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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 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 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 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 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 - 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. 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 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 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 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 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 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 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 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. 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. 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2003-05-24 03:17 CHAPTER: 4 The Conflict Between Research and teaching What a blessed place this would be if there were no undergraduates!. . . No waste of good brains in cramming bad ones. ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡Leslie Stephen The major role of the universities is to carry on two functions - research and teaching. However, money and facilities are limited. The universities solve this problem by appointing research professors. Such people, they assert, advance knowledge and improve all levels of education directly and indirectly. More specifically they maintain that researchers are ipso facto good teachers. They also assert the converse: To be a good teacher one must be a good researcher. Hence appointment, promotion, tenure, and salary are based entirely on status in research. Although there is justification for the insistence that professors who train future researchers be capable in research, for most of the teaching that the universities are, or should be, offering, the research professor is useless. There is in mathematics, and almost as surely in other disciplines, a direct conflict between teaching and research. One argument advanced in favor of the research man is that he has superior knowledge. But what knowledge does he possess? He is almost sure to be a specialist. The specialist is like a miner who never surveys a landscape but who digs a barely passable tunnel into a mine to research a small lode of gold that may in fact prove to be tin. Such research narrows rather than broadens. What the professor does in his research has little if any bearing on what he has to teach at the undergraduate and even beginning graduate levels. A specialist in some corner of abstract algebra may know nothing about non-Euclidean geometry. In fact, the creative researcher is most likely to be no more than a proficient but limited technician in one minuscule area. The irrelevance of specialized knowledge for teaching is not peculiar to mathematics. A professor of English who has specialized in philology or in the love life of Madame Bovary is not by virtue of this research equipped to teach elementary composition or a survey of literature. Not all mathematical research is specialized. For example, some work on abstractions and generalizations is rather broad. But, apart from the worthlessness of much of this material (see Chapter 3), this work is far too sophisticated for most of the teaching professors are called upon to do. Abstractions and generalizations are meaningful only to students who already have a considerable knowledge of more concrete mathematics. unfortunately, researchers are prone to plunge at once into abstractions and generalizations because these are dear to their hearts. The research professor's knowledge is of questionable value for another reason. Most mathematical research today is "pure"; it has no relevance to problems arising in the real world. But most of the students who take mathematics, about 95 percent, plan to be physical scientists, engineers, economists, actuaries, statisticians, and primary and secondary school teachers. The typical researcher's knowledge is useless to such students. Beyond all the previous reasons for devaluating the knowledge research professors possess, there is an additional one that applies specifically to mathematics education. Mathematical knowledge is cumulative. Just as algebra depends on arithmetic, the calculus on algebra, differential equations on the calculus, and so on, so the researcher's knowledge is accessible only to those who have considerable prerequisite knowledge in his area of research. A common argument often advanced in favor of the researcher is that he evidently loves his subject and will communicate his enthusiasm to his students. One must recognize, however, that research today is - as Professor Truesdell, whom we have already cited, and Blaise Pascal much earlier, called it - far more a trade than a profession, and many people engage in it merely as one way to make a living. Indeed, since the universities stress research as the road to personal advancement, many professors are pressed into research much as draftees are pressed into the army whether or not they are willing to fight. Research is a highly competitive activity, not a labor of love. The pressure to publish is exemplified by the message one chairman sent to the members of his department: "A theorem a day means promotion and pay." Even the enthusiastic professor who is deeply engrossed in his research almost unconsciously assumes that his mission is to stir up interest in his specialty, and accordingly rushes his students toward it at a pace they cannot maintain and at the expense of far more valuable and basic material. He seeks to train specialists even though this training is useless to almost all of his students. Moreover, since prominence and visibility in his field is demanded, the professor undertakes activities that enable him to shine. He will publicize his results at countless conferences and professional meetings. He will pursue grants and consulting