This report details the panel’s findings about the programs based on its analysis of these materials, its advice to the committee regarding the major issues under its charge, and the types of evidence that are needed to enable more complete appraisal of the AP and IB mathematics programs—evidence that is urgently needed.

Before proceeding to report its findings and recommendations, the panel wishes to commend the College Board and the IBO for the ways in which they have responded to changes in the teaching of mathematics: AP by changing its syllabus and introducing technology; IB by introducing portfolio projects and technology. Both organizations have undertaken these changes in a balanced, reasoned way, with input from a wide range of communities. Considering that they are large organizations affecting thousands of students, teachers, universities, and colleges, both AP and IB have made significant and forward-looking changes remarkably successfully. The panel additionally commends the College Board for helping to bring together college faculty and high school teachers in collaborative efforts to improve the teaching of calculus across the secondary and postsecondary levels. These efforts have paid off in more coherent syllabi that are better aligned with what is known about the ways in which students learn mathematics.

While the IBO’s collaborations with IB teachers are an important aspect of the development of IB programs and assessments, collaborations outside of the IBO network, for example, with professional disciplinary societies or colleges and universities, are not currently part of the approach taken to program development. As the IB program becomes more prominent in the United States, the panel encourages the IBO to expand its collaboration efforts to include more members of the U.S. mathematics community. These types of collaborative efforts can increase public awareness of the program and its relationship to the calculus typically taught in U.S. high schools, colleges, and universities.

The remainder of this report is organized into five chapters. Chapter 2 provides an overview of the AP and IB programs in mathematics. Chapters 3 and 4 present, respectively, the panel’s analyses of curriculum and assessment and of teacher preparation and professional development in the two programs. The impact of the programs is examined in Chapter 5. Throughout these four chapters, the panel’s key findings are presented in italic type. Finally, the panel’s recommendations are given in Chapter 6.