The Defeat of the Schools

MOST people — certainly most laymen — would be apt to think that the chief business of the schools is to give pupils at least a modest working knowledge of the subjects of the curriculum. Not a few students of education, it is true, consider that this is a misconception, and that the true purpose of schools is to bring about an adjustment to social demands for which the various subjects are at best only means. Nobody, however, who surveys the conventional working apparatus of courses of study, textbooks, recitations, examinations, and marks can have much doubt that in practice the schools are making the mastery of the curriculum an end in itself. Whether in theory they ought to or not, this in fact is what they are manifestly trying to do.

But they are not succeeding. About that there is no room for theorizing. Nor is their failure sporadic, and confined to a few places where management is unusually bad. It occurs almost universally, in the cities and in the country, in large institutions and in small. The schools go through an elaborate, costly, and exasperating set of motions called teaching natural science, foreign languages, English, and so forth. Yet what is contained in textbooks and syllabi obstinately refuses to transfer itself to the minds of the patrons and stay there. In the grand struggle to get subject matter off the page and into the head, the schools are suffering a spectacular and most disconcerting defeat.

This, I am aware, is a formidable statement. But it is made on formidable evidence. The recent investigation carried on by the Carnegie Foundation in the colleges of Pennsylvania, issued under the title The Student and His Knowledge, which has caused considerable furore over the ignorance of college seniors, is only a drop in the bucket. For proof of the defeat of the schools does not depend on one investigation alone, or on a dozen, or a score, or a hundred. We have here nothing less than the consistent testimony of thirty years of enormously varied research in education.

Since about 1910 many thousands of investigations have appeared, dealing with almost every conceivable aspect of school work. Comparatively few of them explicitly and directly consider the efficiency of the schools in terms of how much subject matter they manage to induce the pupils to learn. Yet a great many, without particularly setting out to do so, throw a most startling light upon the results of education. Taken in the mass, they add up to a consistent, coherent, and extremely impressive body of testimony, pointing towards one conclusion: whatever the goods which our schools are delivering, they are not what one might expect to find in packages labeled science, history, foreign languages, English, and so forth.


Suppose we call the roll of the principal subjects, asking in each case what a person ought to learn if he is to have anything worth calling an elementary working mastery of it, and also to what extent this is really being acquired.

Let us start with mathematics. Here we have the most precise and powerful instrument for abstract thinking and analysis devised by man. This, indeed, is the very essence of the subject. Mathematics is a technique of thinking, and if you have not learned to think in its special language you just have not learned mathematics at all. Such thinking may not be very intricate or advanced; but, all the way from simple arithmetic to differential equations and beyond, it is the same kind of process. That process is quite different from doing sums, because when one is set a sum one is told either directly or by the most obvious sort of hint whether to add, subtract, multiply, divide, or what not, and all one has to do is to follow certain rules and remember certain tables, which clearly is routine rather than thinking. Essentially the job of every mathematician, all the way from a first-grade child to an Einstein, is to take hold of situations and disentangle them by the techniques of the science. A beginner may not be able to deal with very complicated situations, or to carry the disentangling very far. But he must go some appreciable distance along this road — he must be able to decide what treatment the given situation requires, whether addition or multiplication or something else — before he can claim anything that can possibly be called mastery of mathematics.

Now we know beyond peradventure that a very large percentage of children studying mathematics in school go hardly a step in this direction. For instance, the educational authorities in Iowa have carried through an ambitious project known as the 4 Every-Pupil Testing Program.’ Part of that program was an examination for mastery of the material taught in ninth-grade algebra. In constructing this examination it was clear to the experienced workers that they must use only very simple items, or almost every pupil would be defeated. (An ominous consideration at the start. Inexperienced test-makers tend strongly to expect far too much.) Sixty-two such items were assembled, samples being the following: ‘Write a formula for the perimeter of the rectangle. Write a formula for the area of the rectangle. A dealer sold a suit of clothes for $42, making a profit of 20 per cent on the cost; how many dollars did he make?’ Simple enough, one would say; yet genuine problems, because they require not the more recalling of knowledge, but its application to the analysis of situations. Yet it appeared that half of the large number of pupils taking the test, all of whom had taken algebra, could do no more than ten of the items. Other results showed that actual working knowledge of the ostensible content of the algebra course was being acquired in only the most meagre degree.