arrangements that, beyond being profitable, aid his prestige. To attract attention he will seek office in a professional society. All these activities enhance his commercial value and further his personal advancement. What about obligations to students? This is the nethermost consideration. Even loyalty to his institution is not respected. Professors negotiate their own research grants and take them along when they transfer to another institution. In brief, they become denizens of the marketplace. Professors have no more conscience about obligations than has any other group chosen at random. The layman tends to think of research as a genteel, leisurely activity, conducted with an open, disinterested attitude and devoted to the pursuit of truth. Actually it is a fierce battle for survival. Since priority in publication means everything, a researcher must push his work as fast as he can lest someone else beat him to it. Lord Ernest Rutherford, one of the greatest of British physicists, wrote in 1902, "I have to keep going, as there are always people on my track. I have to publish my present work as rapidly as possible in order to keep in the race ...." And the attempt to keep up with the literature in his field will absorb a considerable amount of a researcher's time and energy. The intensity of the competition even obliges researchers to adopt invidious practices more commonly attributed to the business world, such as refraining from telling others what they are trying to do or what partial success they may already have. For the sake of an immediate publication, a researcher may feel compelled to publish shoddy results, even though he may be quite sure that further efforts will produce a far better paper. Research requires an all-out effort and forces neglect or perfunctoriness in teaching. The universities' insistence on research imposes a special hardship on young Ph.D.'s They have just emerged from indoctrination in the purity of mathematics and from the dark recesses of some specialty they have pursued for two or three years. The doctorate conferred upon them is not the certification of a teacher but the official stamp of cultural deprivation. They then receive a three-year appointment during which they are expected to demonstrate their brilliance through publication. But this is just the period when most begin to teach; they must spend time in the preparation of courses that are new to them and in learning much about the art of teaching. After two years of service it is customary to notify these teachers whether their appointments will be renewed. Actually, not even two years can be used to demonstrate their research strength; the journals are overcrowded and many months must elapse before a paper is refereed and even accepted for publication. Since up to the time of their appointment these young teachers did only one piece of research, the thesis, and that was done under the guidance of a professor, they face a formidable task. Even if good teaching is regarded with some favor in their institutions, tyros in teaching certainly cannot expect to shine in this capacity. There is but one human response to such a conflict. It is publish, and perish the students. The folly of expecting young Ph.D.'s to justify their claim to appointment or tenure through publication is evidenced by the case of Albert Einstein. After obtaining a diploma at the Zurich Polytechnic Institute, he sought merely an assistantship in a German university in order to obtain a doctor's degree. But at that time he had no publication to demonstrate his capacity for research. He therefore took a job as an examiner in the Swiss patent office at Berne. Several years later, in 1905, he published three brilliant papers, including the one on the special theory of relativity. Six more years elapsed before he obtained his first university position at the German university in Prague. The requirement of research from young Ph.D.'s was ridiculed recently by a professor of philosophy at an Ivy League institution: "Most of the great philosophers could not have gotten tenure at Blank University; they published their important work after they were forty. Kant didn't write anything for twelve years - he would have been out on his butt." That young men and women are expected, however unreasonably, to show research strength is readily confirmed merely by glancing at employment advertisements in the professional journals. One prestigious university advertised for an assistant professor who would already have published work of high quality and would be expected to continue to be active in research. The applicant was also to present evidence of proved effectiveness in teaching at undergraduate and graduate levels. All this was required from a young man or woman who, if applying for an assistant professorship, would be a Ph.D. of, at most, two or three years' standing. A not uncommon advertisement reads essentially as follows: Wanted: Young Ph.D.'s, ranks of assistant professor and higher. Must have proven research ability. Vita must include publications. Apply to Prof. I.M. Noble, Superior Community College, Worthmore, Nevada. (Salaries readily augmented. Short drive to Las Vegas.) One would think that department chairmen, who can be in close contact with their young Ph.D.'s, would be able to judge potential without requiring publication. But the ability to discern talent is rarer than ability to do research, and many chairmen do not possess it. They often consult a colleague, who may be equally incapable of judging, or an outside specialist who may be biased. Moreover, young people are not likely to be known outside a limited academic circle. The conflict between teaching and research becomes even more apparent when one considers the demands of teaching. Perhaps the first consideration is breadth of knowledge. Commerce students, prospective elementary and secondary school teachers, and social science students are now consumers of mathematics. Engineering and physical science