This report presents results of a 2-year effort by a National Research Council (NRC) committee to examine programs for advanced study of mathematics and science in U.S. high schools. The committee focussed on the two most widely recognized programs in the United States, and the only two of national scope: Advanced Placement (AP) and International Baccalaureate (IB). The committee also identified alternatives to IB and AP and addressed specific questions about advanced study.1 The committee’s statement of task and study questions are found in Appendix C.
While international comparisons of the performance of advanced students served as a catalyst for the study, its primary motivator was the improved, research-based understanding of teaching and learning that has emerged recently, and its application to improving advanced study. In approaching its charge, the committee considered advances in the cognitive and learning sciences. The committee also examined research about the AP and IB programs using information provided by the College Board and the International Baccalaureate Organisation (IBO). Neither the AP or IB programs nor independent researchers, however, have yet gathered or published critical data that the committee sought. Therefore, the committee also relied on materials and expert testimony from AP and IB program officials and teachers for some of the data used in its analyses. More studies are needed to address the many issues that are raised by this report.
The committee found that existing programs for advanced study are frequently inconsistent with the results of the research on cognition and learning. This report describes how program developers, schools, and educators can remedy this situation by considering all components of educational programs: curriculum, instruction, ongoing and end-of-course assessments, and teacher preparation and professional development.
Also examined in depth is the issue of equal access to advanced study. Advanced study is no longer only for an elite audience of exceptionally talented and privileged students; participation has become almost the norm for students seeking admission to selective colleges. Yet minorities, inner-city and rural students face serious limitations in accessing programs. These broader populations of students who could benefit from advanced study are currently limited by their prior educational opportunities, their schools’ ability to provide effective learning environments, and the availability of qualified and effective teachers. Improvements in these areas could significantly expand the population that can be served effectively by advanced study.
Expertise on the committee included scientist-researchers, secondary teachers of AP and IB, science and mathematics educators working on teacher education and issues of access and equity, cognitive scientists, and educational administrators. Panels of experts in the disciplines (biology, chemistry, physics, and mathematics) also advised the committee. The four panel reports provided a critical basis for the committee’s analysis and may be used independently of this volume. They are available online2 and are summarized in Appendix A.
This report is intended for many audiences concerned with high school science and mathematics education in general and advanced study in particular, including program developers, high school and higher education faculty, university and high school administrators, policymakers, and parents.
CONTEXT OF ADVANCED STUDY
Advanced study has wide-ranging effects on curricula, teachers, and students, therefore, advanced courses must be considered within a broader context that includes the schools where the courses are offered, preceding grade levels, and higher education. Advanced study in science and mathematics makes special demands on facilities, financial resources, and personnel at both the middle- and high school levels.
Teachers. Students learn best from teachers with strong content knowledge and pedagogical skills. Lack of access to high-quality teachers may preclude some students, especially minorities and those living in poverty, from pursuing advanced study. All 50 states require licensing of public school teachers; none requires special certification for those providing advanced study. High school teachers see themselves as subject area specialists. They teach up to 175 students per day, and have little opportunity to work with colleagues to improve curriculum or instruction. They frequently cite inadequate support, lack of student motivation, and student discipline problems as reasons for leaving teaching.
Coordination. Academic preparation for advanced study begins in middle school. Mathematics and science courses in these grades often lack focus, cover too many topics, repeat material, and are implemented inconsistently. In mathematics, states are moving toward offering algebra in eighth grade. Increasing numbers of middle schools are instituting integrated science curricula that de-emphasize disciplines. Middle and high school teachers rarely have opportunities to coordinate curricula or instruction for grades 7–12.
Curricular Differentiation. More than 80 percent of middle schools and many high schools direct or allow students to choose their classes in mathematics, science, and other subjects. Other schools offer core curricula that are narrowly focused on academic subjects and allow students few choices. Early differential placement steers some students away from rigorous academic programs. Research indicates that constrained curricula are more effective and equitable in helping students pursue advanced study.