Again, another investigation was carried on in which a test in elementary mathematics was given to a large number of children. When they were simply told to perform certain operations, such as factorization, reduction of fractions, the ‘solution’ of easy equations, and the like, 1000 out of 1200 succeeded. But when problems were set up, which not only were simple, but involved no operations other than those which these children had shown they could perform, only about 300 succeeded. What shall it profit anyone to be able to do a certain kind of sum on instruction but unable to use his skill in a problematic situation? Can we say that such a person has any genuine mastery of mathematics?

Very similar results are reported for geometry. Pupils may be able to repeat the proofs of theorems, or to recite definitions and postulates; but this is no evidence that they can deal with ‘originals’ — that is, with problems for the attack upon which theorems and definitions are only tools. Once more we ask in what sense a person has ‘mastered’ a set of tools which he cannot use. If you feel inclined to say that one cannot learn a proof without thought and understanding, consider this: it has been shown again and again that even very small accidental changes in the proof of a theorem will destroy the ability of many pupils to repeat it. These children know how to prove that the square on the hypotenuse of the right-angled triangle ABC is equal to the sum of the squares on the other two sides. Good! Now call the triangle PQR. A surprising percentage of your group will be rendered helpless. Have they really learned and understood the proof at all?

Moreover, geometry does not stay learned. College freshmen, all of whom had studied the subject within the past two years, were given a test designed for high-school students: 86 per cent of these freshmen were below the highschool norm; 50 per cent did worse than 75 per cent of the high-school students; and 26 per cent did worse than nine tenths of the high-school students. Also, they were conspicuously weak in applying geometric reasoning to problematic situations — that is, in the use of the geometric equipment they had labored to acquire. A subject which has been grasped and understood does not fade from the mind so easily and fast.

Other investigations have turned the spotlight on the intimate processes of pupils who are tackling the job of dealing with simple mathematical problems. Put pupils up against a situation requiring mathematical thinking, and what happens? Do they carry through intelligent methods of attack, rational in themselves even when slips in computation result in wrong answers? Do they experiment and analyze and try out alternative procedures in sonic sort of planned sequence? The author of one important study finds that few of them seem to reason at all, and that reflective thought is not evoked. ‘Instead, many of them appear to perform almost random calculations upon the numbers given. Where they do solve a problem correctly the response seems to be determined largely by habit.’

Still another body of disconcerting evidence is at hand. One would naturally suppose that the longer a person studied a subject, the more mastery of it he would gain. Yet, when tests of mathematical competence which do not simply duplicate the situations and routines of textbook and course are applied, it has often been found that there is little of such gain with time. Apparently pupils are going through textbooks and courses but not effectively gaining in mathematical insight and mastery. Everything comes together in an inescapable conclusion. Mathematics is being energetically taught, but it is not being learned to a degree that would, judged by common-sense standards, seem worth while.


In natural science the situation is much the same. Teachers of physics in twenty-eight schools began to have misgivings about the efficiency of their work and the amount of physics actually penetrating the minds of their pupils. Obviously a person might be able to recite fairly well on assignments prepared ad hoc the night before, or to do fairly well on examinations closely related to the course, and still have no independent mastery of the subject as such. So the teachers constructed a test, which, on the basis of their pooled judgment, represented what one ought to know when he had covered the two topics of mechanics and heat. The results were illuminating, not to say startling. The majority of pupils fell far below expectation. Such questions were asked as: ‘A stone is dropped and takes two seconds to hit the ground; from what height is it dropped?’ ‘How much work is done to raise two pounds one yard?’ These particular problems had never been set, but everyone was supposed to have the knowledge and technique needed to solve them. Inability to answer could only mean lack of mastery of the subject as contemplated in the courses; yet this appeared very generally. Also, it was found that a student’s performance on the independent test had very little relationship to his rating in the course in physics. It was one thing to give correct answers under the special promptings of assignment, textbook, and recitation, but quite another to show a mastery of physics as such.