students also need subject matter different from that for pure mathematicians. Just as it would be folly to require prospective dentists to learn Anglo-Saxon, so it is folly to require that prospective engineers learn the rigorous foundations of mathematics. Even on the graduate level most students are not preparing for mathematical research. The professor should know what material is important for them and fashion suitable courses. But the research mathematician cannot devote time to such matters and so teaches the material with which he is at ease. What else does good teaching demand? Certainly it calls for knowing what backgrounds students bring to the class. Mathematics, at the lower levels especially, is a sequential subject, and a course must start where the prior education left off. To know what freshmen bring to college calls for knowing what the high schools teach. This is especially true today because the high schools have been changing curricula under the influence of new movements. But research professors will not trouble to find out what is being taught. A good teacher gets to know his pupils. Some can be asked to tackle the more difficult problems or do additional work. The poorer ones should be called upon only for work commensurate with their backgrounds. If required to do what is beyond them they will become discouraged. The teacher should get to know his pupils so well that he could grade them without relying upon any examination, though he may give one for other reasons. Good teaching also requires catering to the students, psychological needs - giving encouragement to some, putting pressure to work on others and imparting confidence to those who have been defeated by poor teaching in their prior studies. A good teacher must have a knowledge of other psychological problems that beset students, provide advice on how to study, and offer the stimulus of personal contact. To effectively understand his students the teacher must also accommodate himself to the outlook of young people and be part of their world. A recent study asked about two hundred college sophomores to write 250-word essays describing the greatest mathematics teacher they ever had and giving the reasons for their choices. The characteristic chosen by most students, 78 percent, was, "exhibits a genuine personal interest in students." The second highest-ranking characteristic, "conducts interesting classes," was mentioned by only 53 percent. The fifth-ranking characteristic, "knowing the subject," was named by only 34 percent. (This last figure may well be accounted for by the presumption that this attribute is something every student expects of his teacher and so many did not bother to name it.) Teachers should constantly invite questions from their students. Some researchers are bothered by questions in class that cause them to depart from their prepared lectures or to look up something with which they do not wish to become involved. They prepare "perfect" lectures and regard interruptions as presumptuous or indicative of stupidity. To present the material properly a good teacher must know how young people think. Can a particular abstract concept be presented successfully to freshmen or should its presentation be delayed until the junior year? Will a rigorous approach to the calculus succeed with students who are beginning the subject? In preparing to teach a course the professor must choose the most suitable text from the dozens of available ones. This selection is time-consuming and calls for judging what students on any one level can handle. Even if a professor spends the time but is not judicious in his choice, he is likely to accept a text that is clear to him but, because of inadequate exposition, unduly burdens the student. He must also pursue and keep track of books and articles on ways of presenting ideas effectively. Modifications in curricula, usually needed to meet either changing student backgrounds or the introduction of a new area of application, place an additional burden on the teacher. For example, the invention of computers and their constantly increasing use call for altering some courses to take advantage of the availability of these devices. Remedial work with entering college students, now a major problem, requires special courses. The design of new or modified courses is a task that the good teacher undertakes at the expense of considerable time. A good teacher must be perceptive. He must know what difficulties students have in learning at their stage of the game. It is not sufficient that the professor "knows his stuff." Knowing his stuff too often means that he has forgotten or is oblivious of the obstacles young people encounter in learning elementary ideas. He may regard these as trivial and pass over them as though they did not exist. The alert teacher must also be able to recognize late bloomers and to appreciate that slow thinkers are not necessarily poor thinkers. Finally, a crucial problem in teaching is motivating the students. It does not occur to many professors that other people with different tastes or perhaps a better sense of values may not like mathematics. Students want to know why mathematics or a particular topic is significant, and not just that their professor likes it. Even on the more advanced level, where the professor can count on his students having some inclination toward mathematics, presenting theorems without the proper motivation leaves a class with no more than a meaningless collection of theorems, proofs, and procedures. Most professors are interested in mathematics and so cannot appreciate that there is a need to motivate students. In fact, such professors prefer to teach students whose drive is already so well developed that they do not need additional motivation. A professor's greatest joy is the bright doctoral student - and professors love to boast about their bright students as though they made them bright. Supplying effective motivation is time-consuming and calls for experimentation. It