CHAPTER 5: The Debasement of Undergraduate Teaching

[96]Research is expensive. Research professors command high salaries but cannot be asked to teach many hours. And they teach mainly graduate courses and seminars in which the number of students is small so that the tuition does little to defray the expenses incurred. In disciplines that require laboratories the cost is still greater. Much of the research conducted by professors does not involve students at all and so must be supported entirely by the universities, though governmental and foundation grants do cover some of the cost.

In contrast to research, university undergraduate education is profitable. Students in the private universities pay a high tuition. In the public universities state and city funds plus tuition provide the equivalent. The student body is large; hence the income from undergraduate students is considerable. Why not, then, divert money obtained from [97] undergraduates to support graduate education and research? This is precisely what universities do.

To "handle" undergraduates cheaply - it would be factually incorrect to say "teach" them - the universities have adopted two measures: large lecture classes and the use of graduate students as teachers. Lecture classes, usually taught by research professors, may contain as many as a thousand students. In a few universities some of the students hear the lecture only through closed circuit television, with two thousand to five thousand students hearing one professor.

The objections to large lecture classes, in mathematics at least, are almost evident. Teaching is not solely a matter of delivering material. Students differ in background and ability, and effective teaching calls for knowing the difficulties of each student and being able to resolve the questions each can pose. Questions and answers are more important than a professor's repetition of what can be found in books or what can be put in lecture notes, duplicated, and passed out to the students. Moreover, mathematicians particularly claim to teach thinking. This calls for eliciting responses to stimulating questions, encouraging intelligent suggestions from the students, discouraging poor suggestions (though not to the extent of destroying confidence), and guiding the students to a correct proof or answer by continual probing of their thoughts. Clearly, this cannot be done in a large lecture class.

One defense administrators proffer for the use of large lecture classes - that it permits many students to listen to a famous professor - amounts to just what it says. They can listen and perhaps be kept awake by a booming voice or good acting, but not necessarily learn. At best, a good lecture in mathematics is systematic, complete, correct - and dull. More often it is a monologue, if not a soliloquy; teaching calls [98] for dialogue. The worthlessness of the lecture system is pointedly described by Alfred North Whitehead in The Aims of Education: "So far as the mere imparting of information is concerned, no university has had any justification for existence since the popularization of printing in the fifteenth century." The lecture system is the instrument of last resort and actually an evasion of teaching.

To supplement the large lecture sessions, which some universities recognize as inadequate, students meet one or two hours a week in small groups with a graduate student. The graduate student answers questions, goes over homework, and usually gives the quizzes and grades. Were the graduate students really equipped to do the tasks that the lectures fail to do, the lectures could be dispensed with. But guiding a student to think for himself is an art that can be learned only after years of experience. To recognize and advise on psychological problems as well calls for maturity the graduate student does not have. He also cannot afford the time to keep up with educational trends, and so does not know what background he can or cannot expect of his students. Moreover, he is, naturally, so much concerned with his own progress toward the doctorate that he will almost surely devote as little time as possible to his pedagogical duties.

Where large lecture courses are supplemented by small discussion or problem sections, the professors heading such courses give little or no attention to the graduate assistants who conduct these small groups. Having delivered their lectures, the professors believe that their responsibility for the course has ended. Faced with such indifference on the part of the professors, what inspiration and incentive do the assistants acquire to take their own teaching duties seriously?

Some universities rebut all charges of poor teaching, in particular the charge that they use large lecture classes, by [99] citing the high faculty-to-student ratio. This is a meaningless figure. Many prestigious professors who "grace" the campus teach either not at all or very little. A more meaningful number would be the ratio of faculty teaching hours to student course hours, and even this ratio would not describe the quality of the teaching.

A major two-year study at a very prestigious university to determine what improvements in undergraduate housing could be made uncovered that students did not seek better food, more spacious rooms, or even more members of the opposite sex under the same roof. What they did want most was more personal contact with their professors.