Sequencing. The typical progression of courses in high school mathematics leading to calculus is Algebra I, geometry, Algebra II, trigonometry, and precalculus. Most state high school graduation requirements also include 2 years of science, although college-bound students traditionally take more, usually biology, chemistry, and then physics.
Standards. In science, standards developed by the American Association for the Advancement of Science and the National Research Council call for increased emphasis on inquiry and in-depth study of fewer topics. In mathematics, the standards from the National Council of Teachers of Mathematics emphasize learning of concepts and helping students understand mathematics more deeply. Forty-nine states have developed standards and
curriculum frameworks in mathematics and science. All 50 states test their students and 27 states hold schools accountable for results. The AP and IB programs are not predicated on state or national standards in any subject area, but can complement standards-based reform efforts. Both provide nationally recognized external measures of student achievement, but schools can implement the programs in ways that conform to local or state standards.
Students. High school students face competing time pressures. Typical students work 15–20 hours per week, spend 20–25 hours socializing, 5 hours in extracurricular activities, and 15 hours watching television. Significant numbers of students—particularly those from low-income families—think so much about problems at home that they cannot concentrate in school.
There is an enduring belief that advanced study confers advantages to students in college; thus, ever-increasing numbers enroll in AP courses and IB programs. However, access to advanced study is uneven. Some high schools offer multiple sections in many AP subjects; others provide none. These differences are associated with school size and location, and the availability of AP and IB in a school decreases as the percentage of minority or low-income students increases, especially in mathematics and science. Even where available, students from underrepresented and low-income groups take advanced courses less frequently than students from other groups. Effective strategies for improving student participation in advanced study include eliminating low-level courses with reduced academic expectations, enhancing professional development for teachers, hiring qualified teachers for rural and inner-city schools, providing information to parents about long-term benefits of participating in such programs, and increasing student access to skilled counselors and mentors.
High School–College Interface
To understand the role AP and IB play in college admission decisions, the committee surveyed deans of admission. The survey revealed that participation in these programs is of greatest importance for admission to the most selective colleges. Deans view such participation as an indication of students’ willingness to accept academic challenges, but stated that the lack of such courses at an applicant’s high school typically does not adversely influence admission if a student succeeded in the most challenging courses available at his or her school.
AP and IB examinations are administered each May, but scores are not available until July. Therefore, examination grades from the senior year do not influence college admission, but are used in credit and placement decisions. Students also use these credits to reduce course loads or to meet prerequisite or distribution requirements. As a result, some students may not have to take college courses in specific subject areas, such as mathematics or science. Some institutions minimize this practice by requiring that students enroll in courses at higher levels than those taken in high school. A survey of mathematics and biology departments revealed that the vast majority award credit and advanced placement for AP, and sometimes IB; the amount awarded usually depends on the student’s score.
OVERVIEW OF THE PROGRAMS
Developed in 1955, AP is the predominant national program for advanced courses in U.S. high schools. Eleven separate courses are available in eight mathematics and science subjects. The College Board provides topic outlines for AP courses, generated largely by surveying colleges and universities. However, teachers are allowed considerable leeway in implementation. Elective, end-of-course examinations are designed to be comparable with “typical” introductory college-level courses in a subject area. Originally, the program served only top students from a few high schools. Today, approximately 62 percent of U.S. high schools offer AP. In May 2001, students took more than 450,000 AP examinations in mathematics and science.
The IB program was developed in the late 1960s to provide an international standard of secondary education for children of diplomats and others stationed outside their countries. One goal was to prepare students for university work in their home countries. The IBO authorizes participating high schools; schools must offer a full IB Diploma Programme and cannot offer only a subset of IB courses. While some students take individual IB courses as they would an honors course, most are diploma candidates, taking a program of six or seven courses over two years.
Final examinations are part of the integrated IB Diploma Programme. Assessment consists of both external and internal components designed to measure content knowledge, depth of understanding, and use of specific higher-level cognitive skills for each subject. In May 2001, students from 272 U.S. public and private schools took 50,745 IB examinations, of which roughly 13,000 were in mathematics and science. Teachers also provide internal as-
sessments of students’ practical skills (for example, laboratory investigations in science, portfolios in mathematics), which are judged against established IBO assessment criteria.