also requires breadth of knowledge that the research-oriented professor does not have and may be unwilling to acquire. The natural and historically valid motivation would be supplied by real, largely physical, problems. But because mathematics professors have abandoned the real world, the break from science has also affected pedagogy. A good teacher will take a hand in college affairs. Counseling of students and service on faculty committees and the university senate (through which the faculty cooperates with the administration) are obligations of the entire faculty. But researchers do not deign to concern themselves with undergraduate or even graduate affairs that involve cooperation with other departments and the administration. Hence, the burden falls on the men and women who are primarily teachers, and the conscientious teacher does not shirk it. In short, teaching is a specialty that can be pursued only by people with the willingness to master the art through persistent devotion and experience. It undoubtedly calls for wholehearted and almost full-time effort. All these considerations, which exhibit the vastly different demands of research and teaching, do not include another vital factor, namely, the personalities of researchers and teachers. A teacher must be able to communicate his knowledge. Do mathematics research professors have this ability? In general they are introspective and introverted; they do not feel at ease with people; they shy away from personal contacts. They like to concentrate on their thoughts. They choose mathematical research partly because mathematics per se does not pose the complex problems that are involved in dealing with human beings. To repeat Bertrand Russell's words, ?Remote from human passions, remote even from the pitiful facts of nature, the generations have created an ordered cosmos, where pure thought can dwell as in its natural home and where one, at least, of our nobler impulses can escape from the dreary exile of the actual world.? He also said in his autobiography that abstract thinking destroys our humanity and draws us into ourselves, and he confessed that he was drawn into mathematics ?because it is not human.? Mathematics, then, is a refuge. Research in many fields is a solitary occupation; in mathematics it is likely to be a haven for those with scanty spirit and interests. Would such individuals be likely to communicate successfully with students? The good teacher must be dynamic, articulate, engaging, clear, warm, sympathetic with students, interested in people as much as in ideas, and even a good actor. He not only should have a lively personality but also must have the proper temperament. He must be interested in young people. Their problems, to some extent, must be his. The student who wants to be an English major and rebels at taking a required mathematics course has a case that to him, at least, seems sound. It is the teacher's function to convince him of the value of that course for his life as an educated person. There are many professors who, though they wish to be good teachers and approach the work seriously, apparently believe that the wish is the act. The wish may be father to the deed, but the conception, pregnancy, and labor are missing. These require perception, time, and energy devoted specifically to the requirements of good teaching. Much of this art must be learned from the students. To the extent that the students show comprehension, interest, even excitement, satisfaction, drive to learn more, and response to deliberately posed queries intended to stimulate thinking - to that extent the teaching is successful. But where and in what respects it is not must be observed by the teacher and modification be made to remedy defects. This is far more than even the more student-oriented research professors are willing to do, because they reserve most of their time, thought, and energy for their research. Many researchers are kind, polite, and well-meaning. However, they are also unable to make contact with the students, and some are even afraid to face them. These professors are often quite conscientious. They prepare material carefully; they write it on the board meticulously, and the students spend their class time copying what the professors put there. Such research professors are apparently so unworldly that they have not heard of duplicating machines. Researchers are usually credited with not only the specific talent that enables them to be creative but also with an underlying superior intelligence that enables them to judge wisely and perform superbly in every situation they may face. The question of whether there is a special talent for mathematics cannot be settled by any objective evidence. One certainly must doubt whether there are mathematical genes. Insofar as opinion can answer the question of talent, most notable is the opinion of Richard Courant, who was head of the world's leading department of mathematics in pre-Hitler Germany, at Gottingen University, and who converted a nondescript department of mathematics in the United States into one of the country's leading departments, perhaps the leading one. No one knew more great mathematicians of our century, or knew them more intimately. When asked whether there is such a quality as mathematical talent, Courant replied, "There is no such thing." And then he added, "Rather than ask what special qualities mathematicians possess, you should ask, what do they lack that other human beings possess." Perhaps this response also answers the question of whether researchers possess superior intelligence. Though some administrators might concede a conflict between research and teaching, they fall back on other arguments for insisting on research as the qualification for faculty status. Original research, they say, is the surest proof of intellectual distinction and the surest guarantee that intellectual activity will not cease. Leaving aside for the moment the problem of judging the quality of original