Perhaps the value of the lecture system is evidenced by one wag's story whose point should not be ignored. A professor at a major university was called to Washington so often that he ran into conflict with his lecture schedule. He decided that he would tape his next lecture in advance and have the tape run off for the class. He happened to return to the university earlier than he had expected. Passing his lecture room, he heard his taped lecture being played to the class. Curious to see how the class was reacting, he entered the room. To his surprise there were no students in the room - but on each seat there was a tape recorder. Lectures delivered by tape are, of course, uncommon. But insofar as effectiveness is concerned, they are no different from lectures delivered by professors in person. Large lecture classes and the computerized handling of student registration and records have dehumanized education. It is no wonder that the Berkeley students complained during the period of strong protest in the late 1960s, "I am a human being; do not fold, spindle or mutilate."

The second maleficent cost-cutting practice of the universities is to assign students to small classes of thirty or so with a graduate student, known as a teaching assistant, or [100] intellectual dishwasher, doing all the relevant work - lecturing, grading, advising, determining course content and other matters. These novices are used even to teach the special courses for prospective elementary and high school teachers.

In some universities as many as one hundred to two hundred graduate students do undergraduate mathematics teaching. In 1972 there were 109,000 teaching assistants in all departments of about 250 universities. It is estimated that about 50 percent of the freshman and sophomore mathematics courses in large universities are taught by graduate assistants. Ironically, the very same universities that insist that good teachers must be researchers use graduate students on a large scale.

The reliance upon graduate students as teachers is underscored by events of the last few years. The number of graduate students is declining sharply because jobs in the academic world are now hard to get and fewer students are training for the doctorate. This does not worry the graduate schools so much as the fact that the number of graduate students serving as teaching assistants will not be sufficient to cover the undergraduate classes. Far be it from the minds of administrators to ask professors to teach the elementary undergraduate courses, even though beginning college students need mature teachers more desperately than do advanced undergraduates. Instead, chairmen of university departments canvas the undergraduate schools for bright seniors who might enroll as graduate students and thereby supply an adequate number of teachers.

Many large universities use not only graduate students but also adjuncts (housewives returning to teaching, high school teachers teaching at night, and full-time teachers at other institutions teaching for extra pay). Clearly, these people cannot really immerse themselves in the work. Yet two - [101] thirds of the total number of undergraduate mathematics courses are taught by graduate students and adjuncts.

The graduate student, naturally concerned with his career, will devote himself primarily to his own studies and give short shrift to his teaching. He will hurry through poorly prepared lectures, discourage students from seeing him in office hours, make up poor quizzes and final examinations, and grade almost arbitrarily. Covering the syllabus is a must and the "poor" students who can't maintain the pace are left to fend for themselves. After all, they must be lazy or stupid. They, the graduate students who "made" it, didn't have any such failings and presumably no other cause, such as a student working 20 or 30 hours a week to pay his tuition, enters their minds. If they are permitted to pick texts, young people, hardly aware of the true goals of education or even of mathematics education, pick abominations. Should the teaching assistant feel conscience-stricken, he can ease his conscience by noting how his professors handle their graduate teaching. If, on the other hand, he does do all that conscientious teaching requires, he may never complete his degree - or he may complete it with a poor thesis and not get a job in any reputable institution.

Teachers must have wisdom and wisdom is acquired from experience, not books. It is not a criticism of graduate students that they have not acquired wisdom. It is a criticism of university administrations that they depend upon the widespread use of graduate students and, in most universities, make no formal attempt to teach these young men and women the art and skills of teaching, whether they be the presentation of material, composition of examinations, grading, or advising young students. If a graduate student should, on his own initiative, take a course in pedagogy, he would undoubtedly lose the respect of his mathematics professors [102]

A few of the universities that use graduate students as instructors do try to train them to teach. But such efforts are as likely to be successful as efforts to make water run uphill. Since most universities do not appoint or retain professors who are good teachers, who will train the graduate students? Moreover, as we have already noted, graduate students know that their futures depend primarily on securing a Ph.D. Hence, they must give this activity priority. Their success or lack of success as teachers will not count. Finally, what incentive would a graduate student have to learn how to teach when he knows that the very professor who may be advising him is almost sure to be one who is indifferent to teaching?

