Meeting the Challenge of High School Calculus, III: Foundations

*David M.
Bressoud, *May, 2010

AP and the College Mathematics CurriculumThe AP Program grew fast. By 1956, the original 18 participating high schools had grown to 110, with over four hundred the following year. The growth of the AP Mathematics program is shown in Graph 1. By 1967, over 10,000 students were taking the mathematics examination each year.

Graph 1: The growth of AP Calculus, 1955 to 1973. The first year for separate AB and BC exams was 1969.

There was one significant flaw in the design of AP Calculus: the program was designed to replicate and test only the full year of college single-variable calculus. Many talented students were capable of doing college-level work in calculus, but not at the pace required to complete the full year. In the mid-60’s, the AP Calculus Development Committee began to consider offering an alternate Calculus that would cover only a single semester of college calculus.

This came in the midst of a general appraisal of the undergraduate curriculum in mathematics. In the 1950s and early ‘60s, there was no standardized mathematics curriculum. The MAA’s Committee on the Undergraduate Program in Mathematics (CUPM) appointed a subcommittee, composed of many of the leading American mathematicians of the time [5], undertook to correct this. Beginning with recommendations on the mathematics that prospective engineers and students in the natural sciences would require, in the mid-1960s the CUPM produced A General Curriculum in Mathematics for Colleges [6]. This document appeared in 1965 and, for the first time, laid out a clear and coherent curriculum in mathematics. Many of those who were active on the CUPM, such as Al Tucker of Princeton, also led the development of the AP Calculus program. AP Calculus was seen as a vehicle for extending the college curriculum down into the high schools.

The centerpiece of the CUPM vision was calculus. This was the sequence for which the high school curriculum should prepare those students who were headed into mathematically demanding careers, and this was the sequence on which all advanced mathematics would build. Very much in the spirit of Brinkmann’s original vision, they saw calculus as the course that should be the first course of college mathematics, and they described the two-semester calculus sequence as Mathematics 1 and Mathematics 2. Recognizing that not all students going into the sciences, engineering, or mathematics would enter ready to start with calculus, they also described a one-semester precalculus course, Mathematics 0. But they were adamant that none of these students should spend more than one semester preparing for calculus, and that they considered Mathematics 0 properly to belong in the high school curriculum. In their words:

“Although we recognize that the majority of colleges must now teach the material in Mathematics 0 to some of their students, this subject should be completed in high school and will be to an ever increasing extent. Hence, we suggest that this course be eliminated by admission requirements wherever possible, and, in any case, held to one semester when taught in a college where the high school prerequisites to Mathematics 0 can be met.” [6, p. 9]

The CUPM report also addressed the importance of offering Advanced Placement calculus for a single semester:

“Comparatively few of these high school students with calculus can qualify for a whole year’s advanced placement, so that advanced placement recognition of these able and ambitious students and their teachers will be slow in traditional college programs. We may assume that high schools which teach calculus will teach a year course and an appreciable proportion of the graduates will quality for two semester’s advanced placement in college, but several times as many will quality for one semester’s advanced placement. Thus it will promote the early study of calculus if colleges will offer advanced placement in one-semester as well as two-semester units.” [6, p.20]

In 1969, the AP program launched its Calculus AB program, specifically designed to instruct students in and test a single semester’s worth of calculus.

NEXT: Mathematics 0,1,2 becomes Calculus A,B,C

[5] The subcommittee that prepared this report was chaired by W. L. Duren, Jr. (University of Virginia) and included E. G. Begle (Stanford), A. A. Blank (NYU), Ralph P. Boas (Northwestern), Leslie A. Dwight (Southeastern State College), Marion K. Fort (U. of Georgia), Samuel Goldberg (Oberlin), Edwin E. Moise (Harvard), Henry O. Pollak (Bell Labs), G. Baley Price (U. of Kansas), A. W. Tucker (Princeton), R. J. Walker (Cornell), and Gail S. Young, Jr. (Tulane), with assistance from Louis Auslander, R. Creighton Buck, George Carrier, Charles DePrima, Bernard Friedman, Leonard Gillman, Frederick Mosteller, Barrett O’Neill, A. H. Taub, and A. B. Wilcox.

[6] CUPM, A General Curriculum in Mathematics for Colleges: a report to the Mathematical Association of America, Berkeley, CA, 1965.

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David Bressoud is DeWitt Wallace Professor of Mathematics at Macalester College in St. Paul, Minnesota, and President of the MAA. You can reach him at bressoud@macalester.edu. This column does not reflect an official position of the MAA.

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