research, we must ask what intellectual distinction has to do with teaching. A truly distinguished intellect may be so far above the level of the students he must teach that he will fail to understand their problems and needs, even if he possesses the willingness to do so. As to original research being the surest guarantee that intellectual activity will not cease, many researchers fade out in their thirties and even more do so in their forties. And if they do, they will most likely be dispirited, depressed, and even sour. Unfortunately, we have no figures on how many researchers fade out nor on how their number might compare with those who emphasize teaching and remain intellectually alive in all sorts of activities. Certainly some research men do burn out. The general belief, though its truth is not definitively established, is that science is a young man's game. As P.A.M. Dirac, a Nobel-prizewinner in theoretical physics, once said, partly in jest: Age is, of course, a fever chill that every physicist must fear. He's better dead than living still where once he's past his thirtieth year. It is vital that professors keep intellectually alive but it need not be through research. There are other ways which we shall discuss later. Moreover, what does it. benefit the student if the research professor remains alert but, in view of the nature of modern research, he remains narrow? Many administrators and chairmen argue that some standard for selection must be used, and since research can be measured whereas teaching cannot, it is better not to risk hiring people who are primarily teachers. The argument is false. We have already pointed out (Chapter 3) that it is almost impossible to secure competent judgment of the quality of research and that in fact most current research is worthless. Evaluation of research boils down to quantity of publication; the contents are irrelevant. As long as his peers accept it, a researcher can publish almost anything - and his peers do accept it, because they wish the same treatment. The chairmen and administrators who say that research can be measured whereas teaching cannot are really admitting to counting pages of publication. This measure is as sound as looking at a university?s total expenditures to determine whether it is fulfilling its role as an educational institution. One wonders how administrators would have judged the young Isaac Newton, who, after receiving criticism of a paper he had published, vowed never to publish again. Surprisingly, even in large departments the research cannot be evaluated with assurance. Each person is a specialist in his own field and really knows little, if anything, about the work of his colleagues. Evaluation by committee is no more reliable. Anyone who has worked on committees knows that enlisting several people to share the burden results in each member of the committee expecting the others to do the work and no one contributing anything. Instead, friendship, partisanship, jealousies, favoritism toward one field of research rather than another, gossip, and scraps of information decide the issues. Many department chairmen or committees called upon for one reason or another to judge a faculty member write to specialists in the appropriate field. This recourse to peers is hardly likely to produce a fair judgment. We have already noted (Chapter 3) the defects of the refereeing process, and all of these apply as well to the judgment of published research by peers. Moreover, because fads do play a role, a sound researcher working in a field that has not become fashionable will get a poor rating. Mathematicians are no more discerning of or receptive to new ideas than are small-town politicians whose constituents seem happy with the status quo. The idols of the tribe are not desecrated with impunity. Beyond judgment by a professor's own department, decisions on promotion and tenure, even if recommended by the department, must usually be approved by a faculty committee. In view of today's specialization of research, there may not be even one member on the committee who can understand the research he must judge. And so the faculty committee, too, falls back on quantity of publication. How does one judge teaching? Students are possible judges. However, students are young and their mature evaluation may come years later. Moreover, students differ in their needs and demands. The indifferent student may value just entertainment and will rate high a teacher who is only an actor. The mediocre but conscientious student will appreciate steady-going, clear presentations, but flashes of brilliance from the professor will pass him by or upset him. Such a student wants to know only what to do and how to do it. The really bright student, who can read for himself, wants mainly direction, deep insight, and perhaps challenging problems. Obviously, a typical class will contain all types of students and the professor will get a mixed rating. In P addition, students are influenced by the grades they get. Finally, if compelled to take a course in a subject they dislike, they are certainly going to be antipathetic to the teacher. Hence, evaluation by students, though it should not be ignored, cannot be the main basis for deciding on a teacher's effectiveness. Admittedly, teaching is difficult to evaluate, and good teaching takes many forms. The professor who stimulates and excites students to work for themselves - even when he does little to present the subject matter proper and is even unsystematic in doing so - is certainly a good teacher. The sober, careful expositor who helps students to master the material and gives them the confidence that they will do well, but presumes student drive, is another excellent type. Still another is the professor who may be a dud in the classroom but who builds close personal relationships with his students, spends hours with them on their individual needs, and gives each student the feeling that he has a friend and counselor. A department chairman can do a