What Education has Learned from Psychology, VIII: Individual and Formal Discipline
by Percival M. Symonds - 1959
The statements in educational psychology texts authoritative as they are, have not been seen by many who are confused as to what education can accomplish. This discussion may reach many who would welcome a fresh statement of psychological findings bearing on transfer and formal discipline.
IT MIGHT SEEM AS THOUGH THERE WERE little need for a new statement with regard to transfer and formal discipline, inasmuch as there are already many excellent reviews of the psychological findings relating to these topics1. More than a score of texts in educational psychology published within the past few years have reviewed most adequately the experimental literature dealing with transfer and have drawn applications to education. But there are several reasons why a fresh appraisal of these psychological investigations is timely. One of the perennial controversies that beset American education concerns "formal discipline" or the capacity of education to "train the mind." This issue had remained relatively dormant for some years, but in late 1957 it erupted into the open after the Russians launched the first artificial satellite and the United States was confronted with the fact that it had serious competition from Soviet technology. Facts about transfer and formal discipline are central in the resolution of these controversies.
The statements in educational psychology texts referred to above, authoritative as they are, have not been seen by many who are confused as to what education can accomplish. This discussion may reach many who would welcome a fresh statement of psychological findings bearing on transfer and formal discipline. And there is the possibility that a closer look at the experimental results might lead to new applications, or at least to a new emphasis on the application of these important matters.
The formal disciplinary point of view is deeply ingrained in the thinking of Western culture. It grows naturally out of the Platonic emphasis on the relative independence of mind as separate from the milieu in which it functions.
In the famous Book VII of Plato's Republic, in which Socrates discourses with Glaucon on what shall be the education of future citizens of the Republic, one finds the following dialogue between Socrates and Glaucon.
"And have you further observed, that those who have a natural talent for calculation are generally quick at every other kind of knowledge; and even the dull, if they have had an arithmetical training, although they may derive no other advantage from it, always become much quicker than they would otherwise have been."
"And indeed, you will not easily find a more difficult study, and not many as difficult."
"You will not."
"And, for these reasons, arithmetic is a kind of knowledge in which the best natures should be trained, and which must not be given up."
Here is the essence of the formal discipline point of view. The study of arithmetic (mathematics) quickens the mental faculties, even of the dull, and presumably gives them mental powers that can be used for any mental task. Training the mind is like strengthening a muscle which, when strengthened, can be put to any kind of muscular work, or like honing a knife, which when sharpened, can cut whatever is desired. Note also that the merit of arithmetic is that it is difficult. According to the formal disciplinary point of view, one strengthens and quickens the mind by exercising it on difficult, abstract subjects, just as a muscle is strengthened by lifting heavy weights.
Coming down to more modern times, John Locke was the advocate of faculty psychology and formal discipline. He wrote:
I have mentioned Mathematics as a way to settle in the mind a habit of reasoning closely and in train; not that I think it necessary that all men should be deep mathematicians, but that, having got the way of reasoning which that study necessarily brings the mind to, they might be able to transfer it to other parts of knowledge, as they shall have occasion.3
In 1892 a "Committee of Ten" of the National Education Association expressed the same point of view:
The principal end of all education is training. In this respect history has a value different from, but in no way inferior to, that of languages, mathematics and science. The mind is chiefly developed in three ways: by cultivating the powers of discriminative observation, by strengthening the logical faculty of following an argument from point to point; and by ripening the process of comparison, that is, judgment.
As studies in languages and in the natural sciences are best adapted to cultivate the habits of observation; as mathematics are the traditional training of the reasoning faculties; so history and its allied branches are better adapted than any other studies to promote the invaluable mental power which we call the judgment."4
That this point of view is still very much alive is apparent from the following statement by President Griswold of Yale University:
[The liberal arts] are studies designed to develop to capacity the intellectual and spiritual powers of the individual. Their aim is to make the most of a man in order that he may make the most of his calling, his cultural opportunities and his responsibilities as a citizen. Such was the meaning of the liberal arts in Plato's time and such is it today.5
And what is the testimony of psychology concerning transfer and formal discipline? As is the case in considering so many other topics in psychology, we begin with an often-quoted experiment of William James, remarkable because as a psychological experiment it antedates by many years the experimental approach to psychological problems in this country. In a footnote in Volume I of his Psychology, James tells how he and his students attempted to improve their memories by practice.6 After testing himself by learning 158 lines of Victor Hugo's Satyr, he practiced for thirty-eight days in memorizing the entire first book of Milton's Paradise Lost. At the end of that period he returned to Victor Hugo's poem and found that he was even slower in memorizing it than before. He added that he intended to prosecute his experiments further, but there is no record that he ever did. Years later, however, Winch7 and Sleight,8 British psychologists, verified James's conclusion that one does not improve the ability to memorize by practicing it. This unexpected finding has often been referred to as demonstrating that practice does not necessarily "strengthen" a mental function. Psychology thus early questioned a centuries-old belief!
