The strange role of calculus in the United States

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.

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Fig. 1

Source: Bressoud, 2017

Fig. 2

Source: Bressoud, 2017

Fig. 3

Source: Bressoud, 2017

Fig. 4

Source: research.collegeboard.org/programs/ap/data and personal communication from AP Calculus Chief Reader

Fig. 5

Source: Sadler and Sonnert, 2018, page 312

Fig. 6

Source: Sadler and Sonnert 2018, page 319

Fig. 7

Source: College Board, 1999

Fig. 8

Source: College Board, 2019a

Notes

  1. 1.

    This article uses the terms “college” and “university” interchangeably. Universities have graduate programs; college do not. But the United States has an extensive system of colleges, many of which are as selective as the very selective universities. While universities tend to teach Calculus in larger classes, there is very little difference between colleges and universities in the syllabus or the expectations for this course.

  2. 2.

    Most universities offer a separate calculus sequence for business majors that focuses on basic concepts applied primarily to polynomial functions. While many biology majors take mainstream calculus, their calculus experience is highly varied across institutions. It ranges from no calculus required for the major through courses that are more like business calculus to what is effectively mainstream calculus with an emphasis on biological examples. The calculus described in this article is only mainstream calculus.

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Correspondence to David M. Bressoud.

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Bressoud, D.M. The strange role of calculus in the United States. ZDM Mathematics Education 53, 521–533 (2021). https://doi.org/10.1007/s11858-020-01188-0

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Keywords

  • Mathematics education
  • Calculus
  • Advanced placement calculus
  • Equity
  • MAA Committee on the Undergraduate Program in Mathematics