the great astronomer, Kepler (i 571-1630), he 
 
 I Whewell's work, published in 1837, is an excejUent exhibition of careful English 
 scholarship. T. H. Huxley, in The Advance of Science, p. 74, characterizes Whewell 
 as a man of "great acquirements and remarkable intellectual powers." It would 
 be well if more persons would secure their ideas of scientific method from such works 
 as Whewell's instead of from Francis Bacon's false theories. In contrast with Bacon's 
 ignorance of actujal scientific investigations and ridicule of the methods of his great 
 scientific contemporaries (such as Copernicus) Whewell proceeded to derive correct 
 notions of the nature of scientific thinking by an examination of the methods actually 
 used by great scientists in their work. 
 
1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 37 
 
 describes methods of scientific study and research in general, 
 and, at the same time, gives an interesting account of Kepler's 
 peculiar traits. 
 
 Accounts should include failures as well as successes. WheweWs 
 description. — Kepler's investigations furnish especially good material 
 from which to determine how a great scientist thinks because he 
 left accounts of his whole process of inquiry, including his incorrect 
 ideas and unsuccessful endeavors as well as the correct ones. 
 With these accounts in mind, Whewell wrote the following dis- 
 cussion of how great scientists discover new truths and solve great 
 scientific problems (I, 291-92) : 
 
 Bold guessing. — ^Advances in knowledge are not commonly made without 
 the previous exercise of some boldness and license in guessing. The discovery 
 of new truths requires, undoubtedly, minds careful and scrupulous in examining 
 what is suggested, but it requires, no less, such as are quick and fertile in 
 suggesting. What is invention except the talent of rapidly calling before us 
 many possibilities and selecting the appropriate one ? It is true that when we 
 have rejected all the inadmissible suppositions, they are quickly forgotten by 
 most persons, and few think it necessary to dwell on these discarded hypotheses, 
 and on the process by which they were condemned, as Kepler has done. 
 
 Reasoning on many errors. — But all who discover truths must have reasoned 
 upon many errors to obtain each truth; every accepted doctrine must have 
 been one selected out of many candidates. In making many conjectures which 
 on trial proved erroneous, Kepler was no more fanciful or unphilosophical 
 than other discoverers have been. Discovery is not a cautious or rigorous process 
 in the sense of abstaining from such suppositions. But there are great differences, 
 in different cases, in the facility with which guesses are proved to be errors 
 and in the degree of attention with which the error and the proof are afterwards 
 dwelt on. Kepler certainly was remarkable for the labor which he gave to 
 such self-refutations and for the candor and copiousness with which he narrated 
 them; his works are in this way extremely curious and amusing and are a 
 very instructive exhibition of the mental process of discovery. But in this 
 respect, I venture to believe, they exhibit to us the usual process (somewhat 
 caricatured) of inventive minds — they rather exemplify the rule of genius than 
 (as has generally been hitherto taught) the exception. We may add that if 
 many of Kepler's guesses now appear fanciful and absurd, because time and 
 observation have refuted them, others, which were at the time equally 
 gratuitous, have been confirmed by succeeding discoveries in a manner which 
 makes them appear marvelously sagacious, as, for instance, his assertion of 
 the rotation of the sun on axis before the invention of the telescope. Nothing 
 can be more just, as well as more poetically happy, than Kepler's picture of 
 
38 THE ELEMENTARY SCHOOL JOURNAL [November 
 
 the philosopher's pursuit of scientific truth, conveyed by means of an allusion 
 to Vergil's shepherd and shepherdess. 
 
 Coy yet inviting, Galatea loves 
 To sport in sight, then plunge into the groves; 
 The challenge given, she darts along the green, 
 Will not be caught, yet would not run unseen. 
 
 Devising tests of false suppositions. — We may notice as another peculiarity 
 of Kepler's reasonings the length and laboriousness of the processes by which 
 he discovered the errors of his first guesses. One of the most important talents 
 requisite for a discoverer is the ingenuity and skill which devises means for 
 rapidly testing false suppositions as they offer themselves. This talent Kepler 
 did not possess; he was not even a good arithmetical calculator, often making 
 mistakes, some of which he detected and laments, while others escaped him 
 to the last. 
 
 Willingness to abandon false hypothesis. — But his defects in this respect 
 were compensated by his courage and perseverance in undertaking and execut- 
 ing such tasks; and, what was still more admirable, he never allowed the 
 labor he had spent upon any conjecture to produce any reluctance in abandoning 
 the hypothesis as soon as he had evidence of its inaccuracy. The only way in 
 which he rewarded himself for his trouble was by describing to the world, 
 in his lively manner, his schemes, exertions, and feelings. 
 
 Scientists' method of solving problems. Bold guessing; erroneous 
 guessing; devising tests; abandoning errors.- — Careful reading and 
 study of the above quotation will give us most of the ideas that we 
 need to understand the thinking processes in problem-solving. 
 We may list them briefly as follows : 
 
 1. Bold guessing as the basis of fertile suggesting. 
 
 2. Erroneous guessing, "All who discover truths must have 
 reasoned upon many errors to discover each truth."^ 
 
 ' Huxley {op. cit., p. ss) supports Whewell's statement of the place of guessing 
 or conjecturing in careful scientific thinking in the following words : 
 
 "It is a favorite popular delusion that the scientific inquirer is under a sort of 
 moral obligation to abstain from going beyond that generalization of observed facts 
 which is absurdly called Baconian induction. But anyone who is practically ac- 
 quainted with scientific work is aware that those who refuse to go beyond fact, rarely 
 get as far as fact; and anyone who has studied the history of science knows that almost 
 every great step therein has been made by the "anticipation of nature," that is, by 
 the uivention of h3^otheses, which, though verifiable, often had very little foundation 
 to start with; and, not unfrequently, in spite of a long career of usefulness, turned 
 out to be wholly erroneous in the long run. 
 