Other opportunities for advanced study in high school are available through local-, state-, and nationally sponsored programs. These include collaborative programs between high schools and postsecondary institutions, specialized schools for high-ability learners, distance learning programs, research internships, and academic competitions. Many programs award college credit to high school students, but less is known about transferability of credits earned in these alternate programs compared with qualifying scores on AP or IB examinations.
DESIGNING PROGRAMS BASED ON RESEARCH ON LEARNING AND PEDAGOGY
The goal of advanced study is to promote development of deep conceptual understanding and the ability to apply knowledge appropriately. Accordingly, the committee developed a framework to guide its analysis of advanced study and to evaluate the degree to which existing programs accomplish this goal. This model also can guide the development of new programs.
The concept of “learning with understanding” is concerned with knowledge and how it is organized. Effective instruction is focusesd on enabling learners to uncover and formulate the deep organizing patterns of a domain, and then to actively access and create meaning around these organizing principles. Learning with understanding also helps students develop the ability to evaluate the relevance of particular knowledge to novel problems and to explain and justify their thinking. As students learn and practice these skills of critical reflection, they become able to apply knowledge in multiple contexts, develop adaptive expertise, and serve as active members of learning communities.
Seven Principles of Human Learning
Seven research-based principles of learning can provide a framework for designing effective curriculum, instruction, and assessment—three facets of classroom activity that teachers can orchestrate to promote learning with understanding. These principles also underlie the design of effective preparation and professional development for teachers, which, along with cur-
riculum, instruction, and assessment, helps create a system that focuses on student learning:
Learning with understanding is facilitated when knowledge is related to and structured around major concepts and principles of a discipline.
A learner’s prior knowledge is the starting point for effective learning.
Metacognitive learning (self-monitoring) is important for acquiring proficiency.
Recognizing differences among learners is important for effective teaching and learning.
Learners’ beliefs about their ability to learn affect learning success.
Practices and activities in which people engage during learning shape what is learned.
Socially supported interactions strengthen one’s ability to learn with understanding.
Design Principles: Curriculum, Instruction, Assessment, and Professional Development
The committee’s framework for appraising advanced study programs encompasses the intentional and systematic design of curriculum, instruction, assessment, and professional development within the context of advanced study. Consideration of these program elements is based on the principles of learning and on theory and research on instructional programs. Education systems frequently address each element separately, but all four must be aligned and work together synergistically to facilitate deep conceptual understanding. The following examples of design principles for curriculum, instruction, and assessment reflect what is known about human learning:
Effective mathematics and science curricula are coherent, focus on important ideas within the discipline, and are sequenced to optimize learning. They provide ample opportunities for exploring ideas in depth and for developing familiarity with the discourse and modes of inquiry of the discipline.
Teaching for understanding begins with careful consideration of students’ thinking. It employs multiple representations and tasks. Effective teachers create learning environments that foster development of students’ understanding and skills. They orchestrate classroom discourse in which students conjecture, present solutions, and argue about the validity of claims.
Assessment for understanding is aligned with instruction and with desired learning outcomes. It is multifaceted and continuous and includes both content and process dimensions of performance.
Successful implementation of advanced study that promotes learning with understanding also depends upon creating opportunities for teachers’ continual learning, and requires sufficient resources to support professional development. Effective professional development for mathematics and science teachers emphasizes deep understanding of content and discipline-based methods of inquiry, provides multiple perspectives on students as learners, and develops teachers’ subject-specific pedagogical knowledge. It treats teachers as active learners, builds on their existing knowledge and beliefs, and occurs in professional communities where there are opportunities to discuss ideas and practices as colleagues.
