David M. Bressoud, March, 2010
The phenomenal growth of the Advanced Placement® program is often seen as one of the great success stories of American high school education. It brings challenging, college-level courses into the high schools and enables students to demonstrate that they are ready for college-level work. Success on the AP exams is one of the most effective predictors of success in college. AP Calculus, one of the oldest and most prestigious of the AP courses, is often seen as a standard-bearer for the program. Yet, as I wrote in the Chronicle of Higher Education in January , AP Calculus can also be as much a stumbling block as a steppingstone to a career in mathematics, science, or engineering.
If AP Calculus was accomplishing the purpose for which it was intended—enabling talented high school students to place into a more advanced course based on evidence that they have successfully completed college-level work in high school—then one would expect the phenomenal growth in the AP Calculus program to be accompanied by increased enrollments in Calculus II during the fall term. In fact, from 1990 until 2005 while the number of students taking the AP Calculus exam increased from 75,000 to 250,000, the fall enrollment in Calculus II actually decreased, from 110,000 to 106,000.
This should be an issue of concern to the entire mathematical community because it is part of a pattern of stagnation over the past quarter century in the number of students pursuing college mathematics at the level of calculus and above. Despite increasing demands for a mathematically sophisticated workforce in engineering, finance, and the information, biological, and physical sciences, and despite greater numbers of students taking more and higher-level mathematics in high school, the flow of students through the requisite college-level mathematics has not increased.
This past spring, 305,000 students took the AP Calculus exam. They represent about half of the students who studied some form of calculus while in high school. Most of the students who are candidates for careers in mathematics, science, or engineering now see calculus for the first time in high school. There is anecdotal evidence that the push to get students into calculus while still in high school is, for many of them, short-changing the preparation needed to succeed in subsequent mathematics courses. There is also anecdotal evidence that, except for the best students or those who have experienced the best teachers, a high school calculus course articulates poorly with the expectations of calculus as taught in college.
One response has been to increase the rigidity of the gatekeeper role of placement exams. If this means redirecting more of these students back into college algebra or pre-calculus courses, then I believe that this is counter-productive. It discourages bright students with the potential to succeed in advanced mathematics from even attempting it.
I believe that the proper response has three components:
- Get more and better information about students who study calculus in high school. How many of them are deemed unready for calculus when they get to college? How many retake Calculus I, and how successful are they? What are the factors that affect their decisions? How important is it to future mathematical success to study calculus while in high school? If we want to improve decisions about whether to study calculus while in high school, then we need to have good evidence of its benefits and dangers.
- Establish and enforce guidelines for high-school programs offering calculus. There is nothing inherently wrong with the growth of AP or other high school calculus. In fact, now that these programs have become the norm, students at schools that do not offer calculus are disadvantaged. There is not even anything wrong with a course that does a little calculus as long as this is in the context of solid preparation for college-level mathematics. But however calculus is offered in high school, it must be designed to facilitate success in college mathematics for all students who take it, rather than creating obstacles for all but the very best.
- Re-examine first-year college mathematics. Colleges and universities must ensure that there is an appropriate next course for every student who has studied calculus in high school, whether or not that student is ready for a first college-level course in calculus. We cannot afford simply to ignore what these students have done and know. There must be courses for these students that acknowledge and build on what they have learned while preparing them for further mathematics.
Over the next several months, I intend to elaborate on the themes raised in this brief piece specifically addressing:
- The loss of students from mathematics at the level of calculus and above and the evidence that the growth of the AP Calculus program has played a role in this decline.
- The historical development of the AP Calculus program and the reasons why, for most students, high school calculus does not articulate well with college calculus.
- The information that we have and the information that we need.
While much is known about the effectiveness of AP Calculus for those students who have earned and chose to use college credit (see AP Calculus: What We Know, Launchings, June 2009), the effect on most students of studying calculus in high school is generally unknown. This article will summarize what we know, what is currently being investigated, and what we need to begin studying.
- The need for guidelines.
What does it mean to be ready for calculus in high school? What standards should there be for the structure of such a class and for those who teach it?
- What our colleges and universities need to do in response to these changes in the preparation of our incoming students.
 David M. Bressoud. The Rocky Transition from High-School Calculus. The Chronicle of Higher Education. January 17, 2010. http://chronicle.com/article/High-School-Calculus-The-E/63533/
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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 firstname.lastname@example.org. This column does not reflect an official position of the MAA.