Meeting the Challenge of High School Calculus, V: Overcoming Ignorance

David M. Bressoud, July, 2010

In my column of June 2009 [1], I looked at what we do know about those who study calculus while in high school. I will not repeat that information here, but I will summarize what is known:

  1. We have a pretty good idea of how many students study calculus of some form in high school each year, about 600,000, roughly twice the number who take the AP Calculus exam. This constitutes 20% of all high school graduates.
  2. We have much less precise knowledge of what happens to them. We know the number of students who earn 3, 4, or 5 on the AP exam, just over 200,000 in 2009, but not how many of each category are entitled to use their credit, nor how many of these actually do use it. We do not know what happens to those who do not earn or use credit for calculus taken in high school. Very little is known about what happens to students who have gone through a dual enrollment program in calculus.
  3. Of the students who earn and choose to use college credit in calculus in order to place into a more advanced course, we do know that they generally do well, though even the most recent of the published studies now relies on data that are over ten years old. Recent studies undertaken at the University of California, San Diego and the University of Illinois at Urbana-Champaign [2] suggest that a 3 on the AB exam is problematic for advanced placement, but that students with a 4 or higher on the AB exam or a 3 or higher on the BC exam are at least as well prepared for mainstream Calculus II as the students who have taken Calculus I at that university.

Two studies that are currently underway should help us understand the effects of the movement of calculus into the high schools. Both studies are sponsored by the REESE program of the NSF Division of Research on Learning in Formal and Informal Settings.

  1. The Factors Influencing College Success in Mathematics (FICS-Math) study out of Harvard will identify factors in the high school preparation, including the taking of calculus while in high school, that influence success in Calculus I. This study should also help to identify the relative benefits of AP Calculus and other forms of calculus instruction.This study is currently analyzing data collected in fall, 2009.
  2. The MAA’s study of Characteristics of Successful Programs in College Calculus will provide national data on the number of students enrolled in Calculus I who have passed through each of the different types of high school calculus, as well as further information on the effect of each type of program on success in Calculus I. This study will be collecting its data via a national survey to be conducted in fall, 2010.

But that still leaves many unanswered questions. In particular:

[1] D. M. Bressoud, AP Calculus: What We Know, Launchings, MAA Online, June, 2009.

[2] Private communications from Alison Ahlgren at UIUC and Bruce Arnold at UCSD.

[3] National Center for Education Statistics, National Education Longitudinal Study of 1988,

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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

This column does not reflect an official position of the MAA.