AP Examined

David M. Bressoud, December 2010

Phil Sadler and three of his colleagues have recently published a collection of essays on the Advanced Placement Program that place my discussion of AP Calculus in a larger context. It is titled AP: A Critical Examination of the Advanced Placement Program [1]. Many of the essays focus on the Advanced Placement courses in Biology, Chemistry, and Physics, but there is some information on the relationship of these courses to AP Calculus, and a good deal of general information on the Advanced Placement program.

One of the most informative articles is the first, Tim Lacy’s account of the history of the AP program. It greatly expands on my column, Meeting the Challenge of High School Calculus, III: Foundations, and shows that while the Kenyon project was the direct precursor of AP, there were several significant projects before the early 1950s that fed into the creation of the AP program.

I was intrigued to learn that the AP program continued to lose money through the 1960s and that the early 1970s were a time when its growth halted across the board. This is evident in the AP Calculus numbers, which were generally stagnant from 1969 to 1973 and saw their only decline at the end of this period, dropping from 15,186 in 1972 to 14,310 in 1973. Lacy references Rothschild [2] who postulates that this was the result of a late ‘60s, early ‘70s educational backlash against elitism.

Lacy also documents the movement toward greater access to Advanced Placement that began in the 1970s and continues to drive the remarkable growth of this program today. He repeatedly raises the troubling question of the motives behind this growth. Knowing many of the players within the College Board, I know that the motives are mixed. There is an honest desire to make this program available to and beneficial for all students, regardless of race, ethnicity, or economic status, but there is also an acute awareness of the effect of this growth on the bottom line and a lot of pressure to ensure that it continues.

Maureen Ewing, Kristen Huff, and Pamela Kaliski, who all work for the College Board, provide a useful overview of how ETS and the College Board ensure the reliability and validity of the examinations. Reliability deals with the consistency of the examinations across years and different forms of the exam as well as internally between the multiple choice and free response questions. Having been involved in both the construction of these exams and the post-administration analysis, I know how seriously reliability is measured and treated.

Validity refers to the usefulness of the exam as a measure of what the student knows and is prepared to do. As I’ve explained in earlier columns (see, especially, AP Calculus: What We Know), all of the studies that have been conducted show that students who earn a 3 or higher on the AP Calculus exam are at least as well prepared for Calculus II as students who have passed a mainstream university Calculus I course with a C or higher. On a regular basis, the College Board surveys the mathematics departments that receive the bulk of the AP Calculus scores to ensure that the AP syllabus is covering all of the topics that are important for almost all mainstream Calculus I courses.

I believe that the AP Calculus program is doing a pretty good job of what it was designed to do: certify those students who have learned enough calculus that they are ready to go onto the next course. But the AP program is being sold as much more than that, as a way of improving our schools by bringing college-level expectations into the high schools. The big, unanswered question that the College Board has never studied—or if they have, they have never released the data—is whether the AP program in itself is of benefit to students. They have released lots of data showing that students who have been through an AP course do much better in college than those who have not. But these data are worthless if there are no controls for the factors that lead students to take an AP course.

The three articles of Part III report what we do know about the benefit of AP science and mathematics, controlling for other variables. The first article in this section, by Robert Tai et al, draws on the NELS:88 data [3], an extensive longitudinal study of course taking patterns of the high school class of 1992. It shows that even after controlling for socio-economic status, parental education, and academic achievement (measured by SAT or ACT scores), students who take the AP Calculus exam, irrespective of their score, are four times as likely to major in a physical science as those who did not take the exam. This is interesting but not surprising, and it gives no hint of the direction, if any, of a causal relationship.

The second article of Part III, by Sadler and Sonnert, reports some of the findings of their study Factors Influencing College Success in Science. They investigated the effects of AP courses in Biology, Chemistry, Physics and Calculus on subsequent success in the first college course in Biology, Chemistry, or Physics. Sadler and Sonnert controlled for socio-economic status, race, gender, parental education, type of high school (public or private), high school English grade, SAT/ACT scores, and year in which they took the first college course in that science subject. For Biology and Physics, simply taking an AP course in the subject conferred no statistically significant advantage when they studied that subject in college. It did help prepare students for college chemistry. Across all three sciences, earning a 3 or higher on the AP Calculus course was correlated with a substantially better grade (6 to 8 points on a 100 point scale) in the corresponding college course. Intriguingly, simply taking AP Calculus did result in a small (about 3 points) but statistically significant increase in the college grade for all three subjects, even with all other variables controlled. Performance in high school English was also a small but statistically significant factor (2 points).

Duffy’s article, the third in Part III, looks at persistence and performance among students at the University of Tennessee at Martin, comparing students with AP credit, students with dual enrollment credit, and students who entered with no college credit. These students were measured on persistence to a second year, graduation within five years, first year GPA, and final GPA. Not surprisingly, the first two groups did considerably better on all measures. But once the author controlled for sex, race, parental education, ACT score, and high school GPA, there were no statistically significant differences among the three groups in these four measures.

Part IV addresses policy issues: Does it make sense for states, districts, and individual schools to push for the expansion of AP programs? Does it make any kind of economic sense by reducing time to degree? Is it an effective means of closing the achievement gap?
Kristin Klopfenstein demonstrates that any reductions in time to degree that might come about because of Advanced Placement credits are insignificant.

William Lichten describes the failure of a concerted effort to expand the availability of AP courses in Philadelphia public schools. For those schools whose average SAT-V score is under 400, most had passing rates below 5%. The highest passing rate among these schools was only 33%. Lichten acknowledges that there is potential talent in these schools, but one cannot expect success if these students and their teachers have not been adequately prepared for the challenges of college-level work.
Klopfenstein and Thomas as well as Dougherty and Mellor survey what is known about the effectiveness of AP programs as a means of closing the achievement gap. Dougherty and Mellow summarize the existing research in four points:

  1. There is no evidence that taking an AP course improves college performance unless the student takes and passes the AP exam.
  2. Students from racial, ethnic and economic groups that are underrepresented among college graduates also have low rates of passing AP exams.
  3. In the absence of an AP exam, the high school grade for the AP class does not necessarily reflect the level of mastery that has been achieved.
  4. Eighth grade test scores are a strong predictor of the ability to subsequently pass an AP exam.

In other words, dropping AP courses into a high school will not turn around students whose PreK-8 education has not adequately prepared them.

There currently is a lot of money from both the Gates Foundation and ExxonMobil that is directed toward putting good AP programs into disadvantaged high schools. I see nothing wrong with this as part of a larger effort to turn around inner city and rural schools. But if it is not part of a general overhaul of the entire preK-12 system, then it does little if any good.

[1] AP: A Critical Examination of the Advanced Placement Program, edited by Philip M. Sadler, Gerhard Sonnert, Robert H. Tai, and Kristin Klopfenstein, Harvard University Press. 2010.

[2] E. Rothschild. Four decades of the Advanced Placement Program. The History Teacher, 32(2), 175–176.

[3] US Department of Education. 2008. National Education Longitudinal Study of 1988 (NELS:88).

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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.