The use of graduate students to teach freshman and sophomore courses is especially reprehensible. Beginning students find the transition from high school to college difficult, even traumatic. Many have not learned how to study, how to use a library, and how to live in a strange environment. Freedom from parental guidance leaves some desolate and others irresponsible. During the first year especially students need help and advice, and it is during that year that they are put into the hands of a graduate student who has yet to grow up himself.

Allowing graduate students to take complete responsibility for conducting courses is sometimes defended on the ground that there are not enough qualified professors to handle the mass of students. This is not true; good teachers for undergraduate courses have been in plentiful supply for the past twenty or thirty years.

The use of graduate students is defended on other grounds. They can earn money to support themselves while studying. Many do need to earn money, but it should not be at the expense of the undergraduates, who are paying for and need high-grade instruction. Another defense is that [103] graduate students, many of whom will become professors, need to acquire experience in teaching - to learn by doing. One wonders whether administrators who assert this would go to a first-year medical student to cure an illness. Graduate students should acquire experience, but they can do so in ways that do not sacrifice the undergraduate. Graduate students can observe and can serve as informal tutors to help students having difficulties. They can give a few lectures in the presence of the professor, who can then offer constructive criticism.

Still another argument for the use of graduate students as teachers is that they are more enthusiastic about teaching than many of the professors. But if their enthusiasm outweighs their shortcomings so that they can serve as well as professors, then the correct interpretation of that argument is that many professors should not be professors at all.

If their alleged enthusiasm does not suffice to justify the use of graduate students as teachers then surely as young people they would have empathy with the undergraduates. Quite the contrary. The graduate student is competent in mathematics, else he would not undertake graduate study. On the other hand, since 95 percent of the undergraduates are not very successful in mathematics, the graduate student is most likely to be contemptuous of those who have difficulties in mastering what he took in stride.

The use of graduate students as teachers has been challenged in the past, and one defense offered by administrators is that tests show no difference in results whether undergraduates are taught by graduate students or by professors in large lecture classes. Of course, tests do not measure inspiration, insight, pleasure or displeasure, the perhaps unnecessary hardships students have to undergo to achieve performance, and the psychological lift or damage [104] to the student. But let us for present purposes accept tests as a measure of teaching effectiveness. The results cited by administrators prove nothing. Large lecture classes are as bad a teaching measure as the use of graduate students; hence the test grades are equally bad. A significant difference might be expected between students taught in small classes by professors and those taught by graduate students. And if, in fact, the small classes were taught by professors who are teachers, the tests would show which type is superior. However, for the test results to be significant a large number of students should be involved. But few, if any, universities have mature teachers to handle a sizable number of small sections. Given poor teachers, even students taught in small classes are not likely to do better than those taught by graduate students.

Entrenched professors, who benefit in lighter teaching loads and high salaries, also defend the use of graduate students and proffer the same self-serving arguments as do the administrators.

Very belatedly, in 1975, the American Mathematical Society and the Mathematical Association of America set up a joint committee on the ?Training of Graduate Students to Teach.? In view of their immaturity, their relative ignorance of content and pedagogy, and the pressure on graduate students to earn a Ph.D., training graduate students to teach will be as effective as training a six-year-old to run a four-minute mile.

Are the universities being fair to undergraduates? Tuition in private universities, and tuition plus state and city support in public universities, do more than meet the costs. What the universities prefer to do is to save money on the undergraduate instruction and spend it on high salaries to attract highgrade or prestigious research professors. Research is also a legitimate function of the university, but it is carried on by [105] cheating the undergraduates of their due. To use large lecture classes conducted by professors who are unwilling or unable to teach, or to use inexperienced, immature, and preoccupied graduate students is unethical and amounts to robbing Peter to pay Paul.