 "The geocentric system of astronomy, with its eccentrics and its epicycles, was 
 an hypothesis utterly at variance with fact, which nevertheless did great things for 
 the advancement of astronomical knowledge. Kepler was the wildest of guessers. 
 Newton's corpuscular theory of light was of much temporary use in optics, though 
 nobody now believes in it." 
 
ig2o] PROBLEM-SOLVING OR PRACTICE IN THINKING 39 
 
 3. Skill in devising means of testing the truth of guesses. 
 
 4. Willingness to abandon an erroneous guess or hypothesis. 
 Kepler succeeded though handicapped by slowness and by poor 
 
 calculations. — In addition to these characteristics of reflective 
 thinking as found in the work of great scientists, it is interesting to 
 note that Kepler succeeded wonderfully in spite of certain personal 
 handicaps. For example, "He was not even a good arithmetical 
 calculator, often making mistakes, some of which he detected and 
 laments, while others escaped him to the last." When one recalls 
 what an important factor mathematical precision is in modern 
 scientific method, he can appreciate what a handicap Kepler 
 labored under. Moreover, he was not rapid in devising means of 
 testing his suppositions, but he compensated for this lack "by 
 his courage and perseverance in undertaking and executing such 
 tasks." In general, these characteristics of Kepler suggest that 
 a person, for example, a pupil, may be a very competent thinker 
 and, in the long run, very successful in solving problems, yet be 
 very slow and laborious in his methods of criticism and verification. 
 Scientific biographies reveal '^how we think." — Such accounts as 
 Whewell gives of the personal efforts of scientific workers to solve 
 problems help us to understand the actual mental processes involved 
 in skilled thinking. On the basis of this understanding, we can 
 proceed to give pupils practice in doing similar thinking. In 
 recent years the psychological writings of William James and 
 John Dewey have especially emphasized the nature of these thinking 
 processes. From their discussions educators may derive help in 
 understanding "how we think" and how to practice pupils in 
 thinking. In the next article, we shall present briefly Dewey's 
 description of "how we think" and then conclude the series of 
 articles with section IV on "rules for practicing pupils in problem- 
 solving." 
 
PART IV 
 
 Synopsis of this series of articles.— The three preceding articles contained 
 (I) a discussion of "problems of everyday Ufe"; (II) four "actual lessons" 
 from the University of Chicago Elementary School illustrating practice in 
 problem-solving from the kindergarten through the upper grades; and (III) a 
 discussion of "how skilful problem-scdvers think" as illustrated by Whewell's 
 description of the methods of thinking used by great scientists. The present 
 article will continue this phase of the discussion and conclude the series with 
 Section IV on "rules for practicing pupils in problem-solving." 
 
 m. HOW SKILFUL PROBLEM-SOLVERS THINK (Concluded) 
 
 Dewey's notable account of "how we think.'' — Professor John 
 Dewey is himself one of America's greatest thinkers and is at the 
 same time a trained psychologist who has specialized in the study 
 of thinking processes. Consequently, his book How We Think 
 (1910) deserves very special study. It should be read carefully 
 time and again in order to grasp its detailed meanings. I have 
 known a number of students, and even writers upon education, 
 who have studied the book superficially and, as a consequence, 
 failed to grasp some of its most significant points. Some of his 
 most fundamental ideas, for our purposes, are contained in the 
 three following paragraphs. The headlines are not in the original, 
 and the paragraphing is slightly altered. 
 
 Origin in some perplexity. — ^We may recapitulate by saying that the origin 
 of thinking is some perplexity, confusion, or doubt. Thinking is not a case 
 of spontaneous combustion; it does not occur just on "general principles." 
 There is something specific which occasions and evokes it. General appeals 
 to a child (or to a grown-up) to think irrespective of the existence in his own 
 experience of some difficulty that troubles him and disturbs his equiUbrium, 
 are as futile as advice to lift himself by his boot-straps. 
 
 Form a tentative plan based on analogous past experience and prior 
 knowledge. — Given a difficulty, the next step is suggestion of some way out — 
 
 40 
 
PROBLEM-SOLVING OR PRACTICE IN THINKING 41 
 
 the formation of some tentative plan or project, the entertaining of some theory 
 which will account for the peculiarities in question, the consideration of some 
 solution for the problem. The data at hand cannot supply the solution; they 
 can only suggest it. What, then, are the sources of the suggestion ? Clearly 
 past experience and prior knowledge. If the person has had some acquaintance 
 with similar situations, if he has dealt with material of the same sort before, 
 suggestions more or less apt and helpful are likely to arise. But unless there 
 has been experience in some degree analogous, which may now be represented 
 in imagination, confusion remains mere confusion. There is nothing upon 
 which to draw in order to clarify it. Even when a child (or a grown-up) has a 
 problem, to urge hun to think when he has no prior experiences involving some 
 of the same conditions is wholly futile. 
 
