Directing study

Preface

The aim of this book is to direct study toward mastery through creative thinking. The following may be looked upon as major aspects of the discussion: (i) to present various illustrative procedures; (2) to provide a theory and a plan of organization of classroom work in which this sense of mastery and power may be gained by students; (3) to indicate ways of dealing with individuals of varying achievements in the same group so that each student instead of the class-group becomes the educative unit; (4) to suggest shifts in emphasis from the traditionally assigned lesson in which pupils are asked to memorize or paraphrase and recite passively, to directed and controlled classroom activity (study) in which all pupils are participating, reacting agents all the time, and are moving forward, inspired by the challenge of problem-setting situations; (5) to move steadily from classified groups and group-mediocrity to individual activity and the co-operating spirit ; (6) to propose as a guiding idea to all teachers that we give boys and girls things to do in the doing of which they will find out what we would like to have them know. It is becoming increasingly evident that incalculable sources of human power yet untapped await liberation from repressions and inhibitions of traditional pracvi PREFACE •

tices, and that we can confidently look for a new day to dawn in education when we devise ways of rewarding students not for having brains but for using their brains.

The point of departure, stated in the most recent categories, is the proposition that, if one boy's I. Q. (Intelligence Quotient) is 8/10, another 9/10, another 13/10, then it is the problem of education to develop methods that will insure the full release of powers in every individual. The boy with an index of 9/10 ought to be induced to do 9/10 of his algebra, language, science (any study) with a real mastery. By the same token, the girl with an index of 13/10 should be rewarded for a corresponding achievement with nothing short of 13/10 of her algebra, language, science, or any other study. In spite of any assumptions about native capacity, society will probably continue to reward the individual who uses his "talent," be it one, two, or five.

I have had especially in mind upper-grade and high school teaching in this discussion. Parents who participate so generously in assisting their children. in getting the lessons assigned by teachers may well be interested. The improvement of teaching is held to be imperative in the inspiriting task of securing adequate schooling for the youth of the nation. While the discussion is centred about the problems of education in the Junior and Senior High School, Normal Schools and Colleges of Education will no doubt be vitally interested in the issues presented and discussed. Institutions for the training of teachers are now in a

PREFACE vii

strategic position to direct in productive ways the movements for supervised study, co-operative learning, project-teaching, measurements of education, learning for mastery, and creativeness in thinking. All these movements come to a focus in the habits of work which boys and girls are developing.

The task of education, as I see it, is the production of a people capable of thinking, and with a mental attitude which is tolerant, fearlessly honest, expectant of change, and creative. We need a mind capable of analyzing problems in the light of facts. The High School age is full of possibilities for the development of this proposition. In fact, if curiosity were not throttled, this view might be accepted as thoroughly sound in every stage of education.

We make the individual. Our public educational institutions are not certifying agencies, maintained to select the "called and chosen." The more hopeful view is that democratic education is concerned with the production of desirable changes and the prevention of undesirable habits in all individuals. The great teacher is the one able to stimulate curiosity, to foster interest in the search for knowledge, and to develop enthusiasm for the challenge of a problem. To guide mental life is the supreme work of the real teacher. Not the least significant factor in the development of a new general method, if it is to be a major achievement, will be the removal of inhibitions to learning.

To a very large number of my colleagues and other good teachers who have assisted me in working out illustrative procedures and in developing many viii PREFACE

phases of the thesis presented in this book I am tinder lasting obligations. To Dr. F. M. McMurry, whose book, "How to Study and Teaching How to Study," has been a constant challenge for more than a decade, I am indebted in a very direct sense. - He suggested thinking periods, as a substitute for recitation periods. We ought to be prepared now for the change.

H. L. M.

Contents

CHAPTEtt PAGE

I. A Manual of Suggestive Procedures . . i

II. Administration of Directing Study . . 59

Chapter I A Manual Of Suggestive Procedures

Most parents send their children to school in the expectation that the teacher is in possession of something which is to be passed on or over to the pupils. The majority of students attend lectures with the same notion, and go to books to get what the author has to say. The emphasis in the use of text-books is too often along these same lines of absorption of subject-matter. School architecture betrays a philosophy of education; the furniture is arranged with a view to instillation. The devotion to "learning" as the acceptance of facts is remarkable in this age of scientific questing. The learner is almost universally regarded as a recipient. Communicated facts, all along the line — in mere telling, in reading the book, in listening to explanation, in sitting before the moving-picture — constitute the essential basis of "learning."

