1
Introduction

Excellence in science and mathematics education is a critical need and goal for the United States. Programs for advanced study, particularly the Advanced Placement (AP) and International Baccalaureate (IB) programs, are major contributors to science and mathematics education at the high school level. Large numbers of high school students seek access to these courses, and many colleges use them in their admission decisions. High school curricula are strongly affected by these programs, since schools often structure their courses in the middle-school and early high school years to facilitate participation in advanced study.

This report presents the results of a 2-year effort by a committee of the National Research Council (NRC) to examine programs for advanced study of U.S. high school mathematics and science (calculus, biology, chemistry, and physics). As part of the scope of the study, the NRC asked the committee to “… explore the current status of high school mathematics and science education by means of an in-depth look at programs designed for advanced students, such as the AP and IB programs.” The study focuses on AP and IB because these are the only advanced secondary science and mathematics programs of national scope. However, the availability of and participation in these programs are highly variable, with large differences among schools and their student populations.

The primary purpose of this report is to use the results of recent research on learning, curriculum, instruction, assessment, and professional development as lenses to examine educational programs for advanced secondary science and mathematics in the United States. We are now in a position to ask whether the AP, IB, and other programs of advanced study as currently implemented are as effective as possible, and how they might be improved.



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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools 1 Introduction Excellence in science and mathematics education is a critical need and goal for the United States. Programs for advanced study, particularly the Advanced Placement (AP) and International Baccalaureate (IB) programs, are major contributors to science and mathematics education at the high school level. Large numbers of high school students seek access to these courses, and many colleges use them in their admission decisions. High school curricula are strongly affected by these programs, since schools often structure their courses in the middle-school and early high school years to facilitate participation in advanced study. This report presents the results of a 2-year effort by a committee of the National Research Council (NRC) to examine programs for advanced study of U.S. high school mathematics and science (calculus, biology, chemistry, and physics). As part of the scope of the study, the NRC asked the committee to “… explore the current status of high school mathematics and science education by means of an in-depth look at programs designed for advanced students, such as the AP and IB programs.” The study focuses on AP and IB because these are the only advanced secondary science and mathematics programs of national scope. However, the availability of and participation in these programs are highly variable, with large differences among schools and their student populations. The primary purpose of this report is to use the results of recent research on learning, curriculum, instruction, assessment, and professional development as lenses to examine educational programs for advanced secondary science and mathematics in the United States. We are now in a position to ask whether the AP, IB, and other programs of advanced study as currently implemented are as effective as possible, and how they might be improved.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools BACKGROUND 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 1   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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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools sciences and mathematics in the United States that year.2 Clearly, these are no longer programs only for an elite audience; participation in some form of advanced study has become almost the norm for students seeking admission to the most selective colleges. Advanced study programs can affect students’ future opportunities, and the quality and availability of these programs have become central concerns. As the United States becomes more diverse, racial and socioeconomic gaps persist in high school students’ access to and success in advanced study. While minority participation in advanced mathematics and science courses has increased substantially during the past 20 years (National Science Foundation [NSF], 1999), inner-city and rural schools, especially those with high percentages of minority and poor students, are still less likely to offer these courses (Ma and Willms, 1999). Many schools in low-income communities remain ill equipped to provide advanced study, in part because they are less likely than schools with greater resources to have highly qualified teachers or sufficient laboratories, equipment, and other curriculum materials (Darling-Hammond, 2000; Ferguson, 1991, 1998; Greenwald, Hedges, and Laine, 1996; Murnane, 1996; Wright, Horn, and Sanders, 1997). In addition to these gaps, there are parallel disparities in access within racially and ethnically diverse schools. In these schools, African American, Hispanic, and Native American students and those of low socioeconomic status are much less likely than white or Asian American students to enroll in upper-level mathematics and science courses even when such courses are available (Atanda, 1999; Horn, Nunez, and Bobbitt, 2000; Ma and Willms, 1999). Those who do enroll are much less likely to fare as well as white or Asian American students on national examinations. These facts represent a major challenge for advanced study programs. A number of additional trends and concerns make this an appropriate time to analyze programs for advanced study of science and mathematics: Changes in science and mathematics—Rapid advances (e.g., the tremendous progress in molecular biology) mean that traditional course content may be inadequate for the future. Demands for accountability—There is increasing pressure from policymakers and the public for school accountability, and participation in advanced study is often used as a measure of school quality. Connections to earlier years and higher education—Since learning of science and mathematics tends to be hierarchical, advanced programs in 2   These numbers are estimates based on IB Worldwide Statistics.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools these subjects have major implications for the earlier years of schooling and vice versa. Similarly, as introductory college courses evolve and their emphases change (see, for example, NRC, 1999d), it is important to review the secondary courses that precede them. Teacher shortages—A teacher shortage of immense proportions is projected to emerge in the next few years in many districts. These shortages are likely to be particularly acute for science and mathematics (National Commission on Mathematics and Science Teaching for the 21st Century, 2000; NCES, 2000b). Teaching in advanced programs requires extensive knowledge of both subject matter content and pedagogical methods. Thus it is unclear how the staffing needed to implement and maintain the quality of these programs will be provided in the future. This problem is especially severe in schools with large populations of minority and poor students, where shortages of qualified science and mathematics teachers are already daunting (National Commission on Mathematics and Science Teaching in the 21st Century, 2000). Economic forces—The increasing demands of a knowledge-based economy add to the importance of providing advanced courses in mathematics and science for as many students as are motivated and prepared to enroll in them. Information technology—Advances in information technology are transforming work, teaching, and learning, creating new opportunities for instructional delivery. For example, distance learning is now being used to deliver advanced study programs to schools that have few resources, small student populations, or insufficient numbers of teachers to offer a program within the school. Assessment—Better understanding of the uses and impact of assessment with regard to classroom dynamics and student learning creates opportunities for fundamentally changing and improving programs of advanced study (see, for example, NRC, 2001a). BRIEF OVERVIEW OF THE PROGRAMS The AP program was launched in 1955 by the College Entrance Examination Board, commonly referred to as the College Board,3 to provide college-level courses for advanced high school students. The program currently consists of 35 courses in 19 subjects, including 11 courses in 7 science and mathematics subjects.4 An individual school can choose to offer any number 3   The College Board is an independent, not-for-profit membership organization. Membership includes colleges, universities, and secondary schools. 4   See http://apcentral.collegeboard.com/courses/overviews/ (February 11, 2002).

