The National Science Foundation and the U.S. Department of Education commissioned this study following the publication of a disappointing assessment of the performance of U.S. students in advanced mathematics and physics, which was part of the Third International Mathematics and Science Study (National Center for Education Statistics [NCES], 1998). This international comparison appeared to show that U.S. students of advanced mathematics and physics lagged behind their counterparts in other countries. However, a more recent study indicates that this pessimistic assessment may have been unwarranted because the original sampling included many students that should not have been classified as being in “advanced” courses. Indeed, a second administration of the test to U.S. students enrolled in AP calculus and AP physics showed that, in this sample, the AP calculus students performed better than those in all other countries, and the performance of the AP physics students was substantially above the mean of the other countries (Gonzalez, O’Connor, and Miles, 2001). One important lesson from these comparisons is that the percentage of U.S. students taking bona fide advanced courses is too small compared with other countries.

Although international comparisons served as a catalyst for this study, the need to undertake the study was clear for other reasons as well. Perhaps most important, a greatly improved understanding of the conditions for successful teaching and learning has emerged in recent years. These advances have been summarized in several NRC reports, including How People Learn: Brain, Mind, Experience, and School (Expanded Edition) (NRC, 2000b). The present analysis demonstrates that programs for advanced study are frequently inconsistent with the findings of this body of research on cognition and learning. We show how program developers can remedy this situation by considering all the components of educational programs when developing their courses: curriculum, instructional methods, ongoing (curriculum-embedded) and end-of-course (summative) assessments, and opportunities for teacher preparation and professional development.

Another factor contributing to the urgency of this study is the rapid growth of the AP and IB programs. In 2000, there were 433,430 AP exams taken in math and science, compared with only 164,333 in 1990 (College Entrance Examination Board [CEEB], 2000c),1 and the number is expected to continue to grow rapidly in the future. The IB program had about 19,000 degree candidates in 2000, and roughly 13,000 IB exams were taken in the


The College Board, which oversees the AP program, does not keep track of who or how many students enroll in AP courses, but estimates that about 30–40 percent of students enrolled in a course do not take the exam. If that holds true for all courses, then 433,000 AP exams in science and mathematics translate to about 580,000 enrollments.

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