In the proposed procedure, not less, but vastly greater, use will be made of communicated facts. The situation to be avoided is a mass of unleavened dough. What we need to do is to see to it that the salt has not lost its savor. Enough should be done in the field of self-discovered facts to hold in solution the great mass of communicated material; enough work in self-discovery to create a genuine taste for analysis and to develop appreciation of man's task in building our civilization.

A taught me mathematics [or any other thing for that] too often means that A instilled into me some of the knowledge he possessed, that he inoculated me with it. Surely that is superficial and erroneous. The fundamental truth is that he put me en rapport with mathematical processes, and such success as was attained is properly described as my adjustment to this quantitative aspect of reality and that of it to me. The adjustment was not of me and him, but of me and this department of truth. And the issue is vital. For we all know that A is sometimes so imbued with the conception of instillation that he is a positive hindrance to adjustment, well meaning and enthusiastic though he may be.*

Montessori has made an invaluable contribution to procedure for creative thinking. The child is brought into vital relations with his problem. The form-board, for example, is the subject-matter. The prisms and cylinders of different sizes and the arrangement of moulds into which these may be fitted constitute a major part of the controlled environment. The child faces his problem with something to do. If he places the blocks in their respective moulds without difficulty, then there is no challenge to thinking. Or, to put it in another way, if there is no "fumbling and success," no thinking will be initiated. With Dewey, mind is the instrument by which we overcome obstacles and thinking takes place only when action is checked. If the child comes to the placement of the last block — prism or cylinder — and finds the form into which he tries to place it too small, he is at once confronted * Adamson, The Individual and the Environment, p. 28.

with a real problem. What has been done must be reconsidered. He may see at a glance that some piece has been placed in a form too large for it; he may have "to throw down the type," as it were, and start all over, not once, but many times. In this situation the business of the teacher is to watch with an Emersonian respect.

But the old education is impatient with watching. The teacher or the book steps in and tells the child just what to do, or actually does it for him. The institutional teacher rearranges the pieces on the child's form-board and shows the child how easy it is (for him — the schoolmaster). As hopefully expect the child to learn to lace his own shoes by doing it for him everlastingly, as to expect mastery and creative thinking as a positive outcome of our conventional practices. Even the questions (so-called), intended to guide the pupil in a learning situation, are so framed as to disclose the answers, thereby destroying the basis for creative thinking.

The exponents of efficiency in education will urge the necessity of economy and "results." It will be shown that we do not have time to wait on the child's procedure of "fumbling and success." Perhaps all we need to say in this connection now is to suggest that any move on the part of a teacher in the pupil's dilemma in a learning situation should not checkmate the pupil. In the interests of economy a particular stumbling-block may be removed. The aim should be to assist the learner to further effort in the solution of his problem. We shall attempt to indicate in these illustrative procedures that where there is no problem there is no thinking.

For the past five years a class in Plant Life (9th and 10th grade Agriculture) in the University of Wisconsin High School has been conducted under geared-up Montessori principles and in accord with the procedure suggested in Exercise I, page 6. The materials of the course were set out in concrete forms and the question as a factor of control was used with rare skill.

In every subject the materials of instruction should be so fabricated as to enable the pupil to check up his thinking. The objective means of checking up one's work will not be so evident in all subject-matter as is the case in the form-board; yet there are unrealized possibilities of organization of both subject-matter and procedure to this end. Much of the lack of intelligence in school and college is due to lack of necessity for rigid intellectual discipline and a definite responsibility for whatever thinking goes on. The professions of education and medicine may yield to the profession of engineering in the following vivid and rather severe, perhaps unfair, contrast:

Fortunately for us, most diseases are self-eliminating. But it is natural for the physician to turn this dispensation of nature to his advantage and to intimate that he has cured John Smith, when actually Nature has done the trick. On the contrary, should John Smith die, the good doctor can assume a pious expression and suggest that, despite his own incredible skill and tremendous effort, it was God's (or Nature's) will that John should pass beyond. Now the engineer is open to no such temptation. He builds a bridge or erects a building, and disaster is sure to follow any misstep in calculation or fault of construction. Should such a calamity occur, he is presently discredited and disappears from view. Thus he is held up to a high mark of intellectual rigor and discipline that is utterly unknown in the world the doctor [or the teacher] inhabits. (Civilization in the United States, p. 455.)

It is maintained that engineers head the list in intelligence, being rated 60 per cent higher than doctors. The rating of doctors above (or below) teachers is not disclosed, nor is it to be assumed that the work of teachers can be checked up with such exactness as that of the engineer. Nevertheless, the position is maintained that the profession of teaching may be made a challenge to intellectual rigor and discipline comparable to the challenge that comes to the engineer. This high ground is not to be reached by mechanical methods, by dismissing John Smith from the class or school, by burying curiosity alive, nor by any presuppositions about God's (or Nature's) will to the effect that John can't learn it. With the engineer we need to cultivate the courage and develop the technic to build bridges in the face of self-created obstacles.

