The strange role of calculus in the United States
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ORIGINAL PAPER
The strange role of calculus in the United States David M. Bressoud1 Accepted: 26 August 2020 © FIZ Karlsruhe 2020
Abstract In the United States, the first course in single-variable calculus is considered tertiary level mathematics. Initially offered in high schools as a means for strong students to do college-level work, it is now taken by over 20% of high school students and perceived to be a prerequisite for admission into selective colleges and universities. This article describes the growth of this phenomenon and its effects on issues of educational equity. Because U.S. schools are funded locally, there is tremendous variation in the availability of calculus instruction in high school, with the most privileged students having the greatest access. This has profound effects on issues of equity because few universities are effectively addressing the vast disparities in student preparation. This article concludes with observations on what can and should be done to ameliorate the strange situation in the United States with regard to calculus. Keywords Mathematics education · Calculus · Advanced placement calculus · Equity · MAA Committee on the Undergraduate Program in Mathematics
1 Introduction In the United States, the first course in single-variable calculus is considered tertiary level mathematics. In the 1950s the College Board’s Advanced Placement program began offering this university course to increasing numbers of high school student with the intention of allowing mathematically strong students to do university level work while still in high school. Over the past several decades, calculus offered in high school has grown to the point where it is now perceived to be a prerequisite for admission into selective colleges and universities. Today it is taken by over 20% of high school students. At the same time, universities have not adapted to this growth, still teaching their first calculus course as if students had never before seen the material. To appreciate the issues surrounding calculus instruction in the United States, it is important to understand some of the idiosyncrasies of its public school system and its tertiary education. In the U.S., most public school funding is raised within the community in which the schools are located. Because of this, decisions on funding levels, curricula, and staffing are made locally. This means that there * David M. Bressoud [email protected] 1
Macalester College, Saint Paul, MN 55105, USA
is tremendous disparity across the country in what courses are offered and how teachers are prepared to teach these courses. This is especially true for calculus in high school. Because of the lack of uniformity in access to calculus in high school and widespread reluctance by universities1 to recognize calculus learned in high school, most college Calculus I classes in the United States contain students who are completely new to the terminology and concepts of calculus and students who have already demonstrated proficiency in all of the topics to be c
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