In the decade that followed James's report, the mental measurements movement got under way and in 1901 Thorndike and Woodworth reported experiments on transfer in the estimation of areas, lengths, and weights and on training in various forms of observation and perception. Other experiments, too numerous to mention here, studied transfer of discrimination and sensorimotor associative habits. The outcome of these experiments showed the possibility of some transfersometimes positive, sometimes negative, usually close to zero. Thorndike and Woodworth summarized these results succinctly: "Improvement in any single mental function rarely brings about equal improvement in any other function, no matter how similar."9 Learning to play the piano may transfer to the organ because of the similarity of the keyboard, but there may be interference because the touch on the two instruments is so differentone strikes a piano key, but one presses an organ key. Learning to play tennis may transfer to the playing of badminton, but the strokes are quite dissimilar and there may be difficulty at first in learning badminton after one has become skilled in tennis. The study of Latin may result in an increase of English vocabulary, especially in words with Latin roots, but there is no assurance that this transfer will take place.10 Learning to take notes in class in high school may set the pattern for taking notes in classes in college. Learning to use the resources of the library in one's home town may establish skills which promote efficient use of the university library.
Thorndike and Woodworth summarized their findings in the following statement: "Spread of practice occurs only where identical elements are concerned in the influencing and influenced functions."11 Here we have the first use of the famous phrase "identical elements." But it was not until 1906 that Thorndike generalized this brief statement with these words: "These identical elements may be in the stuff, the data concerned in the training, or in the attitude, the method taken with it. The former kind may be called identities of substance and the latter identities of procedure."12
These formulae have had a tremendous impact on educational theory and practice. It is probably too much to assert that the theory of identical elements has been the sole influence in the widespread shift in the curriculum away from formal, abstract subjects toward more practical and useful subjects, but it undoubtedly exerted an influence by lending support to the shift. The theory of identical elements has provided the sanction for practical arts education and life adjustment education. It has helped to eliminate Latin and Greek and ancient history from the secondary school curriculum. This trend has been salutary, for it has provided millions of children with an education that has greater functional value than the old classical education.
But the movement undoubtedly has gone too far, and its excesses have made it a laughingstock and whipping boy. As we shall see later, substance or content has been interpreted too narrowly and this practice has deprived abler students of subject matter which has a wider application than some which may be put to immediate and practical use. There is a well-founded reaction against a too-narrow interpretation of identical elements.13 But as Margaret Mead has so aptly put it, the reaction should not be a pendulum return to the older curriculum, but a spiral ascent to more abstract material which would have wider transfer value. It would be folly to return to the extreme formalism which characterized the curricula of earlier generations.
Of the two varieties of identical elementsthose of content and those of procedure or methodthe former has received more stress. This has been a misplaced emphasis, in this writer's judgment. Knowledge has multiplied so rapidly that no one, not even the expert, can know all about any subject, or even any narrow aspect of a subject. The moral of this should be that teachers need no longer feel an obligation to "complete" a subject; that is, to cover all that is included in a textbook, a syllabus, or a course of study. Instead of aiming at completion, a teacher would do well to plan to cover less ground and to put more stress on method and procedure in the ground covered. Students need to be helped to learn the most efficient methods of study, the use of materials, and skills that will help them in their learning. They need to be given detailed guidance in how to use a book, the library, the materials in the laboratory. They need help in learning how to concentrate, to avoid distraction, to plan, to take responsibility. The aim of the teacher should not be to "cover" the term's work in algebra, grammar, geography, but to help students to work independently so that if they wish, they can "complete" the textbook or the syllabus on their own. Helping students to acquire skills and methods is the best assurance that learning will transfer.
Increasingly, preparation for the specific skills of a given occupation is provided on the job, and more big corporations are establishing "schools" in which to train competent workers.14 What business and industry want the public school to provide is training in the basic skills of language and number and in general methods of work, so that those who seek jobs will be well grounded in these areas.
Vigorous work on transfer is still being carried on in experimental psychology under the general rubric of "stimulus generalization." Stimulus generalization refers to the phenomenon that a given response b may be made to stimuli a1, a2, a3, which resemble more or less closely stimulus a, to which the response b has previously been learned, and this concept of stimulus generalization defines the problem of transfer.
The early studies of transfer, showing that the amount of transfer was much less in most functions than was popularly expected, did not satisfy the proponents of formal discipline. Perhaps the experiments tested the possibility of transfer in functions that were too narrow, or possibly one finds growth in mental power only in the study of a "subject," as Plato suggested. Thorndike tested this possibility in what is now a classic experiment.15 On the assumption that growth in mental power can be measured by increase in score on mental tests, he tested high school students at the beginning and end of a school year with specially constructed measures of selective and relational thinking and generalizing and organizing abilities. Then he compared the results for students having programs that differed in only one study, in order to determine the growth in mental ability that could be attributed to a single study. The outcome demonstrated that gains on a mental test could not be attributed to any single subject of study. Whereas the average gain was 11.1 points, the best gain that could be attributed to a subject was in the neighborhood of 2.5 points. Thorndike repeated this large-scale study three years later, with similar results.16
An interesting additional finding of the study was that the best 1 per cent in initial ability gained an average of 20.5 points whereas the lowest 1 per cent gained only 1.5, while the difference in gain between the best and the poorest subject of study was in the neighborhood of 3.5. Thorndike's own interpretation of these results has often been quoted:
The chief reason why good thinkers seem superficially to have been made such by having taken certain school studies, is that good thinkers have taken such studies, becoming better by the inherent tendency of the good to gain more than the poor from any study. When the good thinkers studied Latin and Greek, these studies seemed to make good thinking. Now that the good thinkers study physics and trigonometry, these seem to make good thinkers. If the abler pupils should all study physical education and dramatic art, these subjects would seem to make good thinkers. These were, indeed, a large fraction of the program of studies for the best thinkers the world has produced, the Athenian Greeks.17
Nearly two decades later Wesman repeated Thorndike's study using standardized achievement tests to measure growth in subjects as well as the before-and-after measure of general ability. With improved statistical procedures Wesman again verified Thorndike's original findings.18
Thorndike attributed the greater gains of those with the initial high scores to native ability which we call intelligence. Today we would prefer to say that the greater gains were made by those who had learned how to improve in general ability, placing the emphasis on method, rather than on inherent ability.