It is perfectly possible to become so obsessed by the instruments of education as to inhibit vital learning. The specialist and the pedant are both open to this danger. The former tends to lead the pupil who is not so tall as a rule into the narrow channel of specialization or within high protective tariff (pedagogical) boundaries, and too often suffocates him among the dust of detail, for the specialist is still able to see beyond the narrow margins of detail and catch something of the meaning of making the detail a witness to a great and universal significance. The pedant, on the other hand, too often superimposes subject-matter, method, problem, "project," leaving the pupil an everlasting minor. All of this is a disregard of the democratic ideal in procedure. The consent of the governed is denied. We want to indicate in these suggestive procedures a life basis, a plan of participation, a means of a shared life, a kind of mutuality in which the pupil becomes a partner in a developing subject and in a self-realizing, self-originating plan. The hope is that even greater levy on facts, information, and data (accredited subject-matter) will be made than is possible in the recitation system or the lecture method.

Many suggestions in directing procedure for creative thinking have been incorporated in the discussion. The reader may loop them up in this connection as he chooses.

For point of departure. (This exercise is of inestimable value for all teachers, including parents, from the kindergarten to the graduate school.) The building (creation) of any story will serve the purpose here. The aim is to furnish the mind with something to work on with a real question in front of some potential answer.

Bill (seven or eight years of age). "One time there was a man left on an island all alone." (More data may be furnished if the experiment calls for further facts, such as: in this man's home there was a picture of a ship, or this man's father was a captain, etc.) Now, raise the question. "How did this man come to be left on the island ? " Bill will find a solution.

Bear in mind, the old education would have the learner read the story and reproduce it, or the learner would be told the story (answer) and asked to repeat it. In the quest for creative thinking the child works out his own story, recreates the story within a controlled environment. The new teacher furnishes the mind with something to think with.

Bill (further on in the challenge). "One day your

Robinson Crusoe got sick. What could you do in your own home that your Robinson Crusoe could not do? What would your Robinson Crusoe do?" Bill will work it out.

The text of Defoe's Robinson Crusoe may be used after raising productive questions in the minds of our boys and girls. The teacher knows the standard story. His task is to think it in terms of challenges, and then to set forth data which will stimulate curiosity, and cunningly put a question which the data suggest. All of the text material may be aligned ("covered") in this procedure after the challenging questions are raised, and the creative genius of the boys and girls is given a chance to express itself.

The leit-motif of all history is suggested in this plan of approach. The time may come when history up through the high school will be studied with a view to building minds capable of analyzing problems in the light of facts.

II Social Studies and Science

For any year of the junior or senior high school. (The college needs it.) Data. Radio work. Wave-lengths (bands) in the air. Broadcasting news. A committee of radio experts of many nations sitting in Paris. The experts proposed that specific wave-lengths of high frequency be allocated (assigned) to each nation.

Questions. — Why? Any bearing on a League of Nations ?

Procedure. — Pupils (including girls) do not need to be assigned readings in order to answer intelligently these questions. They may be presented the data and at once try their wings on the questions. First, discussion in terms of experience and broadcasted knowledge among youngsters to-day and then readings followed by a productively written chapter on "The Relation of Science to Modern Life," or "The Development of Radio."

This experiment was carried out in a large class of ioth-grade pupils and incidentally tried out on a half-dozen college seniors (men) . The latter failed ignominiously. They appeared dazed. They had been corrupted to the very roots under the doctrine of "learning" as the acceptance of facts, and before the data and questions they appeared helpless. They could have taken notes on a lecture or read assignments, and they could, no doubt, have reproduced and recited with rare brilliancy. The boys and girls were alert to the questions in the light of the data presented. One little girl said: "The nations will have to agree on a distribution of wave-lengths, or else all news will be broadcasted, and then there would be no secrets. Nations would have to behave." A boy said: "The fact of getting together and agreeing to assign each nation a particular set of wave-lengths would mean unity." Another with a free mind at work said: "Each government would have a machine tuned for each nation and would catch any messages sent from one to another, but the governments would agree not to broadcast each other's private affairs," etc. (The discussion would have been illuminating to our statesmen.)

III For Any Grade above jtr and below the 17TH

For "substance of doctrine" as well as a realizable procedure in any school.

Problem (or challenge). — The development of a scientific (experimental) attitude. Data. Two characters representing :

(a) The "Old World"

Key. "Old World" is closed.