great deal to evaluate a teacher. He can make it his business to have frequent discussions on what topics the professor chooses to teach in a given course and how he presents his course. The chairman can get to know a teacher's character and temperament, his interest in teaching, his choice of texts, the kind of examinations he gives, and his availability to students. Teachers can themselves demonstrate expertise by writing a good text, an expository paper, or developing a better pedagogical approach to a topic. However, there is no objective and certainly no quantitative measure of teaching ability. Judgment enters here as in the evaluation of research and as, in fact, in all the important decisions men are called upon to make. And administrators who are not qualified to exercise judgment should not be allowed to serve in positions where they will be required to do so. Around the turn of the century William James said that the social value of a college education was to be able to recognize a good man when you saw one. But this ability is not possessed by most administrators. To decide whether a teacher is good they ask him to supply letters of recommendation (usually written by those who are no better judges than the administrator), and they ask for a list of his publications. Despite the inescapable need for applying true judgment instead of resorting desperately and fruitlessly to quantitative data, many administrators are unwilling or fearful to apply it. Judgments may be wrong, but all one can expect of a good administrator is that he is right most of the time. The saddest fact about the evaluation of teaching is that most administrators don't care whether a teacher is recognized as superb by colleagues and students. Teaching just does not count in the universities. Of course administrators deny this. All things considered, the very nature and demands of research and teaching are so diverse, the personalities and abilities required so different, that only a rare individual with an abundance of energy can undertake to excel in both areas - at least during the same period of his life. Generally, good performance in teaching is in inverse proportion to efforts in research. Of course some research men may be willing to teach, but ability to do so is another matter. Their wisdom may be consumed in their research. Though any attempt to compile statistics on the number of mathematicians who were or are both good researchers and good teachers would be a massive task with much room for misjudgment, it is significant that two of the three men commonly selected as the greatest mathematicians present relevant case histories. Newton was a professor at Cambridge University and was known to be a very poor teacher. At times no students at all attended his lectures, and of those who did attend, few understood him. The paucity of students did not disturb him, but he was almost paranoid in his concern to receive credit for his creations. Though not a bad lecturer, Gauss did not care to teach and said so. In 1802 he wrote to the physician and amateur astronomer Wilhelm Olbers: "I have a real aversion to teaching. For a professor of mathematics it consists of eternal work to just teach the ABC's of his science; of the few students who go on, most continue to gather a file of information and become only half-educated, whereas the rare gifted students will not allow themselves to be educated through lectures but instead learn by themselves. And through this thankless work the professor loses his precious time." Gauss attracted only a few students to his lectures, whereas his colleague, Bernhard Friedrich Thibaut, who contributed very little to mathematics, had a hundred. Gauss gave the same lectures with very little variation, year after year. The third of the 'greats,' Archimedes, was not a professor and, moreover, lived at a time when education was conducted so differently that his case is irrelevant. In recent years not many great researchers have expressed in print their attitude toward teaching. But Godfrey H. Hardy, one of Great Britain's leading professors in the first half of this century, did so in his A Mathematician'sApology. "I hate 'teaching'," he wrote, "and have had to do very little, such teaching as I have done having been almost entirely supervision of research; I love 'lecturing' and have lectured a great deal to extremely able classes; and I have always had plenty of leisure for the researches which have been the one great permanent happiness of my life." One understands why Hardy titled his book A Mathematician?s Apology. In our own time the researcher's lack of interest in teaching is patent. When a university seeks to attract such a person, it offers not only money, but also a light teaching load - the lighter the better. The university officials know that researchers do not want to teach. Beyond the small number of teaching hours, the researcher is offered the privilege of devoting some of those hours to a course or seminar in his own specialty. Many researchers have said frankly, "Universities would be fine places if there were no students." Quite a few have expressed their contempt for undergraduate teaching and often can be heard at evening social gatherings to bemoan the fact that they must meet an undergraduate class the next morning. They sneer at the mere teacher and act condescendingly toward the students whom they regard as dull and unworthy of their attention. Such researchers may know the mathematical theory of ideals, but they are certainly not familiar with the ideals of teaching. They present familiar techniques mechanically, and when faced with the inevitable consequence that the students are bored and baffled, they criticize the students for lack of interest. Actually, it is the professors who are not interested. By continuing to teach the same old techniques, they avoid thinking about how to present the material. Admittedly, there are also people engaged primarily in teaching who would be graded A only for