These results showing that school subjects do not have disciplinary value in and by themselves have been difficult to accept, but they have been substantiated by much research on the value of having studied separate subjects. C. A. Smith reported, after having correlated grades in the various high school subjects against college grades in the freshman year at the University of Wisconsin, that "very little difference in value can be placed on success in the various fields of study in high school in predicting the student's success in college."19 Powers found that those who had not taken chemistry in high school did about as well in college chemistry as those who had.20 Floyd discovered no statistically significant difference between the achievements in biology, chemistry, or physics of a college group which had had general science in high school and the group which had not.21
Douglass came to a similar conclusion: that "there is no significant correlation between the number of units of credit earned in high school in any subject matter field and scholastic success in college."22 A similar finding has been reported by Hoff.23
Ulmer found that there was little transfer from ordinary geometry classes to ability to reason in general.24 (This is not Ulmer's main conclusion, which will be discussed later.)
Briggs demonstrated in a careful experiment that pupils who had intensive instruction in English grammar did not excel similar pupils without this instruction in such functions as ability to see likenesses or differences, ability to test reasons, ability to reason in arithmetic, ability to reason syllogistically, and the like.25
Rugg demonstrated that the study of demonstrative geometry transfers to other abilities, all of which, however, depend on spatial visualization and the ability to manipulate spatial elements of experience.26
The experimental results have not been uniformly on the negative side, and in particular the study of Latin has been found related to superior subsequent academic achievement, even when intelligence has been eliminated as a factor. Sorenson, whose investigation reached these conclusions, interestingly enough did not attribute the results to the Latin. He says, "Only one thing can be definitely said about the completion of three or four years of Latin. It marks a student as a good student."27 Sorenson would attribute the greater ensuing success to selective factors in part, which he suggests is an expensive method of selection. And one might add that the study of Latin may have contributed valuable habits of study to those who stayed with the subject.
Smith and Douglass also found that "students who study Latin in high school may be expected to make, on the average, slightly higher marks in their first year at an arts college than pupils of equal ability who have studied German or who have studied no foreign language."28
The evidence is conclusive and the conclusion inescapable that one does not achieve mental power by means of a particular subject of study. Mental power intelligenceif it can be achieved through study must come not by virtue of the subject matter but through the methods employed and hence learned. Mental growth depends primarily on how a subject is taught and on the emphasis in its teaching. With regard to the issue with which this article was introduced, the evidence leads to the further conclusion that if an aim of education is to increase mental power, the primary emphasis in teacher preparation should be not on mastery of subject matter but on pedagogical method, and this, of course, gives support to the importance of professional education in the training of a teacher.
The point was made in an earlier article in this series ("Reward," Teachers College Record, October 1955) that the essential difference of opinion today in psychology does not reside in the traditional schools (behaviorism, connection-ism, or field theory) but in the assumption as to the mechanical or cognitive nature of mental processes. Thorndike and Hull adopted a mechanistic position which they believed to be the only scientifically tenable one and the majority of contemporary experimental psychologists have endorsed it. Mind was conceptualized in terms of stimulus and response, experiments were set up on a trial-and-error model with no interference through instruction or guidance. Behavior which was determined by cognition, understanding, and dependence on the application of knowledge and principles was thought to be imperfectly analyzed, and there was believed to be something mystical about a psychology based on the intervention of such intervening variables. But just as hydrogen and oxygen have their own properties which are not recognizable when they are combined to produce water, and water loses its properties when broken down into its chemical elements, so mental processes depending on cognition lose their characteristic properties when analyzed into stimulus and response. The methods of experiment of James, Wood-worth and Thorndike meet scientific criteria, but unfortunately they prevent the discovery of possibilities of transfer through cognitive means. Any statistician will tell you that it is impossible to prove the null hypothesis. James, Meumann, Winch, and Sleight may have shown that memory cannot be trained through practice, but they have not proved that memory cannot be trained.
If it were not for the fact that James and the others came first, used accepted experimental procedures, and have established reputations, the later experiment and demonstration by Woodrow in 1927, which is of far greater significance than these earlier experiments, would have attracted more attention, for Woodrow demonstrated that memory (in a general sense) could be improved by teaching certain techniques of memorizing.29 Woodrow's experiment, in addition to providing mere practice in memorizing, instructed the subjects in methods of memorizing which can conveniently be summarized under seven simple rules. The group so instructed did much better in every one of six tests given at the end of the experiment than a control group who merely practiced memorizing. This demonstrated that by giving attention to certain principles underlying the act of memorizing, definite improvements in the ability could be made.
The classic experiment which is usually reported as providing evidence for the possibility of transfer by a cognitive approach is that of Judd. Although Thorndike reports Judd's experiment forthrightly in Volume II of his Educational Psychology along with other experiments available at that early time,30 as Thorndike's students we were led to believe that there was something not quite reputable about Judd's experiment that he had failed fully to analyze the conditions of the experiment, with the result that his conclusions were somewhat confused and that with an adequate analysis they could be subsumed under the general formulae "identity of content" or "identity of method."
