Meeting the Challenge of High School Calculus, III: Foundations

*David M.
Bressoud, *May, 2010

Contents of this article:

Beginnings

AP and the College Mathematics Curriculum

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

Succeeding Decades

Growing ConcernsJaime Escalante died Tuesday, March 30, 2010 at his son’s home in Roseville, California. This great teacher and the record of his experience with AP Calculus that was immortalized in the 1988 film Stand and Deliver have been among the factors driving the increase of AP Calculus. The lesson that we should carry away from his story is that, with appropriate instructional support, all students can be successful in seriously advancing their abilities in mathematics. Furthermore, all students deserve access to an education that stretches their mathematical knowledge. Unfortunately, the received lesson too often has focused on the fact that this was a calculus class and concluded either that completion of calculus in high school guarantees preparation for college-level mathematics, or, even worse, that failure to take calculus in high school closes off the prospect of a technical or scientific career.

This month’s column looks at the first decades of the AP Calculus program, from its origins in the 1952 College Admission with Advanced Standing program until 1990, a convenient stopping point before delving into the many changes of the past two decades and, coincidentally, the year in which I began my association with the AP Calculus program. There were two big events that occurred during this period that have shaped this program: the first was the initial decision that the Advanced Standing course in mathematics should be calculus, the second was the decision in late 1960s to split the AP Calculus program into the AB and BC programs. Jaime Escalante’s story is a piece of the growing acceptance and expansion of the AP Calculus program over the two decades 1970–90.

BeginningsIt began at Kenyon College. In 1951, a group of faculty raised the question of how one might encourage teachers and students at strong secondary schools “to pursue a liberal arts education at a pace appropriate to their ability and their teachers' interests and skills.” [1] Their president, Gordon K. Chalmers, believing that this was an effort worthy of pursuit, convinced the presidents of eleven other colleges [2] to join in an exploratory study of College Admission with Advanced Standing (CAAS). Eleven subject committees, including mathematics, were established, and the entire enterprise was underwritten by the Ford Foundation’s newly established Fund for the Advancement of Education.

Heinrich Brinkmann of Swarthmore College chaired the original committee for mathematics [3]. The first question was what constituted college work in mathematics. In 1952, calculus was still commonly taught as a sophomore course, preceded by a year of what today we would call precalculus, including analytic geometry. The CAAS gave the high schools a great deal of flexibility in deciding what their college-level course should cover, describing three options then commonly found in the represented colleges:

- A year-long course covering college algebra, trigonometry, analytic geometry, and calculus,
- The “Griffin text”:
An Introduction to Mathematical Analysisby Frank Loxley Griffin, which provides an integrated approach to college algebra, trigonometry, analytic geometry, and calculus, or- Calculus, with some analytic geometry.
It is not clear at what point the program narrowed its focus to just calculus (with analytic geometry), but this was the case by 1956 when the College Board took over the examinations.

By the spring of 1953, CAAS had lined up seven high schools that were willing to run an experimental program beginning in the fall of 1953. By that fall, the group of high schools had expanded to eighteen. Students in the accelerated mathematics program would receive an intensive year of algebra, trigonometry, and analytic geometry, followed by a year of college calculus. At the same time, the Educational Testing Service (ETS) was contracted to administer the examinations.

The first mathematics examination was pilot-tested in the spring of 1954 on freshmen at the twelve colleges and 120 high school students in the eighteen participating schools. The following fall, the College Board, then the College Entrance Examination Board, agreed to provide a permanent home for this program, rechristening it the Advanced Placement program and retaining ETS as the organization that would administer the examinations. The CAAS exams were given in ten subjects in the spring of 1955. The mathematics exam was taken by 285 students. The first exams administered under the auspices of the College Board and officially labeled as Advanced Placement were in 1956.

The early reports of the CAAS [4] make it clear that, despite its name, the purpose of this program was neither to accelerate students nor to shorten the time spent in college, though these were recognized as possible outcomes. The intention always was to provide enriching learning experiences, to ensure that our ablest students are given challenging material that develops the quality of their understanding, rather than the quantity of what they have learned.

NEXT: AP and the College Mathematics Curriculum

[1] William H. Cornog, Initiating an Educational Program for the Able Students in the Secondary School, The School Review, Vol. 65, No. 1 (Spring, 1957), pp. 49-59, http://www.jstor.org/stable/1083613

[2] The other colleges participating in the CAAS were Bowdoin, Brown, Carleton, Haverford, MIT, Middlebury, Oberlin, Swarthmore, Wabash, Wesleyan, and Williams.

[3] The members of the mathematics committee were Julias Hlavaty (Bronx High School of Science), Elsie Parker Jonson (Oak Park and River Forest High School, Illinois), Charles Mergendahl (Newton High School, MA), George Thomas (MIT), Volney Wells (Williams College), and Heinrich Brinkmann (Swarthmore College).

[4] College Admission with Advanced Standing: Final report and summary of the June 1955 evaluating conferences of the school and college study, March 1956.

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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.