the speed with which they can empty a classroom. A bad teacher is a small-scale disaster that wreaks havoc as long as he lives. Some would claim that ego and approval of the peer group are factors favoring the pre-eminence of research. Darwin did say,"My love of natural science. . . has been much aided by the ambition to be esteemed by my fellow naturalists." Yes, scientists do love recognition by their peers, especially since the time of Pythagoras. For mathematicians the peers consist, reasonably enough of fellow mathematicians - a society conditioned by the universities to approve only research. If the peer group were encouraged to grant recognition to teaching it might in fact do so. In any case, ego and approval from the peer group need not impel a frenzied rush to publication. True ego would demand genuine accomplishment, even if the attainment of it were to take ten years. In view of the conflicting demands of research and teaching, how can responsible men continue to affirm that research professors are automatically good teachers and that good teachers ought necessarily to be seriously involved in research. It is understandable that researchers cannot believe that they are not good teachers. It would hurt their pride; and they are proud to the extent of egotism. Moreover, since so many are naive about what lies outside their own research, they uncritically accept these tenets. They would be shocked if they were to request their students, at the end of a course, to answer a questionnaire asking them to check one of the following: The teaching in this course has been a) excellent, b) good, c) fair, d) poor, e) execrable. But their confidence in their teaching ability is so firm that they do not see the need to question their own effectiveness. One would think that chairmen of departments would be more responsive to their obligations to the students, but they are not. Since chairmen are anxious to show that they can build and maintain research strength, they favor researchers. Thus, the chairmen, too, sacrifice the students. Many chairmen prefer researchers because they know only research and with unconscious immodesty seek men in their own image. Teaching they do not understand and so they regard it as unimportant. It is more surprising that administrators accept such crass doctrines without evidence. It is their responsibility to foster teaching and research, and they should know whether researchers can also supply the teaching needs of students. But the administrators of even a moderate-sized university are far removed from the activities of the individual departments, and so they are unable to judge the quality of the faculty, the reasonableness of the extent or quality of the offering, and the quality of the teaching, even if that should be a concern. They concentrate on budgets and maintenance of regulations. A good bookkeeper could do what many deans and vice-presidents do. University administrations are staffed largely with people who strive hard to perpetuate what they do not understand. In such matters as teaching and research they are naive and merely repeat what they have heard. These administrators, too, do not see the need to check their beliefs. Many administrators who know that research is in direct conflict with teaching profess nevertheless that research is a prerequisite. Why? What these administrators really seek is prestige, and any measure that builds prestige is favored. Whereas fifty and more years ago they sought to obtain it by attracting socially elite students, in today's world the medium is research. Since teaching can be appreciated only by students, whose opinions do not count in the adult world, teaching is not valued. Researchers, on the other hand, publish, and so their names and their university affiliations receive publicity. Because research is considered (certainly by those doing research) to be a mark of genius, it is accorded glory that reflects on the universities sponsoring it. It is the mink coat of the university world. Researchers win Nobel prizes, awards from professional societies, election to the National Academy of Science, and other such honors, and these, too, build up the prestige of the universities employing them. In The American University Professor Jacques Barzun mockingly suggests that universities have used the formula ¡¡¡¡¡¡¡¡¡¡ Vip = £¨2p + 5n £©/ f or Visible Prestige equals twice the number of Pulitzer prizes plus five times the number of Nobel prizes divided by the total number of faculty to measure their prestige. Of course this formula will not quite do for mathematicians; their work is not awarded Pulitzer or Nobel prizes.* However, election to the National Academy of Sciences or high office in a professional society may substitute for Nobels and Pulitzers in Barzun's formula. It matters not whether the honors are deserved (see Chapter 11); if the university can parade them in its literature, or if they receive five-line notices in the newspapers, that suffices. It apparently has not In an article in the New York Times Magazine section of November 21, 1976, Saul Bellow, winner of the Nobel Prize for Literature in 1976, quotes his wife, Alexandra, a professor at Northwestern University, to the effect that Nobel excluded mathematicians because his wife's lover was a mathematician. yet occurred to administrators that a more effective means of building prestige would be to hire a Madison Avenue advertising firm, but no doubt that soon will be done. In their unbridled quest for prestige the universities do not rely solely upon researchers. The professor who heads a large project, such as space exploration, who travels frequently to Washington, or who receives newspaper attention for whatever he does is as desirable for faculty status as the most competent research man. So also are high government officials who can still in some way be named as faculty though they do nothing to further the legitimate activities of the universities. There is ample evidence that