 Plan not accepted until carefully examined and criticized. — If the suggestion 
 that occurs is at once accepted, we have uncritical thinking, the minimum of 
 reflection. To turn the thing over in mind, to reflect, means to hunt for 
 additional evidence, for new data, that will develop the suggestion and will 
 either, as we say, bear it out or else make obvious its absurdity and irrelevance. 
 Given a genuine difficulty and a reasonable amoimt of analogous experience 
 to draw upon, the difference, par excellence, between good and bad thinkmg 
 is found at this pomt. The easiest way is to accept any suggestion that seems 
 plausible and thereby bring to an end the condition of mental uneasiness. 
 Reflective thinking is always more or less troublesome, because it involves 
 overcoming the inertia that inclines one to accept suggestions at their face 
 value; it involves willingness to endure a condition of mental unrest. . . 
 Reflective thmking, in short, means judgment suspended during further inquiry, 
 and suspense is likely to be somewhat painful. . . . The most important 
 factor in the training of good mental habits consists in acquiring the attitude 
 of suspended conclusion and in mastering the various methods of searching 
 for new materials to corroborate or to refute the first suggestions that occur. 
 To maintain the state of doubt and to carry on systematic and protracted 
 inquiry — these are the essentials of thinking.' 
 
 Dewey's text; state of doubt plus systematic and protracted inquiry. 
 — In general, this quotation from Dewey gives us the same notions 
 of careful inquiry that we derived from the accounts of Kepler's 
 thinking, namely (i) prolonged careful search for suggested solu- 
 tions, (2) careful open-minded evaluation and testing of each 
 suggestion or plan, (3) suspended judgment, patience to wait until 
 the true solution has been discovered and verified. Since the 
 language of Dewey's paragraphs varies from Whewell's account 
 of Kepler, we can pick up from Dewey some excellent additional 
 phrases to use in our thinking about training in problem-solving. 
 
 'John Dewey, How We Think, pp. 12-13. Boston: D. C. Heath & Co., 1910. 
 
42 THE ELEMENTARY SCHOOL JOURNAL [December 
 
 Perhaps the best of these are contained in the final sentence, "To 
 maintain the state of doubt and to carry on systematic and pro- 
 tracted inquiry — these are the essentials of thinking." 
 
 With such an understanding of the nature of skilful problem- 
 solving as we can derive from these accounts by Whewell and 
 Dewey, and from the accounts of actual problem-solving lessons 
 given earlier in the discussion, we can now proceed to summarize 
 our ideas of how to train pupils in problem-solving. 
 
 IV. RULES FOR PRACTICING PUPILS IN REFLECTIVE 
 PROBLEM-SOLVING 
 
 Assume suitable problem, adequate experience, and interesting 
 dilemma. — At the outset of this section, we may assume (i) that 
 a problem adapted to the pupils' maturity and experience is to be 
 solved; (2) that the pupils have analogous previous experience 
 and related information needed for the solution or they know how 
 to proceed to get this information; and (3) that an interesting 
 dilemma has been created. In other words, we shall assume that 
 a suitable problem for solution has already arisen from some puz- 
 zling situation and that the pupils are interested in solving it. 
 
 Interest in problem increased by competition. — Their interest 
 may arise from the mere instinctive interest in thinking which we 
 described early in the articles and which leads many adults and 
 children to enjoy playful puzzling about all sorts of perplexing, 
 strange, unexpected, or disconcerting occurrences. This instinc- 
 tive interest easily maintains itself and is greatly aided by the 
 instinctive interest in competition. Pupils compete to make appro- 
 priate suggestions, to criticize the suggestions of others, and in general 
 to "win out" personally in achieving the solutions of the major 
 problem and its many subdivisions. 
 
 Teacher's threefold task. — With such an interesting situation 
 created, the teacher's task becomes one of (i) guiding the thinking 
 of the pupils; (2) aiding them when confronted by difficulties that 
 are beyond their powers or which they would waste their time in 
 solving; and (3) eventually making them aware of what good 
 thinking is, so that they may consciously strive for it during their 
 thinking, just as they strive to improve their handwriting or their 
 reading. 
 
1920] PROBLELI-SOLVING OR PRACTICE IN THINKING 43 
 
 Thorndike's parallel for guiding thinking. Finding the road to 
 grandpa's. — The general nature of a teacher's activity in assisting 
 pupils in problem-solving is cleverly suggested by Thorndike when 
 he compares it to assisting a child to discover the road to grandpa's 
 house instead of merely taking him by the hand and leading him 
 there. In such guidance, Thorndike says: 
 
 You must make svu*e (i) that the youngster knows what place he is to try 
 to reach and (2) keeps it in mind. (3) He must also at least know that to get 
 to a place [or to solve a problem] you must keep going and not he down and 
 go to sleep; (4) he must have some knowledge of the direction in which the 
 house lies and of the roads and woods and valley in the neighborhood. 
 
 He starts off correctly and at a cross road [or alternative in the problem] 
 turns to the left. 
 
 "What did you do that for, John?" [asks the guide]. "I don't know." 
 "Where are you going?" "To grandpa's." "Where does that road go?" 
 " To the schoolhouse." " Is that on the way to grandpa's ? " "I don't know." 
 " What comes after the schoolhouse if you go down this road ? " "The chvirch." 
 "How long does it take to go from grandpa's to the church?" "0, a long 
 time." "Is grandpa's near the church?" "No. It is a long way." "This 
 road goes to the church. Is it a good way to go to grandpa's?" 
 
 If your boy is bright enough, he now turns to the right, but soon comes 
 to the end of the road [or the suggestion that is being followed in trying to solve 
 the problem]. "Where do I go now?" says he. "Where do you think?" 
 "I think we go through that field." "Well, try it and see." 
 