How do the universities get away with such practices? They use the prestige acquired by having big names attached to their staffs to attract students; and since American parents want their children to benefit professionally and socially by having them graduate from prestigious universities, they continue to send their children to these places. The public universities offer the added advantage of low tuition, and though they are the worst offenders in the use of graduate students, poorer families have no choice but to send their children there.

In contrast to the universities, the four-year colleges of this country do a far better educational job. On the whole the teaching is conducted by mature professionals, and the classes are small. Unfortunately, this assertion must be qualified. Many of the four-year colleges were founded one hundred to one hundred-fifty years ago by church-affiliated groups so that parents could send their children to schools that would reinforce rather than raise doubts about the truth of their particular religious beliefs. To be sure, the religious ties of the denominational colleges have now become nominal and in many cases have been dropped altogether. But so has financial support from the churches. Also, when travel was more difficult it was undoubtedly necessary to found many small colleges so that they would be accessible to students. These colleges with enrollments of five hundred to one thousand students cannot afford to compete for faculty, to offer an adequate variety of courses, and to maintain adequate facilities, notably a good library. They cannot survive, and the only recourse is consolidation [106] with nearby institutions. Many have gone out of existence. Nor is life easy for the larger four-year colleges.

Endowments and state support that were adequate twenty and fifty years ago no longer suffice. When jobs are scarce the four-year colleges can secure well-trained faculty despite higher teaching loads. But many of these recruits have their eyes on university positions where more stimulating contact with colleagues and better library facilities are available. Therefore, although not pressed to do research at the colleges, they will nevertheless devote most of their time and energy to research in the hope that their work will ultimately attract attention and that a university appointment will be forthcoming. The lure of the lucrative research position is almost irresistible.

Moreover, qualified teachers who accept appointments are generally subject-oriented. Their training and interest are in the subject they undertake to teach, and they continue to seek approval from others in their own discipline. And having been educated primarily by professors who lecture and who presuppose an interest in the subject, these undergraduate teachers tend to do the same thing. Nor does it occur to the usual undergraduate professor, however intelligent, that he must know what background high school students bring to college. Indeed, many of the concerns that should be foremost in the minds of good college teachers are too often recognized either belatedly or never. This is understandable. Not only did they receive no formal instruction in pedagogy, but rarely is there a serious discussion among members of a college department about the problems and techniques of pedagogy; and only extremely rarely does an administrative official undertake to institute such a practice.

Quite often it is not the professors at the four-year colleges who are responsible for poor education. Many of the [107] administrators are not content to play a vital, if less prestigious, role in education. They seek to emulate the universities and demand research as a condition for employment and advancement. Nevertheless, despite all these shortcomings, the better four-year colleges are still the only institutions in which the intent to teach is uppermost. Fortunately, many competent mathematicians who prefer teaching and the congeniality of friendly colleagues to the fierce competitiveness of the large universities are willing to sacrifice prestige for a useful and satisfying contribution to society; they do gladly accept appointments to four-year colleges and devote themselves to teaching. Thanks to them the four-year colleges are the mainstay of undergraduate education. Unfortunately, the universities train twice as many bachelor candidates as the colleges.

Less satisfactory than the four-year colleges are the two-year junior and community colleges. Many are now taking advantage of the scarcity of jobs to get Ph.D.'s from prestigious institutions. In fact, some are insisting that all new faculty appointees have a Ph.D. But the teaching problems of the junior colleges are even more severe than those of the four-year colleges, because all high school graduates are automatically admitted. Ph.D.'s, trained to do research, are not suitable faculty for the two-year colleges.

The low quality of the teaching in most of the institutions wreaks havoc in many directions. The research work done by most professors, as we have already noted, is overvalued. A teacher, on the other hand, influences during his career thousands of young people, many of whom will be leaders in various areas of national life. Their attitude toward education, their decisions about what careers to follow, and their confidence in themselves are determined, or at least strongly influenced, by their teachers. Many a young person has abandoned a scientific career because mathematics [108] proved to be an obstacle, and one may be quite certain that in most of these cases the teaching was the true source of the trouble. Let us recall also that the universities train the high school and elementary school teachers. Hence, what the universities do affects teaching at all levels. (See Chapters 8 and 9.)