Things are fixed.

"Nobody ever did it, therefore it can't be done."

(6) The "New World"

"New World" is open, expectant of change, creative.

"So he buckled in with a bit of a grin at what could not be done, and he did it." (In this experiment a pupil in the class found a poem and boiled it down to this. He was stimulated by the Old World motto.) Procedure.

(a) Now let Aristotle and Sophocles debate with Burbank and Edison. (St. Augustine and Luther might be induced to debate with Bacon and Darwin. A dramatized debate for adolescents is usually a spirited event and elicits the best in the debaters.) The pupils (10th grade or later) will be able to write (create) a play in which these men are the leading characters. They may summon other characters to speak. This was done. The "New World" may have a slave out of the Old World to portray his life; a woman may also be summoned to relate her lot. One girl in working up such a play proposed that she be a fairy and have the boy of the class interested in science become a wizard.

(The fairy played the part of "Looking Backward" from 1950. The play as well as the debate has proved valuable and interesting.)

An enormous amount of "accredited" subject-matter can be looped up in both the production of the debate and the creation of the play.

(b) Data for another part of the challenge

The "Old World" says:

"The acorn can grow only into the oak."

"Wild oats can grow only into wild oats."

"The boy grows up into the man, and the boy can become only what his heredity makes him."

(c) Data (once more) The genius is born, not made, says the "Old World."

Talent is donated. Hence there must always be "those who" can and "those who" can't do it.

The "New World" answers: "New species can be developed by man." Burbank tells us a lot of interesting things. (The pupils work this out.) Mr. Edison, what is your answer to the "Old World" here, when "they say": "We have always had candles and they make the best light ever"? (Let the pupils work all this out. It can be done in discussion, through reading and discussion, through film and written reactions, through debate, through dramatic representation, through writing a chapter in a creative book made by the pupils themselves.)

How is the "New World" going to answer now? (Any live class will be ready

for a thrilling debate. If so,

let it be negotiated.)

Do we make the individual in the "New World"? How?

What is the purpose of education ?

Do you think World" has a date period?

the "Old name-and-

(e) The "Old World" says: "We have always had war and we always will."

Are arts, science, music, architecture, literature nationally bounded any longer?

Do you think there are any "folks" living in the 20th century who really have minds and entertain ideas belonging to the $th, 14th, or 17th century?

What is the "New World's" answer?

(A good time to examine the history of international agreements and co-operations in exhibitions, congresses, Postal Union, Red Cross work, and League of Nations.)

(/) For pupils in the senior high school (and the college) the possibilities and unifying effects of international insurance and the world-wide extension and application of the Federal Reserve Bank may be discussed and worked up into original (creative) chapters. It is wholly superfluous to add that an infinitely greater amount of information will be required in this problem-procedure than is possible under the cut-and-dried lecture system and lesson-assigning, lesson-hearing school where all march in regimental uniformity.

The time to be allotted to this exercise (III) is left to the discretion of the school and its new teacher. There is easily a whole semester's work suggested here for a class in Social Science. Many transmissions ahead are possible in problems of this kind. One week spent in experimental questing along lines suggested in this exercise has proved a profitable venture, not only in senior high-school science and social studies, but also for students (college seniors) preparing to teach. In any case it is well to have the students construct a chapter on some such topic as the "Development of Modern Science."

IV For 6th or jth Grade

Challenge. — The fraction operating in the equation. (One of a few outstanding principles to be mastered.)

Exercise. — %, or %, or %, or %, or % l} or y 2 , or %, or *% of my money is $100. How much have I in each case ?

Procedure. — (Intended to clarify the principle involved.)

Working Materials. — (If the first day of school, let the teacher be provided with a pocketful of pencils and plenty of scratch paper prepared to start work at once; keep every youngster so busy that no time is available for "fooling.")

If jour dogs cost $100, what will five dogs cost? (Work it out orally, finding cost of one dog first and then five dogs.)

Now express it thus:

-r^— = $ioo dogs

Again. If four-fifths of my money, etc., *. e., substitute fifths for dogs. (Subsequently substitute for dogs (the denominator) thirds, sevenths, thirteenths, elevenths, half, halves, sixths.)

A MANUAL OF SUGGESTIVE PROCEDURES 13 Now express it thus:

fifths rrr (of my m.) must equal (?) liitn

Finally express it:

(There will be need of clarifying the idea of unity.)

Above all, see to it that dogs and fifths are denominators. (Teachers, I pray you, dwell on the meaning of denominator.)

Before using the exercises in the book the pupils should make up their own exercises for two or three days, using all sorts of imagery in the denominators employed.