 You rapidly approach a pond [or discouraging difficulty in the problem] 
 and the boy sits down and cries. "I can't find the way to grandpa's." 
 "What's the trouble?" "You can't get around this pond, it's all swampy." 
 "Do you have to go around it?" "Yes. Grandpa's is up there and you 
 have to go around the pond." "Go and look at the pond [or examine the 
 difficulty] and see if you can find something that will help you to get to 
 grandpa's." 
 
 And so on with constant stimulation to the examination of each situation 
 confronted, and with the selection and rejection of ways in the light of knowl- 
 edge of their consequences, until grandpa's house is reached, or until the prob- 
 lem is solved.* 
 
 Five specific rules for conducting problem-solving lessons. — The 
 general impression of methods of guiding pupils in problem-solving 
 which we derive from this little imaginary story may now be for- 
 mulated into the specific rules given below. These rules also sum- 
 marize and definitize most of the points of technique brought out 
 ' E. L. Thorndike, Principles of Teaching, pp. 150-51- New York: A. G. Seiler, 1905. 
 
44 THE ELEMENTARY SCHOOL JOURNAL [December 
 
 in the sample lessons in Section II, plus the characteristics of skilful 
 problem-solving described in Section III of the discussion. 
 
 1. Define problem. — Aid the pupils to define the problem clearly. 
 This rule is important in good individual thinking, but is particu- 
 larly important in group thinking. For example, while writing 
 the preceding paragraphs, I was disturbed by two well-intentioned 
 intelligent persons who were arguing most vigorously, but quite 
 uselessly, because they were talking at "cross purposes." I said 
 to them, "Do you folks realize that you are not talking about the 
 same thing? One of you misunderstood what the other asserted 
 a moment ago." Upon a little inquiry, my statement proved to 
 be true, the parties found themselves in perfect agreement, and I 
 could proceed with my work undisturbed. In college debates, we 
 find some of our best examples of care in defining the question or 
 problem for a group discussion. Many hours or days or weeks 
 may be spent in getting the problem clearly in mind and giving 
 it such a satisfactory wording that definite profitable debating 
 may proceed. In our seventh-grade lesson on sugar production, 
 we noticed that Miss Parker had the class formulate a definite 
 proposition as the basis of the discussion and then she wrote it on 
 the board, so that all got it clearly in mind. In our fifth-grade 
 lesson on London, we found she had written eight carefully phrased 
 problems on the board as the basis of the lesson, and that each one 
 that needed further defining received it in the discussion. 
 
 2. Keep problem in mind. — ^Help the pupils to keep the problem 
 clearly in mind. This rule is necessitated by the large waste of 
 time and energy that results from being side-tracked, even after the 
 problem has been clearly defined. "Scatter-brained thinking" 
 is a term to designate thinking that does not hold definitely to the 
 question. In deliberative bodies that have good rules of procedure, 
 one important duty of the presiding officer is to hold the discussion 
 to the question before the house, and to rule out digressions. In 
 the lessons in Section II, we saw frequent occasions for this pro- 
 cedure; e.g., in the second-grade lesson a child began to talk about 
 dressing a French doll instead of an Arab doll; in the seventh-grade 
 sugar-production lesson, the teacher had difficulty in restraining 
 a boy from discussing " profitable " instead of "possible. " Through 
 
jp2o] PROBLEM-SOLVING OR PRACTICE IN THINKING 45 
 
 such guidance the pupils learn that "keeping to the question" is a 
 characteristic of good thinking. They come to realize this from 
 repeated suggestions from the teacher, such as Miss Parker's 
 remark when the class was discussing the relation of London and 
 the Thames, "It is not a good answer unless it shows how London 
 is related to the Thames." 
 
 3. Stimulate suggestions. Analysis, recall, guesses. — Aid the 
 pupils to make suggestions by getting them {a) to analyze the prob- 
 lematic situation into parts or elements, each of which may suggest 
 a solution; (&) to recall previously known similar cases, or, as in 
 arithmetic • and geography, general rules that may apply; (c) to 
 formulate from vague guesses definite hypotheses or tentative plans. 
 
 Control of one^s own associations is difficult. Gallon. — These 
 rules are among the most difiicult to explain and apply, because 
 fertility in suggesting is probably less easily controlled by a thinker, 
 and consequently by a pupil, than any other phase of thinking. 
 This fact is picturesquely described by the eminent English scien- 
 tist. Sir Francis Galton, a member of the noted Darwin family 
 and well known as founder of the eugenics movement. He com- 
 pares his mind, when solving a problem, to two rooms, one an 
 "audience chamber" in which the main ideas of the moment have 
 the floor, and the other an "antechamber" in which there is a 
 throng of those ideas that are vaguely present in his mind at the 
 time. "Successful progress of thought," he says, "seems to 
 
 depend, first, on a large attendance in the antechamber 
 
 [This] thronging of the antechamber is, I am convinced, altogether 
 beyond my control; if the ideas do not appear, I cannot create 
 them nor compel them to come." 
 