Judd was much more outspokenly critical on his side:
My experience in experimenting with this problem leads me to believe that those who have advocated this doctrine of specific functions have had a very limited view of the facts involved, and have consequently reached a formula of mental organization which is wholly inadequate.31
Judd gave the credit for his experiment to one Scholckow, who had apparently been Judd's student some ten years earlier and to whom Judd gave the basic idea of the experiment. Two groups of pupils in the fifth and sixth grades were given the task of hitting a target under water with a dart. Because of the greater density of the water and the refraction of light through the water, the targets appear more shallow than they really are. In practicing with the target in twelve inches of water one group was given the principle of refraction; the other simply learned the task by practice, with about equal learning results. But when the target was placed in four inches of water the group which had been taught the principle adapted themselves to the new task more rapidly than the group that did not know the principle. "Note," says Judd "that theory was not of much value until it was backed by practice, but when practice and theory were both present the best adjustment was rapidly worked out."
Judd's report of his experiment would be considered quite inadequate today. He presented no data and one does not know whether the results could have occurred by chance. But Hendrickson and Schroeder years later repeated the Scholckow-Judd experiment under acceptable conditions and corroborated the earlier conclusion.32
It is of interest that in spite of the greater scientific prestige of the Columbia-Thorndike-Woodworth experiments and their analysis in terms of identity of content and method, the Chicago-Judd point of view over the succeeding years has provided the more significant experimentation and results of greater significance to education.
The elaboration of Judd's theory of transfer was first made in the field of arithmetic. Thorndike, who made studies of the psychology of arithmetic and algebra, analyzed these subjects into their constituent separate habits, or "bonds" as he called them.33 Although he definitely disclaimed that he thought of these elementary units as having to be learned separately, one at a time ("the psychologists of today do not wish to make the learning of arithmetic a mere matter of acquiring thousands of disconnected habits, nor to decrease by one jot the pupil's genuine comprehension of its general truth"),34 his point of view does lead to a drill psychology. He expressed his real convictions more clearly in the Psychology of Algebra.34a "Modern psychology, however, is suspicious of all cases where habits are supposed to be easily derived from principle. It so happens that the really effective principle is the product of the habits, not their producer. A man's conduct seems to determine his conscience more than his conscience his conduct." So according to this point of view, one learns arithmetical and algebraic procedures by drill or practice, as a result of which he is enabled to understand the principles underlying what he has done.
A decade later Olander reported a very significant experiment.35 He taught children half of the addition and subtraction combinations (55 each) and then later tested them with an examination including all the combinations (100 each). These pupils did as well on the untaught combinations as other children who were given instruction in all the combinations. "A child does not learn number combinations as separate bonds but as a system of interrelated experiences."
Beito and Brueckner conducted a similar experiment.36 Nineteen second-grade pupils were taught 36 addition combinations, always with the larger number coming first. Tests, however, included these same number combinations in the reverse orderwith the smaller number coming firstand on these the pupils did .as well as they had done on the practice form. This may seem like an almost self-1 evident identity to those of us who have mastered arithmetic, but for a young child learning his combinations it is real 'transfer.
In the 1930s two studies, one by Overman37 the other by Thiele,38 demonstrated that when arithmetic is taught by means of principles and generalizations the outcome is learning which is superior to that produced by mere practice.
McConnell also compared the learning of arithmetic by sheer practice as against the development of principles with emphasis on the discovery of these principles by pupils.39 He found that
[a group] taught by the pedagogy of authority, mechanical repetition and relatively discrete connection-forming excelled in immediate and automatic response to the number facts; whereas a group taught by a pedagogy of discovery and verification of meaning and relational learning excelled in tests which put a premium on deliberate and thoughtful responses which resulted in better ability to transfer learning and to manipulate the number facts in mature ways.
Just what does it mean to speak of a principle in arithmetic? Some illustrations will be given so that the reader will know exactly what is being talked about.
If 3 + 2 = 5, then 2 + 3 = 5, or to generalize, if a + b = c, then b + a = c.
5 + 7 = 12 because it is one more than 5 + 6, which is 11.
If 6 + 2 = 8, then 8 - 6 = 2 and 8 - 2 =6, or to generalize, if a + b = c, then c - a = b and c - b = a.
If 3 x 2 = 6, then 2 X 3 = 6, or to generalize, if ab = c, then ba = c.
If 3 x 2 = 6, then 6 ÷7-3 = 2 and 6 ÷ 2 = 3, or to generalize, if ab = c, then c/a = b and c/b = a.
Since our number system is decimal, number combinations can be broken down into 10 or its multiples, that is,
7 + 6 = (7 + 3 = 10) + 3 = 13.
Since 9 + 7 = 16, then 19 + 7 = 26.