A few years ago a comprehensive test to reveal competence in chemistry, including in its scope mechanical operations, the use of formuke and equations, and general information, was given to groups of students in high school, and to college students who had completed freshman chemistry. Let us begin with the showing of the college students. Remember that all of them had finished freshman chemistry; some had taken the subject in high school, and others had not. But on the test there was no significant difference in the performance of these two groups. Apparently the time spent studying the subject in high school as a preliminary to taking it in college was an almost total loss. University teachers might easily think this a severe reflection on high-school chemistry. So indeed it is. But they should not boast too soon. For those who had taken chemistry in high school and had not yet gone further showed up just about as well on the test as those who had taken the subject both in high school and as freshmen in college. Two years of the subject did not give much better results than one, whether that one year was spent in high school or in college.

Moreover, with both physics and chemistry it has been shown that failure is most conspicuous in the learning of those techniques and principles of analysis which are the chief values of these subjects, and on which their practical application principally depends. A smattering of unrelated facts, rather than an insight into integrated, functioning laws, is what is acquired. And even such facts are insecurely learned.

Quite recently investigators have been raising a new question, more fundamental than any I have discussed so far. Does the study of science, including mathematics, teach scientific thinking? Just conceivably this might happen even without the student’s gaining any very extensive or exact information, or any very firm grasp upon techniques and methods of analysis. Of course it is much harder to tell whether a person is able to think scientifically than whether he knows certain facts or is able to use certain techniques, so results here are apt to be less reliable than elsewhere. Still, the attempt has been made rather frequently, with great care and seriousness, and the answer to the question is: No! There is practically no evidence at all that science, as taught in school, makes one more careful about hypotheses, more willing to suspend judgment, more openminded towards alternative views, more able to distinguish truth from hokum. It does not, so far as we can tell, successfully promote these or any other typical virtues of the scientific mind.


Now let us turn to the so-called language arts — foreign languages and English. Regarding the former not much need be said; technical research simply confirms a painfully obvious case. No one can be said to have a mastery of any language unless he can read, write, or speak it, and not much of a mastery unless he can compass all three. The language must serve him as an instrument of communication in its own right, which means not only far more than being able laboriously to translate it by main force of grammar and dictionary, but also something essentially different. How many pupils achieve any such freedom with French, German, or Spanish? Very few! Ask the same question about Latin, and you must change ‘Very few’ to ‘Virtually none.’ It has been shown that, under the conditions commonly found in our schools, a person must study Latin in high school, through college, and for one graduate year before being able to read it as freely as an average fifth-grade child reads English. Given really efficient teaching, an average person can attain a good reading mastery of French, German, or Spanish in two school years. (For Latin one might have to make it three years.) The thing can be done, but it happens all too rarely. What is the use of learning a language to a point below that of mastery?

But what about English? Here too there is a record of failure and defeat. Do pupils in school learn to read their mother tongue effectively? Yes and no. Up to the fifth or sixth grade, reading, on the whole, is effectively taught and well learned. To that level we find a steady and general improvement, but beyond it the curves flatten out to a dead level. This is not because a person arrives at his natural limit of efficiency in reading when he reaches the sixth grade, for it has been shown again and again that with special tuition much older children, and also adults, can make enormous improvement. Nor does it mean that most sixth-graders read well enough for all practical purposes. A great many pupils do poorly in high school because of sheer ineptitude in getting meaning from the printed page. They can improve; they need to improve; but they don’t.

The average high-school graduate has done a good deal of reading, and if he goes on to college he will do a good deal more; but he is likely to be a poor and incompetent reader. (Note that this holds true of the average student, not the person who is a subject for special remedial treatment.) He can follow a simple piece of fiction and enjoy it. But put him up against a closely written exposition, a carefully organized and economically stated argument, or a passage requiring critical consideration, and he is at a loss. It has been shown, for instance, that the average high-school student is amazingly inept at indicating the central thought of a passage, or the levels of emphasis and subordination in an argument or exposition. To all intents and purposes he remains a sixth-grade reader till well along in college.