 Maneuvers for attracting appropriate suggestions. — While Galton's 
 statement that we cannot compel appropriate ideas or suggestions 
 to appear is true, yet we can go through certain maneuvers that 
 will tend to attract or arouse or recall them. 
 
 a) Analytic attention focuses upon one element at a time. — One 
 such maneuver is to proceed to focus our attention on one part of 
 the problematic situation at a time. For example, in the sugar- 
 production problem, the class divided the issue into cane production 
 and sugar-beet production and then focused their attention on the 
 
46 THE ELEMENTARY SCHOOL JOURNAL [December 
 
 former. Holding, then, to the problem of growing more cane, a 
 host of issues were suggested, such as number of growing days, 
 competition with Cuban labor, etc. Similarly, in fitting the front 
 to the cardboard store in the kindergarten, attention was focused 
 for a time on the width, and suggestions "sprouted" for determining 
 this, for marking straight lines by folding, etc. In! studying the 
 growth of London, the fifth-grade class was found breaking the 
 issues up into where the docks would be located, where the ware- 
 houses would be located, and similar questions with factories, 
 homes for workers, fine residence districts, etc. 
 
 Each focused element brings its suggestions. By dividing we 
 conquer. — Thus by actively dividing a problematic situation into 
 certain of its elements, and purposely attending to one of these 
 for the time being and neglecting others, we open up many sources 
 of suggestion which might not have opened so soon had we merely 
 passively regarded the large problem and waited for something to 
 happen. The teacher can often help a class over an apparently 
 insurmountable difl&culty in their problem by merely suggesting 
 that they devote their attention to a certain phase of it which she 
 mentions, or by naming a number of alternative phases, one of 
 which they take up and examine.' 
 
 h) Recalling similar cases and rules that apply. Degrees of 
 assistance. — Recallmg previously known similar cases or general 
 rules that may apply is particularly easy in arithmetic or geography 
 where the material is systematically organized. For example, when 
 asked what conditions must be studied in planning to grow sugar 
 cane, a pupil could say to himself, "Let me see, what conditions 
 
 " The proper location of analysis as a method of control in problem-solving has 
 puzzled me more than any feature of this section. Its value is quite obvious and has 
 been especially emphasized by William James. (See his Principles of Psychology, 
 II, 339-40.) Whether (a) to locate such purposeful analytic concentration of attention 
 under rule 3, as one means of controlling suggestions, or (6) to give it an mdependent 
 place, has been my dilemma. In placing it as a control device under the more general 
 heading of stimulating suggestions, I have been guided largely by my own experience 
 in sdlving geometry exercises. In this case, it seems to me, I commonly focus my atten- 
 tion on a certam angle or a certain Ime in hopes that it will suggest some further 
 possibilities of procedure. By thus controlling our attention, we discount somewhat 
 Galton's point about being unable to control the thronging of the ante-chamber; 
 because the aspect attended to, will, figuratively speaking, invite its own crowd 
 to the room. 
 
IQ20] PROBLEM-SOLVING OR PRACTICE IN THINKING 47 
 
 did we take up for growing cotton and corn?" Similarly, if the 
 fifth-grade pupils who had studied London should later study the 
 growth of New Orleans, they might say, "Let's see, what were 
 some of the factors we brought out in the case of London ?" In the 
 case of mathematics, the procedure of recalling the desired rule is 
 often aided mechanically by turning the pages until an appropriate 
 one appears. The practice of looking up some related discussion 
 in a book is a device that many students and scientists use to start 
 suggestions that may help solve the problem. Such systematic 
 recall may be aided by the teacher in various degrees. For example, 
 in the kindergarten, the teacher may make a very general sugges- 
 tion, such as, "How can we find out how many hinges a door should 
 have?" or the more definite suggestion, "What shall we look at 
 to determine how many hinges a door should have ?" or the very 
 specific suggestion, "Look at the doors in this room to see how 
 many hinges we ought to have on our door." 
 
 c) Guessing. Leaps in the dark definitized as hypotheses. — 
 Guessing and formulating definite hypotheses from the more vague 
 guesses are processes that we found especially emphasized in 
 Whewell's description of scientific procedure. Recently I heard a 
 chemist say that for two years he had tried to obtain a certain 
 reaction in his laboratory without success. He had tried a score of 
 devices in vain. One day, while walking across the campus, it 
 occurred to him to try out a procedure that he had frequently 
 thought of but had always mentally discarded because it seemed 
 too foolish. He went to his laboratory, tried it, and it proved to 
 be the long-sought method. Providing that pupils are' seriously 
 concerned with their problems and have a fund of related experi- 
 ences, such courageous guessing, leaps into mental darkness, 
 should be encouraged. In class discussions, as many such perti- 
 nent guesses are rapidly made, they may be rapidly noted on the 
 blackboards, then the more probable ones taken up and definitely 
 formulated and examined to determine their value.'' 
 
 ^ In high-grade scientific investigations, this "method of multiple hypotheses" is 
 highly esteemed. Its general character is brought out in the following quotation from 
 Dewey {op. cit., p. 75): "Suggestion is the very heart of inference; it mvolves going 
 from what is present to something absent. Hence it is more or less speculative, 
 adventurous. Since mference goes beyond what is actually present, it involves a 
 
48 THE ELEMENTARY SCHOOL JOURNAL [December 
 
 4. Evaluate suggestions. Open-mindedness; criticism; verifica- 
 tion. — ^Encourage pupils to evaluate suggestions carefully by getting 
 them (a) to "maintain the state of doubt," i.e., to delay their final 
 conclusion and to remain open-minded until the matter is finally 
 proved; (&) to criticize thoroughly all suggestions, i.e., to anticipate 
 mentally objections that might be made to them or consequences 
 that might follow; (c) to verify suggestions and conclusions by 
 reference to facts as revealed around them or in miniature experi- 
 ments or in standard scientific treatises. The subdivisions of this 
 rule we found especially emphasized in the last paragraph from 
 Dewey at the beginning of this article. 
 
