### Ferment in the *Monthly* About Collegiate Mathematics

During the five year period 1953-57 at the beginning of the Eisenhower administration and after the end of the Korean War, the *American Mathematical Monthly* manifested mathematicians' dissatisfaction with collegiate mathematics in these early pre-Sputnik years of the "Cold War." A string of reports, reviews, and arguments focused on the need for, in the words of William Duren, a "much-talked about revolution in the mathematics program." The papers linked below, listed chronologically, represent the ferment of this period:

- The Mathematical Training of Engineers. Ralph Hull.
*Amer. Mathematical Monthly*, 60:2 (Feb. 1953) 106-108. Report of presentations and discussion at a 1952 MAA symposium, the second in a series on the changing content of the undergraduate mathematics major.
- Some Observations on Undergraduate Mathematics in American Colleges and Universities. E.A. Cameron.
*Amer. Mathematical Monthly*, 60:3 (Mar. 1953) 151-155. Report of a year-long Ford Foundation-sponsored project in which Cameron visited and described mathematics departments in 33 colleges and universities of the "highest scholastic standing" across the United States.
- Teacher Education in Algebra. C.C. MacDuffee.
*Amer. Mathematical Monthly*, 60:6 (Jun. 1953) 367-375. Lectures from a 1952 Symposium on Teacher Education at the University of Wisconsin responding to entering students' "very spotty preparation in algebra ... even among those who enter the engineering college."
- Mathematics in School and College.
*Amer. Mathematical Monthly*, 60:6 (Jun. 1953) 380-383. Extract from *General Education in School and College*, Alan R. Blackmer, editor, Harvard University Press, 1952. Based on consultation with faculty in elite secondary schools and colleges and "framed with special reference to the better-than-average student," this study reports "a very high degree of consensus" that the standard high school mathematics curriculum (two years of algebra, one of plane geometry, and one of solid geometry and trigonometry) that has "the sanction of the ages" is ready for "drastic alteration and improvement." This study recommends reducing repetition in order to introduce calculus and statistics that will prove useful in college. "The case for statistics," it concludes, "is even more powerful than the case for calculus."
- Elementary and Secondary School Training in Mathematics. S.S. Cairns.
*Amer. Mathematical Monthly*, 60:8 (Oct. 1953) 523-527. Testimony to a 1952 Illinois "School Problems Commission" concerning "the national emergency and associated critical shortage of scientifically trained manpower."
- The NRC-AMS Conference on Training in Applied Mathematics. F. Joachim Weyl.
*Bulletin Amer. Math. Society*, 40:1 (Jan. 1954) 38-44. A summary report of a conference designed "to subject the possible patterns of training applied mathematicians to an intensive discussion ... by both producers and consumers of applied mathematicians."
- Mathematical Teaching in Universities. Andre Weil.
*Amer. Mathematical Monthly*, 61:1 (Jan. 1954) 34-36. Nine pithy precepts (with corollaries) for effective development of mathematical expertise.
- Of Course and Courses. Saunders Mac Lane.
*Amer. Mathematical Monthly*, 61:3 (Mar. 1954) 151-154. In this retiring MAA Presidential Address, Mac Lane urges the design of "modern and coherent curricula" that "exhibit the unity of mathematics" devoid of "traditional impedimenta."
- Freshman Mathematics as an Integral Part of Western Culture. Morris Kline.
*Amer. Mathematical Monthly*, 61:5 (May 1954) 295-306. An argument for "appreciation rather than skill" as the objective of mathematics courses offered to students who do "not intend to use mathematics in some profession or career."
- Mathematics in the Secondary Schools for the Exceptional Student. H.W. Brinkman.
*Amer. Mathematical Monthly*, 61:5 (May 1954) 319-323. Part of a multi-subject *School and College Study of Admission with Advanced Standing* undertaken with support from the Fund for the Advancement of Education. This study, a precursor to the Advanced Placement (AP) program, suggested a revision in the curriculum of grades 10-12 for accelerating students designed so that selective colleges would be willing to give credit for the 12th grade high school course. Their proposal would (a) expand the deductive part of 10th grade Euclidean geometry to apply to algebra and other areas of mathematics, (b) focus the 11th grade on analysis (algebra, analytic geometry, trigonometry), and (c) offer a "substantial introduction" to differential and integral calculus in the 12th grade.
- Special Topics in Applied Mathematics: Introduction and Critique. F. J. Weyl.
*Amer. Mathematical Monthly*, 61:7 Part 2 (Sep. 1954) 1-4. Introduction to a Slaught Memorial Paper containing proceedings of a symposium on "Special Topics in Applied Mathematics," including electric circuit design, signal and noise problems, hydrodynamics, singularities on shocks, and vibrations of a crystal lattice.
- Mathematics for Social Scientists. R.R. Bush, W.G. Madow, Howard Raiffa, R. M. Thrall.
*Amer. Mathematical Monthly*, 61:8 (Oct. 1954) 550-561. Report of a round–table discussion by the faculty of the 1953 Summer Institute of Mathematics for Social Scientists sponsored by the Social Science Research Council. The Institute introduced social scientists to sets, axiomatics, calculus, linear algebra, probability, stochastic processes, and models (e.g., game theory, linear programming). In this paper four members of the Institute faculty discuss the rationale and goals of this course and propose it as a desirable alternative "for most students" to the then-standard calculus-only course sequence in the first two years of college mathematics.
- The First Conference on Training Personnel for the Computing Machine Field. Franz Hohn.
*Amer. Mathematical Monthly*, 62:1 (Jan. 1955) 8-15. Report of a June 1954 conference enumerating personnel requirements of the newly emerging computer field together with desired features of educational programs that recruit and train students for this field.
- Joint Committee of the American Society for Engineering Education (ASEE) and the Mathematical Association of America (MAA) on Engineering Mathematics. R.S. Burington, Jr.
*Amer. Mathematical Monthly*, 62:5 (May 1955) 385-392. Report of a liaison committee between MAA's new CUP and ASEE's Mathematics Division chaired by R.S. Burrington, Jr. Recommendations focus on what mathematics should be taught to students of engineering, who should teach it, and how it should be taught.
- Mathematical Consultants, Computational Mathematics and Mathematical Engineering. J.W. Tukey.
*Amer. Mathematical Monthly*, 62:8 (Oct. 1955) 565-571. Observations about "attitudes" which mathematics departments might take towards the training of mathematics consultants for industry, the mathematics of computation, and the structure of educational programs in applied mathematics.
- The Teaching of Concrete Mathematics. J.W. Tukey.
*Amer. Mathematical Monthly*, 65:1 (Jan. 1958) 1-9. A companion to Tukey's 1955 essay, both being outgrowths of an October 1953 conference on training in applied mathematics (see F. J. Weyl's *Bulletin AMS* article cited above). In this commentary, Tukey reflects on a "syndrome never discussed in open meeting," namely, that while "'applied mathematics' is more difficult than 'pure mathematics' in requiring more maturity and more years of study, ... the students who study in 'applied' fields do not compare in strength with those who go into 'pure' mathematics."