Moreover, the schools are not successful in promoting an interest in reading. Survey after survey has come out with the same general results. Pupils in school, and also high-school and college graduates, read but little. Mediumgrade magazines and fair-to-medium fiction are the chief standbys. Reading choices are made on hearsay, casual recommendation, and display advertising. Education is clearly not producing a discriminating or venturesome reading public. As one investigator concludes, there is no indication ‘that the schools are developing permanent interest in reading as a leisure-time activity.’

The case is the same when we consider the art of writing the English language. No great number of people are going to turn into subtle and imaginative stylists, even with the best of teaching. But properly directed effort over a period of years should certainly equip the average human being with what it takes to express himself clearly, exactly, and correctly in his native tongue. This happens, however, only on the most meagre scale. Investigators use a good many different techniques to reveal the competence and maturity with which a person can express himself in English. One of these is the ratio of the number of dependent clauses used to the number of sentences used, which serves to indicate the complexity of the linguistic pattern turned out. On this basis, to be sure, there is a steady development throughout the school years. But other criteria show that we have little cause for satisfaction. All through high school and well into college we find the most amazing solecisms of grammar and usage persisting. A great many high-school pupils are not able to discriminate between what is a sentence and what is not.

There is yet another highly significant criterion whose application yields some very startling results. This is range of vocabulary. One does not, of course, want people to use five-dollar words in profusion; but without adequate vocabulary equipment it is not possible to express fine and precise shades of meaning. Now word counts show that in the English of students, both in formal compositions assigned in school and in letters, very few words occur outside the thousand most commonly employed in the language. More significantly still, as one goes from senior year in high school to senior year in college, the vocabulary content of written English hardly seems to increase at all. After twelve years in school a great many students still use English in many respects childish and undeveloped; and four years more bring slight improvement.

In the social studies and history the situation is much the same; I shall mention the results of but one typical investigation. A test was constructed calling for knowledge of a range of very simple facts in United States history. It was given to pupils in the upper grades who had covered the field once. They could answer only 15 per cent of the questions. High-school students, who had spent an additional year on material largely identical, could manage 33 per cent. College sophomores, after a third journey over the same pathway, answered, on an average, 49 per cent. Less than half the simplest and most obvious facts assimilated after three exposures! Surely a time-consuming, inefficient process, to say the least.


Clearly, then, the campaign to induce and enable students effectively to master the chief subjects of the curriculum is not yielding any very striking victories.

What about the effect of the schools in building up in people’s minds a stock of general knowledge or information ? This has been a tempting problem for research workers, largely because a general knowledge test is comparatively easy to construct; so we have plenty of material. The Carnegie Foundation inquiry in Pennsylvania, to which I have already referred, dealt with this question, and its results may be taken as representative, though they are played up with unusual impressiveness. It showed that the gain in general information between sophomore and senior year in college, and indeed between high-school and college graduation, was meagre and uncertain. Many college seniors had no wider range of general knowledge than sophomores, and some of them were no better informed than high-school seniors. The report has stirred up considerable comment, but to anyone familiar with the literature of educational research it comes as no surprise.

In this day of encyclopædias, World Almanacs, and public libraries, a large stock of miscellaneous information for ready reference does not seem particularly vital. Even professional scholars can and do look up specific data when and as needed. It is far more important to know where to look for facts, and what to do with them when found, than to be able to produce them from under one’s hat at a moment’s notice. So the very strong and consistent evidence that twelve to sixteen years of schooling leave most people very inadequately equipped with ready-to-use memory knowledge, though highly suggestive, seems of secondary significance.

The other body of experimental results, however, is quite a different affair. These are the investigations dealing with what is known as transfer of training. Probably all of us have at some time been told that a subject which seems useless and futile for its own sake is still worth studying because it helps with some other subject. Latin is said to help with other foreign languages, and to improve one’s English. Grammar is thought to enable one to write and read better. Elementary mathematics is supposed to be an aid to physics. Geometry trains one in reasoning. Such claims are quite familiar. What one learns in one subject is said to transfer to others, and so to help in mastering them.