 a) Maintain state of doubt. Avoid pugnacious stubborn argument. 
 — ^The rule about suspending judgment defines the general spirit 
 that should prevail in the class and in the mind of each inquirer. 
 It raises an interesting question concerning the amount of argument 
 that should be permitted in classes. While argument may be very 
 stimulating to thought and interest, the spirit of argument is often 
 just the opposite of the spirit of open-minded inquiry. Argument 
 is often closely akin to fighting; the more your opponent hits you, 
 the harder, and frequently the more blindly, you hit back. I have 
 seen pugnacious, argumentative boys in upper-grade classes, who 
 cared nothing about careful evaluation of their suggestions, but 
 were merely concerned to maintain these at all costs. Where such 
 a spirit is allowed to become strong in a class, the opportunities for 
 training in impartial, open-minded, scientific inquiry are jeopard- 
 ized. The teacher should be herself a model of impartiality in 
 inquiry; she should make this the dominant spirit of the teaching, 
 and should train each pupil to esteem fair-minded search after 
 truth as a high ideal and a desirable personal attribute. 
 . b) Acquire attitude of criticizing suggestions. Anticipate objec- 
 tions and consequences. — Teaching students to criticize, to anticipate 
 
 leap, a jump, the propriety of which cannot be absolutely warranted in advance, no 
 matter what precautions be taken. Synonjons for this are supposition, conjecture, 
 guess, hypothesis, and (in elaborate cases) theory. Since suspended beUef, or the p^jst- 
 ponement of a final conclusion pending further evidence, depends partly upon the 
 presence of rival conjectures as to the best course to pursue or the probable explanation 
 to favor, cultivation of a variety of alternative suggestions is an important factor in good 
 thinking." 
 
ig2o] PROBLEM-SOLVING OR PRACTICE IN THINKING 49 
 
 mentally, possible objections to and consequences of a suggestion 
 or scheme, appears as the notable feature of the work of certain 
 teachers. The actual calling to mind of specific criticisms is a 
 matter of fertility of suggestion, but the general attitude of trying 
 out mentally each suggestion before adopting it can be maintained 
 even in cases where one may be unsuccessful in calling to mind 
 specific objections and consequences. 
 
 c) Verify by known conditions, miniature experiments, and 
 scientific treatises. — Closely related to this mental trying-out is 
 the verification of suggestions and conclusions by reference to known 
 facts as revealed around us or in standard scientific treatises. For 
 example, in the kindergarten construction lesson, a child who 
 wanted to have only one hinge on a door should have felt that this 
 was probably undesirable after examining all doors and finding 
 none with one hinge. Of course, he might have tried one hinge 
 and found that it wouldn't work. Wherever possible, however, 
 in social life, people try to avoid an expensive, poorly conceived 
 experiment if it is possible to determine in advance, from facts 
 already known, that it will be a failure. Often scientific experi- 
 mentation in a laboratory consists in carrying on some process in 
 miniature, or on a small scale, to see if it will work. In primary 
 construction classes, a similar practice is often followed by letting 
 one child try out a suggestion before all adopt it. As further 
 examples of the process of verifying suggestions, we found the pupils 
 in the Arab-doll lesson referring to standard pictures of Arab life 
 to verify some of their plans for the Arab costumes ; and in the 
 sugar-production lesson, we found the teacher provided with a 
 report of the Department of Agriculture and a special scientific 
 treatise on sugar, to use in checking up the conclusions that the 
 pupils reached concerning the possibility of increased sugar-cane 
 production. 
 
 5. Keep discussion organized. Outlines, graphs, summaries. — 
 Help pupils to keep the discussion organized by proceeding (a) to 
 build an outline of the main ideas on the board as they appear in 
 the discussion; (b) to use diagrams and graphs for condensing 
 fundamental facts and relations into a simple picture; (c) to take 
 stock from time to time by summarizing the ground covered and 
 
50 THE ELEMENTARY SCHOOL JOURNAL [December 
 
 the next steps to be taken; (d) to formulate from time to time, as 
 definite propositions, the net outcome of the discussion. 
 
 These last rules are very objective and easy to understand and 
 illustrate. We found an example of building an outline on the 
 blackboard in the sugar-production lesson; of the effective use of 
 a graph to summarize the sugar situation in the same lesson and of 
 a diagram to clarify and summarize the development of London 
 in the fifth-grade lesson. We found the second-grade class taking 
 stock of their plans for the Arab costume, and the fifth-grade class 
 summarizing their facts about the relation of London and the 
 Thames. The concise formulation of definite propositions contain- 
 ing the net outcome of the discussion occurred several times in the 
 sugar-production and London lessons. 
 