ANALYSIS OF AP AND IB PROGRAMS BASED ON LEARNING RESEARCH
Although the AP and IB programs predate contemporary learning research, it is important to use the principles emerging from that research to assess and improve the programs. The committee’s analysis of these programs, based on these principles of learning and supported by the reports of the four disciplinary panels, yielded the following findings:
Principled conceptual knowledge—Although the AP and IB programs espouse an emphasis on concepts and key ideas, this intention is largely unrealized in the sciences. Excessive breadth of coverage (especially in 1-year science programs) and insufficient emphasis on key concepts in final assessments contribute significantly to the problem in all science fields. Although emphasis on learning concepts and key ideas is more evident in mathematics, further improvement is needed, particularly in the assessments, which frequently focus on procedural knowledge at the expense of conceptual understanding.
Prior knowledge—Except for mathematics, these programs do not specify clearly what prior knowledge is needed for success or help teachers to build on what students already know or to recognize student misconceptions. In all subjects, efforts to prepare students properly in the years preceding advanced study are often inadequate. Too many students, especially in physics, take a 1-year advanced course as their first course in the discipline—an inappropriate situation.
Metacognition—Advanced study can increase students’ metacognitive skills, but many programs and courses do not help students develop these skills.
Differences among learners—AP and IB teachers who employ a variety of pedagogical approaches are likely to reach a broader range of learners. Using several sources of evidence of student progress also can provide a more accurate picture of what students know compared with any single measure, such as an examination. The single end-of year examinations and summary scores, as found in AP, do not adequately capture student learning.
Motivation—Students have varied motives for enrolling in advanced study. Designing programs that are consistent with the findings of learning research can increase students’ motivation to succeed in advanced study, encourage them to believe in their own potential, and increase the proportion of students who take and succeed in the course and final examinations.
Learning communities—Teamwork and collaborative investigation are especially important in advanced study. The breadth of course content and the generally short duration of laboratory periods in many schools may be inadequate for such activities. Better use of the Internet and technologies for collaborative learning is needed.
Situated learning—Students need opportunities to learn concepts in a variety of contexts. The AP and IB programs currently do not emphasize interdisciplinary connections sufficiently or assess students’ ability to apply their knowledge in new situations or contexts. Additionally, advanced study courses might make better use of laboratory experiences by requiring students to plan experiments, decide what information is important, select experimental methods, and review results critically. These courses might also draw upon local resources (e.g., science-related industries) to give students experience with varied practices in mathematics and science.
Although AP and IB programs currently are not well aligned with learning principles, they can be revised with this research in mind. The resulting transformations are likely to make the programs more successful in enhancing deep conceptual learning and make them more accessible to additional students.
ANALYSIS OF AP AND IB PROGRAMS WITH REGARD TO CURRICULUM, INSTRUCTION, ASSESSMENT, AND PROFESSIONAL DEVELOPMENT
Students can study topics in depth and develop conceptual understanding only if curricula do not present excessive numbers of topics. Currently, AP and IB programs are inconsistent with this precept. In their written materials the College Board and the IBO acknowledge the importance of depth
and focus, but the breadth of topics covered in their curriculum guides and assessments conveys a different message. Additionally, the College Board models AP course outlines on typical college introductory courses, rather than on the best college courses or educational practices based on research on learning and pedagogy. Since college-level courses vary substantially in content and pedagogy, this approach limits the potential quality of AP courses.
Individual teachers have substantial leeway in implementing AP or IB courses. Therefore, the nature and quality of instruction vary considerably from classroom to classroom. AP and IB programs depart from the model of instruction outlined above by not providing adequate guidance concerning excellent teaching practices in advanced study.
The central principle for designing assessments that foster deep conceptual understanding is that they must be aligned with learning goals and with curriculum and instruction derived from those goals. Because AP and IB assessments exert a powerful influence on curriculum and instruction, it is especially important to ensure that they are designed to foster deep conceptual understanding.
A striking inadequacy of the AP and IB programs is the lack of detailed research about what their examinations actually measure, including the kinds of thinking that the examinations elicit. This concern touches on the tests’ validity and the appropriateness of the inferences drawn from test scores. For both the AP and IB programs, certain kinds of validity research are lacking, including attention to the broader social consequences (or consequential validity) of their assessments.