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools and combination of these courses. The AP program is built around elective, end-of-course examinations that are graded on a five-point scale. The College Board produces content outlines for its courses, largely by surveying colleges and universities about the content of their introductory courses. The national AP examinations are used by many colleges and universities as a basis for granting credit or advanced placement to incoming students. Additional information about the AP program is provided in Chapter 3. The IB program was developed in the late 1960s to provide an international standard of secondary education for a mobile population—primarily the children of diplomats and others stationed outside their home countries for extended periods. One goal was to prepare these students to qualify for university admission in their home countries after schooling abroad. As with the AP program, a final examination developed by the International Baccalaureate Organisation5 (IBO) is a major component of an assessment process that helps determine eligibility for university admission. The examination is supplemented by teacher-devised classroom assessments, such as a portfolio of laboratory reports. Schools cannot choose to offer individual IB courses; they must provide a program of interrelated courses that students seeking the IB diploma take during their junior and senior years. While some students take individual IB courses much as they would an honors course, approximately two-thirds are diploma candidates, taking a full program of six or seven courses over the 2-year period. A detailed course outline and specific goals are provided for the courses. Additional information about the IB program is provided in Chapter 4. As a consequence of the growing belief that all students should have access to quality educational programs, many states and the federal government have advocated an expansion of programs such as AP. Former U.S. Department of Education Secretary Richard Riley called for at least one AP course in every school by 2002 and an additional course incorporated into a school’s AP offerings each year for the remainder of the decade.6 While Governor of Texas, George W. Bush said, “Making Advanced Placement available to students across Texas is one of the best ways to challenge students academically” (Callahan, 2000, [from AP Program 1999, p. 16]). Many states have advisory councils and other structures in place specifically to promote and improve AP offerings. The U.S. education system has changed dramatically since these programs were first established, and the programs and their assessments are now being used in ways that initially were neither anticipated nor intended. The leaders of these programs are aware of the need for reform. For ex- 5   The IBO is a not-for-profit educational foundation based in Geneva, Switzerland. 6   See www.ed.gov/Speeches/02-2000/20000211.html (February 11, 2002).