Swinging out into a new challenge with a clearing up of the fundamental principle involved, using simple, vivid, illustrative material to exemplify the principle, ought to bring pupils into a better and a more abiding understanding of mathematical reality than is exhibited in the endless working of sets of "problems" by formulas, or ready-made patterns.

Challenge. — A set of exercises in arithmetic, algebra, a foreign language, or any other subject in which a number of exercises in some organizing principle is clearly presented. To illustrate:

Factoring in algebra (8th or 9th grade) is the unifying core of a part of the course. After five minutes of general explanation of a new phase of factoring in which the whole class participated, each pupil started into the set of exercises and worked as rapidly as possible. The teacher checked results, guided procedures, explained to any one pupil or group of pupils some principle needing further elucidation, called the whole class to concerted attention when any fundamental concept could be focussed upon economically. The exercises in this illustration involved the differences of squares. Some 60 exercises were listed. In the course of the remainder of the class period the number of exercises mastered ranged from 10 to 55. No upper limit was set. Each pupil worked forward in the challenge at his own best rate.

In a class in geometry, 36 pupils all started at the beginning of a 70-minute class period on a set of 19 original exercises listed at the close of the book on the circle (Wells and Hart). The pupils worked in pairs at the board. Their work was checked as rapidly as enough proof was given to indicate mastery. Five pupils who began 10 minutes before the class period formally began completed the entire set during the class period. The range was all the way from a mastery of 3 exercises to 19 exercises. The teacher was kept busy checking results and suggesting modes of attack to pupils in difficulty. The two boys who finished the entire set 15 minutes before the period was up assisted the teacher in this work.

The same procedure may be employed in word study, work on sentences, reading of literature of a type or period, composition, exercises in foreign language, etc.

Two important matters should be mentioned in this connection: (1) The organizing principle should be clear. (2) No upper limit should be set in the number of exercises. Enough work should be at hand to challenge every ability in the class group. It is not a uniformity that is sought in true education. The unity (not uniformity) is gained by all those co-operations which evolve out of a challenge clearly distinguished as to some organizing principles and a progressive series of exercises within the gripping principles.

VI

ioth Grade (Mathematics: Core — Demonstrative

Geometry)

Challenge. — The Circle. (The material, the best modern texts — Book II.)

Procedure. — (The procedure in this illustration is based upon the work of a class of thirty-eight pupils of very wide ranges of "capacity" and achievement. In fact, a conspicuous minority of this class had been tried and found wanting — pronounced to be, if not "mathematical idiots," at least mathematically disinclined or obsessed by defense mechanisms. One purpose in the experiment was the attempt to demonstrate the feasibility of managing a large section with extremes of "ability" and attainment, well known at the outset.)

(a) When the challenge was entered upon, a word was mentioned about the assignment. The assignment was the circle. For a period of five or six weeks nothing was said about assignment. No daily assignment was mentioned. The individual pupils who needed stimulus were operated on as they needed it.

(b) The class period (70 minutes) was developed into a work period. This class period has never proved too long — always too short. Work begun in class was continued out of class largely upon the initiative of the pupils. Saturday mornings were employed for clinic purposes for any pupils who for any reason (absence mainly) did not make satisfactory progress. Four hours on the job, steady, makes a difference in any struggling pupil. (See Chapter II, p. 71.)

(c) The challenge (the circle) is the organizing principle, and the exercises and propositions furnish the differentials. (See Chapter IV.) The big challenge was broken up into four or five major organizing principles around which and with which discussion could be carried on in a profitable manner. Recitation work, as we ordinarily find it, was deleted.

The following organizing means were employed as principles to think with:

1. A radius perpendicular to a chord.

2. A radius drawn to a tangent at point of contact.

3. Measuring angles. Angles measured by the same number

of arc degrees.

5. Loci problems — a few clarifying principles.

These, or some aspects of them, were written on the board from time to time to guide the thinking of the pupils.

(d) No effort was made to keep the class together. Goal ends were mentioned from time to time. " Now, don't you think we had better be prepared to discuss measuring angles next Monday?" Or, "Would it not be a good idea for you to have mastered our challenge by next Saturday night before 10 o'clock, so that we can all start on loci problems one week from to-day ? " No two pupils were ever found at the same place in any part of the challenge. Responsibility was sought in many ways. The great majority of pupils in a working laboratory do not need to be prodded and supported in their work. After working into some part of the challenge, after mastering some of the working tools, and after learning the game, as it were, by individual guidance and checking of results, the whole class enter into vigorous discussion and snappy response to rapid-fire questions.