 Summary of rules for conducting problem-solving lessons. — The 
 five major rules with their subdivisions presented above describe 
 many, if not most, of the special practices that should characterize 
 a teacher's guidance of pupils during a problem-solving lesson. 
 They may be summarized in more concise form in the following 
 statement: 
 
 To stimulate and assist pupils in reflective problem-solving, the teacher 
 should 
 
 1. Get them to define the problem clearly 
 
 2. Aid them to keep the problem in mind 
 
 3. Get them to make many suggestions by encouraging them 
 
 a) To analyse the situation into parts 
 
 b) To recall previously known sinular cases and general rules that apply 
 
 c) To guess courageously and formulate guesses clearly 
 
 4. Get them to evaluate each suggestion carefully by encouraging them 
 
 a) To maintain a state of doubt or suspended conclusion 
 
 b) To criticize the suggestion by anticipating objections and consequences 
 
 c) To verify conclusions by appeal to known facts, miniature experiments, 
 
 and scientific treatises 
 
 5. Get them to organize the material by proceeding 
 
 a) To build an outUne on the board 
 
 b) To use diagrams and graphs 
 
 c) To take stock from time to time 
 
 d) To formulate concise statements of the net outcome of the discussion 
 
 Primary education no longer mere arbitrary memorization. — The 
 type of training summarized in the foregoing rules differs greatly 
 
1920] PROBLEM-SOLVING OR PRACTICE IN THINKING 51 
 
 from that which prevailed in many schools a generation ago and 
 which was seriously advocated by a prominent American writer 
 on education as late as 1904, when he said the age before twelve is 
 the age for "arbitrary memorization, drill and habituation, with 
 little appeal to children's interest or understanding." Such a theory 
 was based on the assumption that little children cannot succeed in 
 reflective problem-solving. It requires little observation to show 
 that little children solve their problems by the same processes of 
 making and evaluating suggestions that ordinary adults use.^ The 
 great growth that may be made by pupils in reflective ability, 
 through providing opportunities from the kindergarten up, appears 
 when one contrasts the recitations observed in the upper grades of 
 an old-fashioned memorizing school with those in the same grades 
 of a progressive school in which problem-solving methods prevail 
 in construction, expression, liistory, geography, and other subjects. 
 In such a progressive school, pupils in the upper grades are prepared 
 to attack such a technical problem as increasing American sugar 
 production in the effective manner described in these articles, and 
 with a mastery of technical devices of research and inquiry not 
 possessed by some educated adults. 
 
 Both routine drill and problem-solving have a place. — ^Let us hasten 
 to say, however, that this emphasis on problem-solving should not 
 lead to a neglect of routine drill of the t>^e that prevails in the 
 modern scientific teaching of handwriting, spelling, reading, and 
 arithmetic. The necessity of such drill has been amply demon- 
 strated in scientific investigations; and its presence in the school 
 need not interfere at all with the adequate organization of problem- 
 solving. Both may proceed in the same day without mutual 
 interference, e.g., during the handwriting and spelling periods, the 
 most intense, gameful, effective drills may be carried on, with little 
 or no problem activity, while in some of the history and geography 
 periods the most intense reflective problem-solving may prevail. 
 
 Give both habits and standards of good thinking. — Such training 
 in problem-solving should not only give pupils greater skill in solving 
 
 ' For experimental evidence on this point see F. N. Freeman's How Children Learn 
 (Houghton Miflain Co., 191 7), chap, xi on "Problem-Solving or Thinking," and S. C. 
 Parker's Methods of Teaching in High Schools (Ginn & Co., 1915), pp. 326-32. 
 
52 THE ELEMENTARY SCHOOL JOURNAL [December 
 
 problems in special lines, such as construction or geography, but it 
 should also make them eventually clearly aware of what the attri- 
 butes of good thinking are. For example, we suggested that pupils 
 should come to esteem open-minded, impartial, suspended judgment 
 as an ideal, as a personal attribute which they desire to possess. 
 Similarly, we suggested that they learn to be on their guard to 
 hold to the question under discussion. Again, we might have 
 noted under rule 5 that the pupil should learn to appreciate the 
 value of outlines, graphs, diagrams, and summaries as aids to 
 effective thinking, and consciously strive to use these when appro- 
 priate occasions offer. 
 
 Cultivating originality. What does it mean? — The foregoing 
 discussion helps us to define clearly what we mean by "cultivating 
 originality," a phrase that is extensively but often vaguely used 
 in many educational discussions. Very commonly such discussions 
 consist merely of vicious attacks upon drill, routine, memorizing, 
 and imitation, with strenuous appeals to rid the schools of these 
 and to substitute, instead, training in originality and initiative. 
 We have called attention to the fallacy of this position in the pre- 
 ceding paragraphs. So confused, however, is the issue concerning 
 the proper balancing of reflective, original thinking, on the one 
 hand, and routine drill and imitation on the other, that we shall 
 note a few more points concerning it. 
 
 Capacity for original thinking is inborn, varies between individuals, 
 and is often specialized. — In trying to make our discussion concrete, 
 we may think of Edison, Darwin, Newton, and other great origi- 
 nators and inventors as typifying great capacity for original thinking. 
 At the opposite extreme, we have the feeble-minded, many of whom, 
 while able to learn such routine tasks as washing dishes or dusting, 
 have little ability to solve problems. It is perfectly clear from 
 scientific studies of geniuses and the feeble-minded, that the 
 differences between them are due to inner characteristics of the 
 individuals, usually inherited characteristics. These differences 
 cannot be overcome by training. You cannot make^an Edison out 
 of a feeble-minded person. In the intermediate ranks, between the 
 original geniuses and the feeble-minded, the capacity for original 
 thinking is also determined by the individual's native endowment; 
 
igzo] PROBLEM-SOLVING OR PRACTICE IN TfflNKING 53 
 
 if he is well endowed by nature, he may become a skilled thinker; 
 if he is poorly endowed, the best training will still leave him a poor 
 thinker. Moreover, his capacity for original thinking may be 
 specialized, e.g.. a boy may prove quite ingenious in devising 
 mechanical appliances, but fail in working original problems in 
 mathematics. Similarly, a person may rank high in the capacity 
 for original thinking in mathematics, but fail in making original 
 compositions in music, or writing original poems, or devising original 
 plots for novels. For our present purposes, it is sufficient if we 
 can get the teacher to think of each pupil as possessing a certain 
 amount of native capacity for original thinking. Her task is to 
 cultivate each pupil's capacity quite specifically. If he is brilliantly 
 original in geography, give him large opportunities; if he is rather 
 stupid and unoriginal in geography, give him some small easy 
 problems that will give practice for what little talent he possesses. 
 In every case, treat each pupil sympathetically so as to develop 
 such talents as he does possess for the good of himself and 
 society. 
 