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools ample, in 2000 the College Board convened a Commission on the Future of the Advanced Placement Program, asking it to focus on ways of maintaining the integrity and quality of the program while improving equity of access to accommodate greater student diversity.7 WHAT IS ADVANCED STUDY? The committee found that defining “advanced study” for secondary students is surprisingly difficult. Establishing a clear definition of advanced study is problematic in part because these programs share many of the objectives of other high school courses. For example, all courses in mathematics and science, whether “advanced” or not, should encourage students to think about concepts in addition to factual information. Similarly, all courses should engage students in scientific or mathematical reasoning. A number of overlapping definitions are often used to characterize advanced study for high school students in the United States. Some have tended to equate advanced study with accelerated or college-level learning. However, the committee finds this definition insufficient because as discussed in detail later in this report, the inclusion of too much accelerated content can prevent students from realizing the important goal of attaining deep conceptual understanding.8 Furthermore, introductory courses at colleges and universities often do not take advantage of the greatly improved understanding of the conditions for successful teaching and learning mentioned earlier. As a result, they are not necessarily good models for emulation at the high school level. It is possible to enrich students’ learning beyond what is typically found in secondary curricula in other ways—for example, by adding depth or rigorous analysis, applications to new domains, or opportunities for investigation. Thinking of advanced study entirely in the context of obtaining college credit and placement is unnecessarily limiting. For purposes of this report, therefore, the committee adopted a focus on helping students achieve deep conceptual understanding as the primary goal of advanced study. At the same time, committee recognizes that accelerated exposure to college-level content has an appropriate place in some pro- 7   The sponsors of these programs have acknowledged and appreciate the importance of increased access for underserved students. However, it is probable that offering courses alone, without providing support systems for both students and teachers and appropriate prerequisite education in the earlier years, would prove unsuccessful. These issues are discussed at length in Chapter 2, this volume. 8   Conceptual understanding involves the creation of rich integrated knowledge structures around an underlying concept. Understanding is not a static point in learning, but rather a continually developing mental activity.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools grams, provided it is well integrated with the primary goal of nurturing conceptual understanding. THE STUDENT CLIENTELE FOR ADVANCED STUDY For whom are programs of advanced study appropriate? Again the answer is not straightforward. This study did not examine programs intended only for the most exceptional learners, who might constitute at most a few percent of the student population. Exceptional learners sometimes require opportunities that differ significantly from what is needed or effective for other able and well-motivated students; they may need earlier access to advanced material and a faster pace (see Annex 6-1). While it is important to provide challenging opportunities for the most talented students, the primary concern of this study is with programs available to a broader group of highly motivated students with solid academic preparation. This population is limited at least in part by the adequacy of students’ prior educational opportunities, the ability of their schools to provide effective learning environments, and the availability of qualified and effective teachers. It is the committee’s consensus that improvements in these areas could enlarge significantly the group of students for whom advanced study programs such as AP and IB are a realistic choice. Therefore, instead of asking, “For whom is advanced study appropriate?” we think it much more useful to ask, “How can high school science and mathematics education at both the introductory and advanced levels be improved so that a larger number of students will have access to advanced study and a realistic chance of succeeding once enrolled?” Achieving this goal will require fundamental changes in curriculum, approaches to teaching and learning, assessment tools, and teacher preparation and professional development. Both school systems and institutions of higher education will have to change in significant ways. The pathways leading to advanced study begin early. If a student has not developed a sound conceptual understanding of algebra, geometry, and functions, for example, he or she may be lost even in a well-taught calculus class. The committee envisions a future in which the conceptual understanding and habits of mind essential to advanced study are successfully nurtured among a greater number of students than at present. In this hoped-for future, early tracking of some students into academically weak courses is avoided so that each child has a suitable opportunity to develop and demonstrate his or her individual academic abilities and talents. It should be noted that the early high school years are important as well for students who do not go on to advanced study. The programs reviewed

