And yearly expenditures for scientific research and development more than doubled during the thirties. This is not to say that the educated man enjoys a generalized invulnerability to economic setbacks. Men of high ability and advanced training will probably suffer less from hard times than any other sector of society. It would be foolish to say that they will not suffer at all. As a matter of fact-although we all know of many exceptions-the data at hand indicate that on the average the college man outstrips the noncollege man in every measure of worldly success. Taking good times and bad, he is more apt to be employed, gets better jobs, earns more money, and gets more promotions. THE CENTRAL ROLE OF THE COLLEGES AND UNIVERSITIES American higher education has profited immensely by the affection of the American people, but it also has experienced considerable stress as a result of that affection. The more the American people have loved the colleges and universities, the more they have demanded of them. And they have not hesitated to heap herculean tasks upon higher education. On the whole, over the exciting decades of growth, our colleges and universities have found the strength and leadership to accomplish the vital social tasks pressed upon them. It is fortunate that they have, because they are now facing a challenge greater than any they have known. Indeed the tasks ahead are so staggering that sensible people will inevitably ask whether the nation can afford the enormous expense implicit in the growth of its educational system. Our educational institutions are already groaning under financial burdens which they feel incapable of bearing. And now they are faced with the requirement that they double or treble in size. Can the nation afford it? The simplest answer is to ask oneself what percent of the gross national product has been expended upon our educational system, and whether this has increased rapidly in recent years. The astonishing truth is that it has not increased at all and that it is very modest. Indeed, the one anomalous and disconcerting feature of this entire picture of vast growth and vitality in education is that the American citizenry has not faced up to paying the bill. While our educational institutions are suffering from underfinancing and paying their teachers distressingly low salaries, our total expenditures for higher education stand at eight-tenths of 1 percent of our gross national product. Although the past five years have been years of nationwide attention to the financing of our colleges and universities, this percentage is today at the lowest point it has been since 1951. We are spending about one and one-half times as much on tobacco products each year as we spend on higher education; and about two and three-quarters as much on alcoholic beverages. But the problem of financing, grave though it may seem at the moment, is not the only problem facing the colleges and universities as they gird themselves for the years ahead. In the excitement of pyramiding new tasks on the colleges and universities, the American people will do well to remember some old tasks. Most of all, they will do well to remember that the first concern of higher education is the intellectual development of the individual student-not because there is a shortage to be met, not because there is a job to be filled, but simply because we value the realization of individual potentialities. They will do well to remember, too, that excellence is a time-honored preoccupation of the colleges and universities. If the colleges and universities are now wholly committed to the task of educating our national leadership, then they have no choice but to do it with distinction. We shall be tempted, under the pressure of the huge enrollments ahead, to let up on standards. Posterity will not forgive us for that. Nor will the judgments which the world makes of America's capacity to exercise leadership be tempered because we were too busy to produce truly great scientists and truly wise statesmen. Another consideration which should be much in the minds of all who are seriously concerned with the future of higher education is the importance of turning out liberally educated men and women. As we have emphasized, individuals of high ability and advanced training are going to perform all of the highly specialized and highly technical roles in the society, all of the scholarly, scientific, and professional roles; in short, they are going to manage the society. Whether as top business executives, government administrators, professional men, teachers, technological experts, or scientists, they are going to have the guiding role in shaping our future. This means that our colleges and universities must produce not only specialists, but men with wisdom and breadth and a sense of values commensurate with their destined roles of leadership. Intelligence un tempered by wisdom, competence unguided by a sense of values-these could be our downfall as surely as ignorance and incompetence. In short, we must turn out men whose technical skills are matched by their breadth of comprehension, by their grasp of their own heritage, by largeness and liberality of mind. In the years ahead the able youngster is going to receive very special attention. He is going to have lavish facilities placed at his disposal for the development of whatever gifts he may have. Such treatment entails deep obligations. If we do not give our able youngsters a profound sense of this obligation, if we do not give them an abiding sense of responsibility to the society which has dealt with them so generously, we shall have done an injustice both to them and to the nation. It cannot be said too often that more college degrees may not necessarily bring any increment in virtue or wisdom. Whether we shall have a steady flow into our leadership ranks of wise, liberally educated men and women with the creativity and the sense of values which the future demands, or whether we shall have a paralyzing flow of skilled opportunists, timeservers, and educated fools, depends wholly upon the sense of values which guides our efforts. MATHEMATICS TEACHING* [Reprinted from School Science and Mathematics, January 1958] PROMISING PRACTICES IN MATHEMATICS TEACHER EDUCATION A Report from the Midwest Regional State College Conference on Science and Mathematics Teacher Education Compiled by John A. Brown, professor of mathematics, State University Teachers College, Oneonta, New York INTRODUCTION This report of the mathematics sections consists of comments and quotations selected by the one responsible for compiling the report from the papers presented at the Conference. The excerpts are chosen as representative statements of the theme of the paper. It is regrettable that the papers cannot be reproduced here in their entirety. There will be three parts to the report; namely, Trends in Secondary School Mathematics, Teacher Education in Mathematics, and Reports of the recorders of the two discussion groups. TRENDS IN SECONDARY SCHOOL MATHEMATICS Maurice L. Hartung, University of Chicago The point of view represented by Hartung recognizes a need for a movement toward courses that emphasize modern mathematics. These courses are organized around fundamental concepts: set, sentences, relation, function, etc. In these courses, modern logic plays a dominant role; the interest is in the structure of deductive systems. A century ago Weierstrass in Germany and others began what may be described as the arithmetization of analysis. This was an intensive effort to make analysis rigorous through a fundamental clarification of the basic concepts. About the same time, George Boole in England, and later Whitehead and Russell, and others began to work on fundamental logical concepts in an analogous movement, and this has led to modern logic and the extensive use of symbolic methods in logic. The problem posed for the curriculum now is how these modern points of view and the modern exploitation of the basic concepts may be introduced into the secondary schools. In present accelerated courses, the curriculum has not changed radically. These changes include less solid geometry of the classical Euclidean type, less time on trigonometric solutions of general triangles using logarithms, more analytic geometry and calculus. The lines between geometry, trigonometry, algebra, etc., are breaking down, and emphasis is shifting, but the content is of a type which we all recognize as similar to what we studied in the early years of college. It was pointed out that "older mathematics had roots in the soil of empirical method" and that modern mathematics has moved far away in the direction of abstraction, and study of itself. Has it moved too far? Scientists should be interested in this issue. In curriculum terms, the problem takes the following form: Does the second type of program (the modern, abstract approach) meet the needs of future engineers and scientists? It does, if they go far enough up in these fields, but what about the practitioners? Also, the engineering courses, and books, and instructors, are to a large extent built on the traditional content. Hartung suggests that: Curve fitting, elementary statistics, experimental design, and dozens of other ideas are outside the scope of the traditional program, but must be (and to a limited extent, now are) brought in. It is, I think, worthy of note that the "modern mathematics" approach promises a rich payoff *Information assembled by the committee staff related to matters under discussion in the hearings on Science and Education for National Defense. |