universities seek prestige rather than quality. University Y has a fine mathematics department but nevertheless offers Professor A of University H a handsome salary to leave H and join Y. Now whatever good work A may be doing he can do just as well at H as at Y; hence the world does not benefit by the change in locale. But if A has prestige that will accrue to Y, that suffices for Y to invite him. Universities give all sorts of reasons for attracting people from other institutions. Of course, if A's subject is basic and there has been no one to teach it, or if a college decides to add graduate work and wishes to build a research faculty, the offer is justified. But these sensible reasons are much less frequently operative than the desire to acquire or enhance prestige. Universities hire professors the way some men choose wives - they want ones that others will admire. The drive for prestige is evident almost everywhere. One university president making his maiden speech in that capacity to a group of faculty, alumni, and friends of the university opened his speech by mentioning the Nobelprizewinners, National Book Award winners, and other prominent figures who were members of the university staff. This opening was evidently intended to impress the audience. At no time during the speech did the president mention any notable feature of the teaching function of the university. Ironically, this same university had reduced its retirement age to sixty-five and therefore, in effect, dismissed some very capable men and women, while continuing to appoint prestigious outsiders who were past sixty-five. Why do the universities seek prestige? The main reason is money. Money has become the overriding concern of administrators. We have already noted that researchers attract government and private foundation money - which is then spent to attract more expensive researchers. Private universities also compete for students because tuition covers a substantial part of the universities? expenses,and students, often on their parents' urging, like to attend prestigious institutions. State universities compete for students so that they can demand more money from their legislatures. But there are intangibles also. Universities are run by individuals, and the prestige of the university enhances the individuals? standing. As Thorstein Veblen remarked many years ago, "Men of 'affairs' have taken over the pursuit of knowledge." Even professors, supposedly wholly devoted to their work, will accept a lower salary at a more prestigious university just to be more visible under the brighter radiance. Though the craving for prestige is the motivating force behind most university actions, research is the socially approved word and, in fact, is one effective means of acquiring and maintaining prestige. Hence, the university administrators in their speeches and writings use the term "research" even when they are fully aware that it is a euphemism for what they really mean. The universities' drive for prestige puts the professors in the anomalous position of being hired to teach, required to do research, and prized for the prestige they accord to the university. The professors react accordingly. Even those who prove to be mediocre in research persist in trying to base their claim for advancement on research, partly because they know that this will count more than any other activity and partly because they are not convinced that their research is minor. They still hope to write the papers that will show their greatness and so are unwilling to devote appreciable effort to teaching and to university and departmental concerns. Others seek visibility in circles that university administrations prize, no matter what is sacrificed in the process. The present qualifications for getting ahead in the professorial career are neatly summarized in the statistics of responses made in 1964 by members of the American Political Science Association: ATTRIBUTE¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡RANK Volume of publication¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡1 School at which doctorate was taken 2 Having the right connections¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡3 Ability to get research support¡¡¡¡¡¡¡¡¡¡¡¡¡¡ 4 Quality of publication¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡5 Textbook authorship¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡6 Luck or chance¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡7 School of first full-time appointment¡¡¡¡¡¡¡¡¡¡ 8 Self-promotion ("brass")¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ 9 Teaching ability¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ 10 The inordinate emphasis on research is a relatively new phenomenon in American universities. We have related (Chapter 2) the fear expressed by Charles W. Eliot in 1869 that research would detract from teaching. Though Eliot may have exaggerated the danger in the late nineteenth century, inasmuch as research in the United States was then in its infancy - and though he did later recognize that the universities must also support research - his fear ultimately proved to be justified. *Sornit, Albert and Joseph Tannenbaum: American Political Science, Atherton Press, 1964. Since the late 1940s the universities have demanded research and only research as the sole criterion for acceptability in the professorial career. This preference reminds one of G.K. Chesterton's remark, "My mother, drunk or sober." The mania for research has produced an invidious system of academic promotion, perversion of undergraduate education, and contempt for and flight from teaching. As Marshall McLuhan would say, the medium is truly the message, and the medium for university mathematics education is totally unsuited for the message. Or, as another professor put it at a recent meeting of the American Sociological Association, "Teaching represents the big vacuum in higher education." 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