The hypothesis of transfer has been one of the chief topics of educational and psychological research. Something like one hundred and seventy published investigations have been devoted to it. Their general and accepted testimony is that very limited transfer takes place. Students who have taken Latin show up no better in other languages than those who have not; nor do they read better, write better, spell better, or use larger vocabularies in their native language. It has been shown again and again that work in English grammar has almost no value as an aid to the accurate and competent use of the English language. Persons who have spent a great deal of time studying grammar do no better either in composition or in reading than others who have had little or no grammatical training. Teachers of physics frequently complain that when pupils enter their courses they seem to forget all the mathematics they ever knew, and research backs up such grumblings. As to the argument that geometry teaches people to reason better about things in general, it is preposterous, and advanced without a shred of evidence.

The cumulative results of this long list of investigations are authoritative and accepted. They are summarized in almost every elementary textbook on educational psychology, and are one of the commonplaces at teachers’ gatherings. Practically every professionally trained teacher in America has heard the news that transfer of training does not take place, though without a very critical or adequate insight into the evidence.

When one studies a subject, any benefits there may be accrue within the subject itself and not somewhere else. Such is the ascertained fact. (I state it broadly, and without various, not unimportant, qualifications.) But the proper inference from it, the moral of the tale, is hardly ever pointed out. Transfer of training ought to take place. Its failure to do so is a reproach to teaching. When pupils cannot use their mathematics in a physics course, something must be wrong. Perhaps they never really learned their mathematics in the mathematics course! Latin, with its close affiliation with other languages, ought to help with French, Spanish, and German, not to mention English. When this fails to happen, it is a reflection upon the teaching of Latin. Again, English style is, in a sense, applied grammar. So when we prove that learning grammar does not improve English expression — and this has been proved to the hilt — the inference must be that grammar was pretty badly learned.

Lack of transfer is not a law of nature or a fiat of the Almighty. It is an indictment of teaching. Learn Latin as it should be learned, and it will help you with other languages. Acquire a real grasp of mathematical thinking, and it will not fail you when you tackle physics. The investigations on the transfer of training simply go to swell the great volume of evidence that the schools, in their attempt to generate adequate and worth-while masteries in the subjectmatter fields, are meeting with defeat.


Why should all this be so? How does it happen that Johnnie Jones and Susie Smith spend a good deal of time on various subjects with such disappointing returns? What can we do about it?

The trouble is that Johnnie and Susie set up a ligne Maginot of sheer mental inertia, through which the attacking forces of education cannot break. For this the fault is ours far more than theirs. It is their inevitable and instinctive reaction to the whole apparatus of an education centring about the traditionally determined curriculum. We are trying to sell Johnnie and Susie an unsalable bill of goods.

Let us see as simply and clearly as possible just what we are asking them to do. We assume a standard body of content, including, by way of illustration, the atomic law, the conditions leading up to the American Revolution, the Tragedy of King Lear, and the skills required for solving a quadratic equation. Obviously Johnnie and Susie cannot learn everything in the world, though in an earlier and simpler day some very considerable thinkers did suppose that an educated man was one who knew everything. To-day, however, the proposition is manifestly impossible. Since life is short and school days fleeting, Johnnie and Susie can assimilate only a very small fraction of human culture. So we must make a selection.

How do we make it? We make it on the basis of nothing more intelligent or reassuring than long tradition. The material taught in the schools goes far back through the years, some of it to a remote antiquity. Of course, like every other tradition, it has altered somewhat with the passage of time, but slowly and superficially. It has a sort of independent life of its own, which is highly resistant to change. Textbooks and syllabi tend to be based on previous textbooks and syllabi. Teachers tend to purvey what they themselves have learned. The pattern of the basic curriculum is extraordinarily rigid, and has never been critically reconstructed from the ground up, except in a few favored institutions. In the main the schools continue to teach it for no better reason than that it has always been taught.

Now how much confidence can we have that a body of content so selected is really worth learning? Surely very little! Can we say that it is a balanced and representative sampling of the best and finest that the human spirit has achieved and is achieving? By no means. In the standard curriculum there is some fine gold, but also an unconscionable quantity of dross. If we wanted to give our convenient inquiring friend, the Man from Mars, an idea of the best in human culture, we would hardly hand him a set of school texts and syllabi. Why should we do it with Johnnie and Susie? Or can we say that what we offer is vitally related to the interests, concerns, and needs of young Americans? Again the answer is: No! Nothing of the sort has been considered in making the selection. Indeed, it is notorious that this material has been assembled in advance, without any reference to the kind of people who are supposed to learn it.