The term "generalization" is used confusingly in psychology with two separate meanings. First a concept is a generalization. When we speak of "chair" we refer not to a specific article of furniture in a certain house, but to a whole class of pieces of furniture meant to be sat on. So generalization refers to such concepts as water, redness, threeness, to run, democracy, existentialism. But generalization also refers to a statement or proposition connecting two or more concepts, typically a statement that expresses a relationship. "Water runs downhill" relates the two concepts of "water" and "downhill" by a relationship between them ("runs down").40
The generalizations which transfer may be of either type. We say that a concept generalizes when a child after learning that "bad" is the opposite of "good" can tell you that "little" is the opposite of "big."41 Concepts or generalizations of the first type need not be expressed in words to be effectiveone can respond to red without saying or thinking the word red. Also generalizations in the form of principles need not be expressed in words or similar symbolic representatives to be effective guides to action. Indeed, there is some ground for believing that a generalization in the form of a principle or proposition is learned or understood primarily if it is reacted to appropriately, and the verbal or symbolic expression of the principle merely translates it into the individual's verbal system, where it can be used and remembered in connection with other verbally expressed generalizations.42
In order to learn a principle one must first be familiar with the concepts that are included in the principle. If in Judd's experiment one is to respond to the principle, "To hit the target, aim at a point lower than that at which the target appears," one has to know what is meant by target, aim, lower than, and appears. One could not make use of this rule unless he knew with reasonable accuracy and familiarity the meaning of these terms. If a child is to respond to 6 + 2 = 8, he must know the meaning of 6, 2, 8, + and =.
In learning a principle one must be able to perceive the relationship. That means that he must be able to perceive two concepts simultaneously with clarity and meaning and also to perceive the relation between them. For instance, we are told in physics that
watts = amperes X volts.
This relationship probably means little to most persons because they have very hazy notions of what is meant by watt, ampere, and volt. Does it help to know that ampere refers to the strength of an electrical current, volt to its pressure, and watt to the amount of electrical power available or consumed? Does it help to know that the electricity ordinarily furnished by city power companies is at 110 volts, that the fuse one screws into the fuse box determines how many amperes of electrical current the line can accommodate, that the strength of a light bulb is measured in watts, and that monthly electricity bills are figured in terms of kilowatts (1000 watts)? Does it help to compare electrical power with the power to be derived from a waterfall? The height of the falls will correspond to the volt, that is, the pressure. The amount of water that goes through the turbines at the bottom of the falls would correspond to the ampere or amount of electrical current; and the power produced, which is the product of the pressure of the water times the amount of water, would correspond to the watt as a unit of electrical power which equals the number of volts times the number of amperes. In addition to these definitions, facts, and analogies, these concepts and the relation between them acquire additional meaning and familiarity through use.
Principles may exist at several levels of generalization and abstraction. On the lowest level they may be little more than rules of procedure. "Aim at a point lower than that at which the target appears." Slightly more general would be, "The deeper the water the more one has to lower his aim from the apparent position of the target." Still more general, "Light rays that pass from air to water change their direction so that the angle of incidence is increased." Or again, "When light passes from one medium to another of different density the angle of incidence changes and becomes greater on entering the medium with higher density." Or finally, "For light passing from air to water sin i/sin r = 1.33, where i = angle of incidence and r = angle of refraction." It should be obvious that the ability to comprehend these principles depends on one's level of intelligence or mental maturity. The lower the level of generalization the less the possible transfer (as in the case of the first rule given above), but the more persons that can comprehend and act on the rule. The higher the level of generalization the greater the possible transfer, but it requires higher intelligence to comprehend the principle and to perceive its applications. If one teaches too narrowly and concretely, what one teaches will be understood by more people, but there will be less transfer; if one teaches too abstractly, fewer will comprehend, but there is greater possibility of transfer for those who do.
There is much discussion currently over the importance of studying mathematics in secondary school and college. There is both a value and a danger in sluicing larger numbers of students into the study of mathematics. The value comes from the greater power that may be at the command of more people to apply mathematical principles more widely. But the danger comes from requiring the study of a subject which will be only dimly or partially comprehended, with the possibility of less transfer than the study of subjects on a more concrete level.
Many of the principles of mathematics and science apply in everyday affairs. For instance, there is a movement on foot to introduce into college (or even high school) mathematics certain new topics dealing with the theory of groups, fields, sets and functions.43 An inspection of these topics reveals that they treat in highly abstract and generalized form very fundamental propositions and principles, including the simple principles which may be used in the teaching of beginning arithmetic. Obviously a child first learning arithmetic is not ready for these rules in the generalized form in which they are presented in the theory of groups, fields, or sets. And there is also the danger that the college student, in studying these basic principles in generalized form, may simply learn them as abstract propositions with little appreciation of their application to basic arithmetical processes. There is danger, then, of teaching both too narrowly and too abstractly for the greatest transfer.
Olander and Beito and Brueckner demonstrated that it is not necessary to practice or drill on all reactions that one is to make and that it is possible to short-circuit the learning process by teaching some general principles. But it was also pointed out in an earlier article in this series, "Learning Is Reacting," that effective learning does not take place by teaching principles without practice. For the most effective learning there must be a judicious combination of theory and practice. Just what proportion of these two ingredients leads to the most effective transfer is not known. Presumably the duller and less mature child requires more manipulating experiences, whereas the brighter and more gifted one is able to apply general principles more quickly and accurately and with less experience. Both groups, however, need the experience that comes from manipulating the materials before the skills become fluent and automatic.