Though students are the chief victims of poor mathematics education, the fate of mathematics itself is also imperiled. The mathematical strength of any country or civilization depends not only on the geniuses who produce brand-new worthwhile results. Indeed if these geniuses were isolated and unappreciated their output would be voices in the wilderness. Mathematical knowledge must be kept alive and transmitted to younger people. Even a scientific breakthrough is of questionable value in a society that does not know how to absorb it. To recognize and properly educate even the future mathematicians, the educative process must be widespread and many good teachers must be available. Talent is found in the most unexpected places, and unless a teacher is competent and alert it will be overlooked again and again. It was an obscure teacher who recognized the ability of Gauss, one of the world's greatest mathematicians, and who recommended that the Duke of Brunswick support him. Gauss's father, a bricklayer, certainly could not have sent him to a university. Whether or not good teachers themselves contribute to research, they are sowers of seeds that take root in the minds of young people, some of whom will be Gausses and others of whom will enable society to profit from the work of the Gausses.

Despite the importance of teaching, an importance far greater than most research, the good teacher has no place in the present-day university world or even in those four-year colleges that insist on research as a requisite for faculty status. Thus, in higher education the teacher, however [109]excellent, who refuses to bow before the gilded idol of publication, finds fewer and fewer outlets for his talent. In an atmosphere where research alone is valued, the teacher is made to feel that he is a failure, that he really does not belong but is tolerated as a second-class citizen because by some oversight he acquired tenure. For him promotions are slow and salary, where not legally prescribed, remains far below that of the research man. He is regarded as a drag on the department, which somehow has been stuck with him. As one writer about the current scene put it, college professors are now divided into two classes, entreprenurial professors and teaching professors - or winners and losers.

In the most prestigious universities, and in many of the would-be prestigious ones, there is not a single tenured mathematician who is there primarily because he is a teacher. Administrators sometimes admit this but claim that instead they offer an intellectual climate and an opportunity for undergraduate students to mingle with intellectually challenging fellow students. But all of this is an indigestible ersatz for the food that students should be receiving from competent teachers. Moreover, if the teaching is really unimportant, why should tuition pay for faculty salaries? Ironically these same administrators want their own children to have good teachers and don't hesitate to speak up when their children fail to get them.

In contrast to teaching, research has acquired a sanctity and research professors an air of sanctimoniousness even when their papers are rubbish, though not clearly recognized as such through their veneer of terminology and symbolism. To do research is nobler and a higher mission than to teach. Communicating knowledge to one hundred or one hundred-fifty students a year is not valuable. But a paper in a journal which no one may look at is. Significant communication does not rank with insignificant scribbling.

[110] Tenured professors with reasonably good salaries do have a measure of freedom. They need not publish a large number of pages per year and can devote part of their time to students without risking much. However, professors are a cross-section of human beings. The thousand-dollar raise that might be obtained if one does more research does beckon. The accolades of colleagues and professional organizations are sweeter than the accolades of students, and the prestige of research outweighs the prestige of great teaching.

Curriculum and requirements for the bachelor's degree are being reexamined in many universities and colleges today. Deans and professors who tried to appease students during the protests of the 1960s by abolishing almost all requirements of specific courses for the degree are now convinced that the liberalization went too far. Of course, curriculum and degree requirements are important.

But these reforms are not the most important ones that should be undertaken. The best curriculum, whether for required or optional courses, will be manhandled under present teaching conditions. The research professors will continue to ignore bulletin descriptions and teach what they please, and the graduate students will bungle thoughtfully planned subject matter because they are not qualified to teach.

The same remarks apply to the continual discussions about lines of command, delegation of responsibilities, review procedures, and all other organizational problems of college and universities. An automobile manufacturing company may have an efficient organization and blueprints for the ideal car, but if the available gasoline is poor, the organization and blueprints are all but worthless.

I am very grateful for the kind permission of Professor Kline's widow, Mrs Helen Kline for this book to be reproduced.