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools in this report have a profound influence on the course structure and coursetaking patterns of all students throughout the high school years. Moreover, AP and IB teachers—who are often among the best in their schools—are a critical resource for the entire high school system. STUDY CHARGE AND APPROACH The charge to the committee was as follows: … to consider the effectiveness of, and potential improvements to, programs for advanced study of mathematics and science in U.S. high schools. In response to the charge, the committee will consider the two most widely recognized programs for advanced study: the Advanced Placement (AP) and the International Baccalaureate (IB) programs. In addition, the committee will identify and examine other appropriate curricular and instructional alternatives to IB and AP. Emphasis will be placed on the mathematics, physics, chemistry, and biology programs of study. The committee was charged with answering the following questions:9 What does research tell us about the ways in which high school students learn science and mathematics? To what extent do the AP and IB programs in mathematics and science incorporate current knowledge about cognition and learning in their curricula, instruction, and assessments? To what extent do AP and IB programs encourage teaching approaches that are consistent with current research on effective instructional practices? How do final assessments generally, and AP and IB assessments in particular, influence instructional practice? What does research tell us about how teachers learn to teach, and about effective professional development opportunities? What is the impact of student assessment on the learning process, and how could student assessment be used to improve student learning in advanced courses? To what extent do the IB and AP programs reflect the best in current thinking about content and curriculum for teaching mathematics and science? How can the goal of equitable and broad access to programs for advanced study best be pursued? 9   The full text of the committee’s statement of task can be found in Appendix C; only a subset of the questions to be addressed is presented here.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools How does the interface with higher education affect programs for advanced study in secondary schools? In approaching its charge, the committee considered research about how people learn and gain expertise in a discipline. The committee found surprisingly sparse empirical data about either the AP or IB programs. For example, systematic information is lacking about how the AP and IB programs are actually implemented in U.S. high schools. Systematic data about the AP and IB examinations are also scarce, as is information about the long-term effects of AP and IB participation on student learning and achievement. Because neither independent researchers nor the AP or IB programs have gathered and published much of the data the committee sought for this study, it was necessary to use instead available program materials and expert testimony from program officials and experienced AP and IB teachers. As this report notes throughout, more studies are sorely needed to address the many issues and questions raised herein. The committee was composed of scientist-researchers, secondary teachers having considerable experience with both the AP and IB programs, scientists and educators with expertise in the preparation of teachers and in issues of access and equity, experts in the cognitive sciences, and educational leaders. (Biographical sketches of the committee members are provided in Appendix B.) The committee held seven 2- to 3-day meetings over a period of 2 years, convened several small-group meetings, and interacted extensively between meetings. Representatives of the AP and IB programs and experts on science learning met with the committee. Deans of admission and chairs of science and mathematics departments in a diverse group of colleges and universities were surveyed about their uses of AP scores. These surveys and their results are described in Chapters 2 and 10, this volume. Given the differences among the four disciplines under the committee’s charge, panels of experts in each of the disciplines were convened to advise the committee. Each panel included at least one representative from each of the following categories: an expert on pedagogy in the discipline, an accomplished university teacher-scholar, a secondary teacher involved in advanced programs, and an educational researcher with a strong base in the discipline. The panels met for two 2-day sessions during the summer of 2000. The charge to the panels, the set of questions they were asked to consider, and a summary of their findings are included in Appendix A. Each of the panel reports was submitted to a group of independent reviewers for analysis and improvement, using procedures identical to the review process for all NRC reports. The panels’ analyses and recommendations were an important source for the information on which the analyses, conclusions, and

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools recommendations of this report are based. The names and institutional affiliations of the panel members are provided in the front matter of the report. To keep the size of this volume reasonable, only summaries of the panels’ findings and recommendations are included in Appendix A; the full text of their reports is available online for reading or downloading.10 AUDIENCES FOR THE REPORT This report is intended to be useful to a variety of audiences concerned with high school science and mathematics curricula in general and advanced study in particular. Those who determine the shape of advanced study programs should find many opportunities to improve their programs along the lines suggested in this report. High school teachers should be interested in the analysis, which they can use both to develop useful teaching ideas and to press for changes in their schools that will enhance advanced study opportunities and make the programs effective for more of their students. It is hoped that university faculty members will see the importance of interacting with their secondary school colleagues and of encouraging deep conceptual understanding among their students, especially those who might become teachers. It is also hoped that university administrators will better appreciate the influence of their policies regarding admission and credit or placement for advanced study on both high schools and their students. Middle school and elementary school teachers should attain a better understanding of what they can do to prepare their students for advanced study at a later time and, in so doing, to enhance academic opportunities for all students. The report should be of value as well to policymakers and administrators at both the K– 12 and university levels, who have a vital role to play in promoting the practices that research has shown to be effective and in providing the resources their teachers need to make advanced study successful for larger numbers of students. Finally, this report is intended to assist parents in being informed advocates for educational quality in science and mathematics. OVERVIEW AND STRUCTURE OF THE REPORT Chapter 2 provides essential background for this report, including the policy context of advanced study, the roles of middle schools and high schools in preparing students for these programs, and problems related to the supply of qualified teachers. It also addresses issues of equity and access to advanced study programs, factors that affect the success of students who enroll in advanced study, and the interface of secondary advanced study 10   At www.nap.edu/catalog/10129.html/.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools with colleges and universities. Chapters 3 and 4 introduce the AP and IB programs in some detail, while Chapter 5 provides a brief overview of some alternative advanced study programs. Chapter 6 summarizes the results of research on human learning that are critical for the present analysis. Chapter 7 extends these findings to the design of curriculum, instruction, assessment, and professional development as they relate to advanced study. The report next turns to a detailed analysis of programs for advanced study, an analysis that is influenced strongly by the panel reports in the four individual disciplines. Chapter 8 presents an analysis of the programs from the perspective of research on learning, while Chapter 9 considers them from the perspective of curriculum, instruction, assessment, and professional development of teachers. Chapter 10 examines appropriate and inappropriate uses of these programs and their assessments of students. Finally, Chapter 11 presents the committee’s recommendations for change.