In succeeding pages of this discussion, certain other findings relating to transfer will be considered in less detail. Even though there are unlimited possibilities in transfer from the applications of general principles to particular situations and conditions, such transfer does not take place automatically. Indeed, unfortunately in most instances and for the large majority of pupils, transfer takes place only for those applications of a principle which are pointed out by a teacher and on which a pupil has some opportunity to practice. Conclusive experimental evidence for this statement has not been provided. But Ulmer, in a carefully controlled experiment, demonstrated that when geometry is taught with an emphasis upon the application of principles of reasoning to nongeometric situations, there were marked gains on a general test of reasoning; but that in classes where there is not this emphasis, the gains on the reasoning test were only slight. "What is commonly regarded as superior geometry teaching has little effect upon pupils' behavior in the direction of reflective thinking unless definite provisions are made to study methods of thinking as an important end in itself."44
This means that the teacher is an all-important factor in making transfer possible. The extent to which transfer takes place for the majority of pupils depends on the extent of the applications which are pointed out by the teacher. The exceptional pupil is really a genius who* extends the application of principles which he is taught in one class to subjects and situations which have not been pointed out and which transcend the particular subject matter in which the principle is developed. Slavson writes, "In work with hundreds of parents, I found that many of them, though intelligent, trained in their professions, with a good understanding of child psychology, transgressed the most essential elements of mental health," a statement which he backs up with copious illustrations.45
However, it is possible to have higher order learning patterns which may be called the "principle of the overdrive" to borrow a term used in automobile mechanics. Harlow has revealed the possibility of "learning sets." He demonstrated that it is possible for monkeys to "learn how to learn" and he states, "This learning to learn transforms the organism from a creature that adapts to a changing environment by trial and error to one that adapts by seeming hypothesis and insight."46 That is, it is possible that a teacher, by emphasizing application, by encouraging his students to hunt for and find applications and to be alert for applications, may help them to develop a sensitivity to new applications of familiar principles. That this is possible has been demonstrated by Schroeder and Rotter, whose experiment showed that flexibility in the attack on problems was something that could be learned as a trait that had transfer possibilities.47 But, here again, more can be expected from brighter students for whom the principles have greater clarity of meaning.
The emphasis in the foregoing discussion has been on using or finding a new application for a familiar principle; the converse also comes under the heading of transfer: using or finding the appropriate principle that will aid in the solution of a given problem. Craig, in an experiment in which subjects were instructed to find in multiple choice items the one word in a group of five words that "does not belong," that is, does not fit in with some organizing principle that binds the other four words together, demonstrated that "the amount of transfer increases as more and more clues are provided to aid discovery of the basis for the correct answer."48
One matter of teaching procedure has not yet been satisfactorily resolved and is still a source of controversy: Should a learner be given clues and hints or even expressly stated formulations of principles and their applications or should he be required to discover them? There seems to be a tendency on the part of teachers to believe that there is merit in requiring a child to discover principles and their applications. Herbert Spencer wrote on this matter as follows: "Children should be led to make their own investigations, and to draw their own inferences. They should be told as little as possible and induced to discover as much as possible."49
The experimental results by McCon-nell and Thiele already mentioned used pupil discovery of principles as part of their experimental method, with the assumption that discovery was an important and inherent part of the experiment. Thiele says, "If the principle of discovery be sound, there will be small need for 'demonstrating' or 'explaining' or 'telling,' or 'showing' on the part of teachers."50
Stacey, using material similar to that used by Craig, found that children learn better when they proceed by a process of self-discovery than when they are told the answers.51 But Craig's experiment, together with a supplementary experiment reported by Craig,52 demonstrates that there is an advantage to guiding students with appropriate hints in the discovery of the principle that would serve as the key to a given item in the exercise. The difference here seems to be that in the Stacey experiment children were told the answers, but in the Craig experiment they were given hints and aids through the arrangement of the material, a special statement that there were principles that determined the correct answers, and finally a short general statement of the relationships common to a group of items. A close look at the Thiele and McConnell studies will reveal that the subjects in these studies were given about as much assistance in discovering principles as Craig gave the subjects in his study.
On the basis of the Craig studies it would seem that there is an advantage in assisting pupils to find principles and their applications. Of primary importance is experience with the materials that permits a child to make reactions toward the material; but merely telling the child the principle without giving him an opportunity to react to it is sterile. The greatest gain is made by organizing the materials, directing attention to them, and the like, so that children are helped to react to the principle and hence to discover it. One should not expect them to discover, unaided, principles in science, mathematics, and language that it has taken the best thinkers of all ages to discover. Certainly, students are given considerable assistance in an organized experimental laboratory course in science by having the materials and conditions of each experiment described in detail.
A recent study by Kersh indicates that whereas assistance in discovering the principle may lead to greater understanding, when the principle is discovered without aid, it somehow is better assimilated and remembered.53 Apparently the independent discovery results in a more complete network of relationships.54
If learning is effectively to transfer, then the situations to which it is to transfer must be real to the learner. This presents one of the most difficult problems in all education. If the school waits until the pupil meets a real problem in life, then he will have left school before important learnings can take place. Most pupils still in school have not themselves actively faced problems in insurance, investment, installment buying, filing income tax returns, and similar financial problems that an adult has to master. It is true that he sees his parents wrestling with these problems, but typically parents do not openly discuss their financial problems with children, and the child only feels their pressure obliquely. In short, experience must precede transfer; one cannot transfer or apply a principle to a situation with which he is not familiar. A wise teacher will create experiences, such as the investment of the proceeds of a school fair, but it taxes the teacher's ingenuity to find or to create experiences which would provide opportunities for pupils to apply all of the general principles which modern education expects them to learn. And there are grave doubts if abstract theoretical learning is of much value. Certainly one cannot teach amortization as a topic in arithmetic with the hope that ten years later a student will use his learning in budgeting the affairs of his business or in making certain entries on his income tax schedule.
