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 [1], 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:
Over the next several months, I intend to elaborate on the themes raised in this brief piece specifically addressing:
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.
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?
Purchase a hard copy of the CUPM Curriculum Guide 2004 or the Curriculum Foundations Project: Voices of the Partner Disciplines.
Find links to course-specific software resources in the CUPM Illustrative Resources.
Find other Launchings columns.