 The pupil must succeed in order to improve. — Such sympathetic 
 treatment may be further justified by the scientific fact that, in 
 any type of learning, a pupil learns through his successes. It is 
 the successful performances, not the unsuccessful ones, that form 
 the correct habits in solving problems and doing original thinking, 
 just as in learning spelling or handwriting. A pupil who never 
 succeeds in solving an original problem will not learn to solve 
 original problems. Owing to the fact that problem-solving, as a 
 rule, necessarily involves erroneous guesses and the testing of these, 
 the teacher is confronted with a very delicate task in determining 
 just how difiicult the problems should be for each pupil, and just 
 how much aid to give him in order that he may succeed and yet be 
 required to do sufficient mental experimentation to secure the 
 necessary practice. 
 
 Standardized graded problems needed. — Great help will be afforded 
 in this dilemma when we have developed in each grade for each 
 subject standardized, published, ready-made problems varying 
 from the easy for the dull pupils up to those of sufficient difiiculty 
 to challenge the ability of the best thinkers in the class. We 
 
54 THE ELEMENTARY SCHOOL JOURNAL [December 
 
 noticed how Miss Parker was engaged in devising such problems 
 with the necessary data for fifth-grade geography/ 
 
 Vary recitations for the timid, the aggressive, the slow, the impulsive, 
 etc. — In the problem-solving recitation, the teacher must provide 
 for individual differences by calling on pupils according to their 
 capacities and temperaments. For example, for the dull pupils, 
 the pupils who have little native capacity, she will save the easiest 
 questions, remembering that they need to succeed in order to 
 profit. The slow but capable thinkers will be taken care of by 
 slowing up the pace frequently for their especial benefit. The 
 timid but capable thinker will be watched carefully and probably 
 given at first easy questions that can be answered in a few words 
 As he acquires confidence from his successful answers to these 
 he may eventually lose his timidity in this particular class. The 
 impulsive thinker who does not stop to evaluate his suggestion 
 before popping it out will need to be retrained, possibly by promis- 
 ing to ignore him if he continues wildly to make suggestions, 
 but to favor him after he has made a well-considered one. The 
 argumentative quibbler will need his spirit changed by being 
 made to realize that the class does not care for his pugnacious, 
 stubborn adherence to a suggestion, but will welcome him if he 
 really tries to aid in an impartial inquiry for the true solution. 
 
 Large project problems often overlook the timid and slow. — It is in 
 problem-solving which centers in large projects that the teacher 
 needs particularly to be self-possessed and resourceful in providing 
 for individual differences. For example, one sixth-grade class 
 spent twelve weeks on a project dealing with the topic '' Ships and 
 Shipbuilding."^ In carrjdng out this project, the pupils undertook 
 a variety of problems of an expressional character. In such teach- 
 ing, the more capable pupils exhibit so much talent in planning and 
 
 ' The pubKshing of carefully prepared printed problems with the data for their 
 solution will greatly facilitate the adoption of problem-solving methods in geography 
 and the social sciences, especially by busy or inexperienced teachers. For examples 
 of such publications for college classes see the series of Parallel Source Problems in 
 History pubUshed by Harpers, and my own Exercises for Methods of Teaching in 
 High Schools published by Ginn. 
 
 * Edith Parker, "A Sixth-Grade English Unit," Elementary School Journal, 
 XV (October, 1914), 82-90. 
 
ipso] PROBLEM-SOLVING OR PRACTICE IN THINKING 55 
 
 devising things to do that they are likely to monopolize the interest 
 of the teacher, leaving little or nothing of a problem type for the 
 slow or the timid pupils to concern themselves with. This fact led 
 Miss Parker, who organized this twelve weeks' project, to emphasize 
 the fact, as we noted above, that in many problem-solving lessons 
 the slow pupils are left entirely out of the game. 
 
 Conclusion of articles on problem-solving. — We opened these 
 articles with an account of the part played by problem-solving in 
 social life. We found both practical and speculative problems 
 interesting children and adults. We found problems of many 
 types, such as mechanical, diplomatic, moral, aesthetic, mathe- 
 matical, etc. In Section II, we presented in detail four actual 
 lessons which gave us concrete pictures of the conversational reflect- 
 ive activity that prevails in skilfully conducted problem-solving 
 discussion lessons. In Section III, we showed how great problem- 
 solvers think. We found them making many suggestions, evaluating 
 these carefully and discarding the erroneous ones, and main- 
 taining an unbiased impartial attitude in their conclusions. From 
 Sections II and III we derived a number of rules for training pupils 
 in problem-solving which we presented in Section IV. We suggest 
 that the reader learn the summary of these rules as given above, 
 and then with concrete pictures of the actual lessons given in 
 Section II, plan to undertake, at least occasionally, to conduct 
 problem-solving lessons in her own teaching. We prophesy that 
 if she is a good thinker herself, she will find great pleasure in trying 
 to develop skill in this important type of artistic teaching. 
 
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