It should be emphasized that transfer by application of a principle is essentially an intellectual act. Individuals with greater intelligence should be able to transfer their learning with less tutelage and with greater self-direction; they should be able to make wider transfer to material and situations that are remote from those in which the principle was first enunciated; they should be able to transfer principles that are more abstract. Whether or not these differences are due to innate ability or to some learned ability cannot be stated, but today psychologists are learning that many of these "learning sets" or "overdrive responses" can be and are learned. This, of course, points to the importance of giving greater attention to methods of procedure in school learning.
In summary, the history of thinking about transfer and formal discipline has shown remarkable shifts, and there is danger that many teachers will fail to keep abreast of these changes and will adopt permanently some outmoded point of view. Traditionally there was belief in the disciplinary value of subjects of study, but psychological evidence has shown conclusively that no subject, as a subject, has capacity to add to mental power. The early experiments of James, Thorndike and Woodworth, to mention only a few, left the impression that transfer, if it takes place at all, does so in small amounts. Educators have interpreted these findings as meaning that emphasis in curriculum revision should be placed on content that has practical value.
But starting with the writings of Judd and continuing with significant experiments in the late 1920s and early 1930s, it was found that there were possibilities for transfer through the application of general principles. This opened up untold opportunities for education to take advantage of possibilities for transfer. Many teachers have, of course, based their teaching on just such principles. But by and large, educational theorists and curriculum specialists have not yet incorporated these possibilities for transfer into teaching materials and practices. Increase in mental power does not come automatically from the study of certain subjects. But there are possibilities for enhancing the use of the mind by attention to methods of learning and studyand these can be accomplished by any teacher in any subject. The pendulum has swung back, not into the earlier position of formal discipline, but into a belief that through the process of generalization it is possible to accomplish transfer and "mental training" on a scale not hitherto believed possible.
1 This is the seventh article in a series by Dr. Symonds on this subject. The first six are available in a single pamphlet published by the Bureau of Publications, Teachers College, Columbia. $1.25
2 Plato, Republic, VII:526.
3 John Locke, Of the Conduct of the Understanding, 1706 (New York, John B. Alden, 1846), p. 20.
4 National Education Association, Report of the Committee of Ten on Secondary School Studies (Washington: Government Printing Office, 1893), p. 168. From the Resolutions of the Conference on History, Civil Government and Political Science held in Madison, Wisconsin, December 1892, Charles Kendall Adams, President of the University of Wisconsin, Chairman.
5 A. W. Griswold, "What We Don't Know Will Hurt Us," Harper's Magazine, 209:76-82, July 1954.
6 William James, Psychology, Vol. I (New York: Henry Holt and Company, 1890), pp. 666, 667.
7 W. H. Winch, "The Transfer of Improvement in Memory in School Children," British Journal of Psychology, 2:284-93, 1908.
8 W. G. Sleight, "Memory and Formal Training," British Journal of Psychology, 4:386-457, 1911.
9 E. L. Thorndike and R. S. Woodworth, "The Influence of Improvement in One Mental Function upon the Efficiency of Other Functions," Psychological Review (1901), 8:247-61.
10 E. L. Thorndike and G. J. Ruger, "The Effect of First-Year Latin upon Knowledge of English Words of Latin Derivation," School and Society, 18:260-70, 1923.
11 Thorndike and Woodworth, op. cit., p. 250.
12 E. L. Thorndike, The Principles of Teaching (New York, A. G. Seiler, 1906), p. 244.
13 J. B. Conant, Education and Liberty! The Role of the Schools in a Modern Democracy (Cambridge: Harvard University Press, 1953); A. E. Bestor, Restoration of Learning; Program for Redeeming the Unfulfilled Promise of American Education (New York: Alfred A. Knopf, 1955); and A. E. Bestor, Educational Waste Lands: The Retreat from Learning m Our Public Schools (Urbana: University of Illinois Press, 1953).
While Bestor has rendered a service in pointing to some of the absurdities to which making the content of education immediately practical and useful has led, the present writer does not subscribe to his attacks on professional education.
14 H. F. dark and H. S. Sloan, Classrooms in the Factories: An Account of Educational Activities Conducted by American Industry (Rutherford: N. J., Institute of Research, Fairleigh Dickinson University, 1958).
15 E. L. Thorndike, "Mental Discipline in High School Studies," Journal of Educational Psychology, 15:1-22, 83-98, 1924.
16 C.R. Brolyer, E.L. Thorndike, and Ella Woodyard, "A Second Study of Mental Discipline in High School Studies," Journal of Educational Psychology, 18:377-409, 1927.
17 Thorndike, op. cit.
18 A. G. Wesman, "A Study of Transfer from High School Subjects to Intelligence," Journal of Educational Research, 39:254-64, 1945.
19 C. A. Smith, "High School Training and College Freshman Grades," Journal of Educational Research, 32:401-9, 1929.
20 S. R. Powers, "The Achievement of High School and Freshman College Students in Chemistry," School Science and Mathematics, 21:366-77, 1921.
21 O. R. Floyd, "General Science as Preparation for the Study of Biology, Chemistry, and Physics," Journal of Educational Research, 31:272-77, 1937.
22 H. R. Douglass, The Relation of High School Preparation and Certain Other Factors to Academic Success at the University of Oregon (Eugene: University of Oregon Publications III, No. 1, September 1931).
23 A. G. Hoff, "The Effect of the Study of High School Chemistry upon Success in College Chemistry," Journal of Educational Research, 40:539-42, 1947.