But this is a fatal weakness. If we ourselves can have no great confidence in the importance of the things we teach in the schools, how can we expect Johnnie and Susie to believe in it? And if they have no authentic sense of the importance and value of the things they learn, they cannot — literally they cannot — learn them well. For the human mind is not naturally docile. It is capable of amazing feats of resistance and rejection, beneath a tame and dutiful exterior. It assimilates into its life and makes its own only those things which, for some genuine reason, seem to matter. Everything else stays on the surface and soon evaporates. This is no recondite scientific discovery, but simple common sense. Everybody knows it from his own experience, though not everybody drags it into consciousness as a guiding principle. Watch Johnnie and Susie at work on some hobby. Then contrast them as they work at school tasks. The difference? Obvious!

Here, I insist, is where our trouble starts. We set up a body of material which, in the nature of the case, must be mastered not because of its intrinsic and manifest appeal, but under some kind of duress. Learning under no urge except external duress, however, is contrary to all natural tendency. Resistances are set up which frustrate the process, no matter how ‘good’ or docile the learner seems. These are the forces which defeat the schools.

Is there a way out? Of course there is. The first necessity is to abandon the idée fixe of a standard body of content which everyone must learn. People young and old learn what matters to them, what seems of genuine moment to them. Whatever fails to come with the authentic impact of reality and need is automatically and fatally rejected. In a very genuine sense each one of us makes his own curriculum; for the only curriculum that matters is the one a person carries in his head, rather than the one in the textbooks and syllabi.

Hence the great necessity is for far more flexibility in our whole treatment of children in the schools, and above all for flexibility in what we ask them to master. Many reformist and experimental schemes have this as their controlling principle, and they succeed in so far as they put it into effect. Teachers should be free to bring to their pupils those portions and aspects of subject matter which are of immediate and living concern. They should not be doomed to keeping a rigid lock step, or to covering a predetermined area.

This does not in the least mean that we shall stop teaching mathematics, natural science, literature, and the like, and substitute current events, wood carving, and cookery. It only means that not everybody will learn the same mathematics, natural science, and literature, and that people will not always learn them in the same internal order and sequence. We seem to have heard that one man’s meat is another man’s poison. Why not apply this hackneyed wisdom here? Any person’s cultural meat — the culture which he is able to assimilate, and which nourishes him — depends upon his present life interests, his status, his needs, his concerns. And our schools must be so organized that it will become possible to choose for a given individual or a given group at a given time those elements of culture which will indeed provide nourishment.

Will this prevent pupils from mastering the ‘logic’ of mathematics, or natural science, or social science? They are not mastering it now! Strange to say, they are not mastering it precisely because we present it to them as a logic. Mathematics, for instance, is a technique or tool of thought. That is its essence, its logic. But we do not learn to use this tool by first studying its inner structure and organization up to a certain point, and then applying it. We learn to use it by actually using it, in no matter how haphazard and fumbling a fashion, upon problems which we really want to solve. So with all the other disciplines. Let us handle our subject matter as something which is alive, and its logic will take care of itself.

To organize the schools in terms of flexibility rather than rigidity is no small or easy task. It calls for much revision of conventional procedures and instrumentalities. Yet it can be done, and in fact the work is going on apace. For the benefit of those conservatives who may think that the way to get children to learn more in school is a return to the good old days of high pressure and rigid requirements, I project one more nugget of ascertained fact. It has been shown that the experimental schools actually produce better subject-matter learning than the conventional schools, with pupils of equal ability. Carry such tendencies further, and we have good reason to expect still more satisfactory results. What we contemplate is, to be sure, a breach with some of our most adamantine traditions and customs. But we have before us the problem of an intelligent rather than a stupid approach to the task which is of such supreme importance in a democratic society — the task of bringing to the individual his birthright of culture. It is a task in which we cannot, afford to, and need not, accept defeat.