Meeting the Challenge of High School Calculus, IV: Recent
History

*David M.
Bressoud, *June, 2010

The Growth of the ProgramGraph 1 shows the growth in the number of AP Calculus tests over the past two decades: from 74,000 in 1989 to 304,000 in 2009.

Graph 1: Growth in AP Calculus and AP Statistics, 1989–2009. Data from AP Data [3] and Larry Riddle (private communication).

This is driven in part by student desire to earn college credit or to have the stamp of approval that AP Calculus confers on one’s transcript when applying to college. But it is driven much more by the educational establishment itself. When states pay bounties to schools for each 3 or higher on an AP exam, schools pay attention and funnel students toward AP programs. When states prescribe that Algebra I in 8th grade is the norm for all students, then those who stay on pace are set to take calculus in grade 12. As I’ve talked with students around the country, the dominant reason for enrolling in AP Calculus is that that was what their peers were doing and what they saw as expected of them.

Because AP Calculus in grade 12 has become the norm for students in the top quartile, students who are mathematically talented or really driven expect that they should take calculus before grade 12. The next graph shows what has happened to the number of students taking an AP Calculus exam before grade 12 just since 2002. What is particularly disheartening about this growth is that, as an MAA survey of several years ago showed, a large number of these students then take no mathematics in their senior year.

Graph 2: Growth in AP Calculus before grade 12. Data from AP Date [3].

In 2007, the MAA used its contacts with high school teachers via the American Mathematics Competitions to determine what happens to students who take calculus before their senior year. We discovered that of the 1880 high schools that responded and that had students who took calculus before their senior year, only just over half, 55%, reported that more than 90% of these students took a mathematics course in the senior year. Slightly over a quarter of the high schools reported that less than half of these students studied mathematics in their senior year. By far, the two most commonly cited reasons for the lack of mathematics in the senior year were “They prefer to take AP courses in other subjects” and “Their intended college major doesn’t require any mathematics beyond first-year calculus.” A lack of courses to take came a distant third. [4]

We cannot and should not require these students to continue the study of mathematics through courses that build on the first semester of calculus, but there are other options for the senior year including statistics, discrete mathematics, or transformational geometry. It is disheartening to see so many talented students view the AP Program as a means of getting their college-level mathematics done and out of the way before they get to college.

## Conclusion

Over the past two decades, as the math wars have raged over how to teach mathematics in grades K-12, the one eternal truth that almost everyone has held is that more mathematics for everyone is good. Too often, this has translated into an acceleration of mathematical topics into ever earlier grades. The result is that calculus in high school, born as an endeavor to ensure that gifted students have an opportunity to work with challenging mathematics, has turned into an expectation, or at least a desideratum, for most of those who are college-bound.

This is an audacious transformation. Unfortunately, it has not been matched with the resources needed to pull it off. It has resulted in large numbers of talented students for whom the mathematical trajectory is arrested at the transition from high school to college.

[3] AP Data, at

APCentral, http://professionals.collegeboard.com/data-reports-research/ap[4] The survey can be found on page 10 of the

AMC 10-A/AMC 12-A Teachers’ Manual, February 6, 2007. The collected data are unpublished.[5] Addition information from a series of articles by Dan Kennedy that appear in AP Central

Calculus & The Reform Movement http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/2108.html

AP Calculus: Back to the Beginning. http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/2107.html

AP Calculus: Evolution of a Computer Policy. http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/2110.html

AP Calculus: Innovations. http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/2106.html

Access pdf files of theCUPM Curriculum Guide 2004and theCurriculum Foundations Project: Voices of the Partner Disciplines.Purchase a hard copy of the

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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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