24 Gilbert Ulmer, "Teaching Geometry to Cultivate Reflective Thinking. An Experimental Study with 1239 High School Pupils," Journal of Experimental Education, 8:18-25, 1939.
25 T. H. Briggs, "Formal English Grammar as a Discipline," Teachers College Record, 14:1-93, September 1913.
26 H. O. Rugg, The Experimental Determination of Mental Discipline in School Studies. Educational Psychology Monographs, No. 17 (Baltimore, Warwick & York, 1916).
27 Herbert Sorenson, "High School Subjects as Conditioners of College Success: Implications and Theories Concerning Mental Factors and Faculties," Journal of Educational Research, 19:237-54, 1929.
28 M. E. Smith and H. R. Douglass, "The Relation of High School Latin to Marks in the First Year of Arts College," School Review, 45:695-701, 1937.
29 Herbert Woodrow, "The Effect of Type of Training upon Transference," Journal of Educational Psychology, 18:159-72, 1927.
30 E. L. Thorndike, Educational Psychology, Vol. II (New York, Bureau of Publications, Teachers College, Columbia University, 1913), pp. 400-401.
31 C. H. Judd, "The Relation of Special Training to General Intelligence," Educational Review, 36:28-42, 1908.
32 Gordon Hendrickson and W. A. Schroeder, "Transfer of Training in Learning to Hit a Submerged Target," Journal of Educational Psychology, 32:205-23, 1941.
33 E. L. Thorndike, The Psychology of Arithmetic (New York, The Macmillan Company, 1922); E. L. Thorndike, The Psychology of Algebra (New York, The Macmillan Company, 1924).
34 E. L. Thorndike, The Psychology of Arithmetic, p. 73.
34a Page 245.
35 H. T. Olander, "Transfer of Learning in Simple Addition and Subtraction," Elementary School Journal, 31:358-69, 427-37, 1931.
36 E. A. Beito and L. J. Brueckner, "A Measurement of Transfer in the Learning of Number Combinations," Report of the Society's Committee on Arithmetic, Twenty-ninth Yearbook of the National Society for the Study of Education, 1930, pp. 560-87.
37 J. R. Overman, The Experimental Study of Certain Factors Affecting Transfer of Training in Arithmetic (Baltimore, Warwick & York, 1931).
38 C. L. Thiele, The Contribution of Generalization to the Learning of Addition Facts. Contributions to Education No. 763 (New York, Bureau of Publications, Teachers College, Columbia University, 1938).
39 T. R. McConnell, "Discovery vs. Authoritative Identification in the Learning of Children," Studies in the Psychology of Learning II, Studies in Education 9, No. 5(Iowa City, University of Iowa, 1934), pp. 13-62.
40 W. A. Brownell and Gordon Hendricksoa, "How Children Learn Information, Concepts and Generalizations, III," in Learning and Instruction. Forty-ninth Yearbook of the National Society for the Study of Education, Part I, 1950, pp. 92-128.
41 George Kreeter and K. M. Dallenbach, "Learning the Relation of Opposition," American journal of Psychology, 41:432-41, 1929.
42 Gertrude Hendrix, "A New Clue to Transfer of Training," Elementary School Journal, 48:197-208, 1947.
43 C. B. Allendoerfer and C. B. Oakley, Principles of Mathematics (New York, McGraw-Hill Book Company, 1953).
44 Gilbert Ulmer, "Teaching Geometry to Cultivate Reflective Thinking: An Experimental Study with 1239 High School Pupils," Journal of Experimental Education, 8:18-25, 1939.
45 S. R. Slavson, Child-Centered Group Guidance of Parents (New York, International Universities Press, 1958), p. 29.
46 H. F. Harlow, "The Formation of Learning Sets," Psychological Review, 56:51-65, 1949.
47 H. M. Schroeder and J. B. Rotter, "Rigidity as Learned Behavior," Journal of Experimental Psychology, 44:141-50, 1952.
48 R. C. Craig, The Transfer Value of Guided Learning (New York, Bureau of Publications, Teachers College, Columbia University, 1953), p. 66.
49 Herbert Spencer, Education: Intellectual, Moral and Physical (New York, D. Appleton & Co., 1860), p. 120.
50 C. L. Thiele, "Arithmetic in the Middle Grades," Chapter 5 in The Teaching of Arithmetic. Fiftieth Yearbook of the National Society for the Study of Education, Part II (Chicago: University of Chicago Press, 1951), p. 80.
51 C. L. Stacey, "The Law of Effect in the Situation with Meaningful Material," in Learning Theory in School Situations, Studies in Education, No. 2, College of Education, University of Minnesota (Minneapolis, The University of Minnesota Press, 1949), pp. 74-103.
52 R. C. Craig, "Directed versus Independent Discovery of Established Relations," Journal of Educational Psychology, 47:223-34, 1956.
53 B. Y. Kersh, "The Adequacy of 'Meaning' as an Explanation for the Superiority of Learning by Independent Discovery," Journal of Educational Psychology, 49:282-92, 1958.
54 Kersh interprets his results as indicating that with no help the group which is completely on its own in discovering the principle remembers the principle better in accordance with the Zeigarnik effect that incompleted tasks are better remembered and the principle enunciated by Gould that tasks accepted as one's own are better remembered than those rejected. Rosalind Gould, "Repression Experimentally Analyzed," Character and Personality, 10:259-88, 1942.