Because high-stakes assessments strongly influence instruction, it is imperative to understand the connections between assessment and instruction in both programs. If instruction is to enhance understanding, assessments should not be predictable from year to year, nor should their content or form be capricious. Assessments in some AP and IB courses are relatively predictable.
At present, neither the College Board nor the IBO supports systematic and continuing professional development for teachers. Professional development opportunities vary in quality and focus and do not consistently re-
flect the notions of learning, instruction, curriculum, and assessment presented in this report. The College Board does not adequately monitor professional development programs that support AP; teachers’ participation in such programs is voluntary. The College Board and the IBO have made progress in providing Web-based resources, workshops, and mentorships, but many teachers still lack access to such resources and opportunities.
Accepting greater responsibility for teacher professional development is a daunting challenge for the College Board and the IBO, whose missions historically have been much more limited in focus. Without improved professional development, however, other efforts to improve advanced study are likely to founder.
USES, MISUSES, AND UNINTENDED CONSEQUENCES OF AP AND IB
Some misuses of AP and IB test scores may have unfortunate consequences, though these have not been studied in detail. For example, in an attempt to quantify the extent to which high schools challenge students, top public high schools have recently been ranked based on the number of AP and IB tests taken. AP and IB assessment data also have been used inappropriately to evaluate teachers or to compare schools. Because of this, the committee is concerned that teachers may emphasize to their students the mechanics of preparing for a test, rather than learning and understanding of important principles. Coverage of content may be superficial and opportunities for inquiry-based experiences insufficient. The committee also has learned that some teachers discourage students from taking AP or IB courses (or the final examinations) when poor performance is anticipated. This form of limiting access occurs in many educational settings, including the most competitive high schools.
Data from AP and IB test scores by themselves cannot support inferences about teacher quality and effectiveness. Students come to advanced courses with different levels of skill and mastery of content that make it difficult to determine the effects of a teacher’s work on student achievement in any particular year. Nor should such data be used to measure school quality. Some schools offer other options that are equally rigorous but more suited to their students.
Unlike the IBO, the College Board has no clear standards as to what constitutes an AP course. With the growth of AP as a perceived standard of excellence and school quality, the incentive to use the AP name inappropriately also has increased. Some schools may label non-AP courses as AP, while others may sponsor AP courses without providing proper facilities and personnel resources.
Students can be affected adversely when preparatory courses are compressed or when students are allowed to skip prerequisite courses without first demonstrating mastery before taking an AP course. However, efforts to prepare students for advanced study often stimulate improvements in prerequisite courses; and this is to be strongly encouraged.
Advances in technology make it possible to create online AP courses and to provide other online support, such as professional development for AP and IB teachers. The potential for growth in this area is virtually unlimited, but so is the potential for problems if suitable quality controls are not established. For example, students who take an AP science course online and earn a qualifying score on the examination may earn college credit or placement without having had any advanced laboratory experience.
Decisions about awarding college credit or advanced placement for qualifying scores on AP and IB examinations are best made on an individual basis, using multiple sources of information. Decisions based on sampling average student performance in courses at typical colleges is not strong enough to infer that all, or even most, AP or IB students who earn a particular examination score are qualified for either credit or placement.
Recommendation 1: The Primary Goal of Advanced Study
The primary goal of advanced study in any discipline should be for students to achieve a deep conceptual understanding of the discipline’s content and unifying concepts. Well-designed programs help students develop skills of inquiry, analysis, and problem solving so that they become superior learners. Accelerating students’ exposure to college-level material, while appropriate as a component of some advanced study programs, is not by itself a sufficient goal.
Recommendation 2: Access and Equity
Schools and school districts must find ways to integrate advanced study with the rest of their program by means of a coherent plan extending from middle school through the last years of secondary school. Course options in grades 6–10 for which there are reduced academic expectations (i.e., those that leave students unprepared for further study in a discipline) should be eliminated from the curriculum. An exception might be made for courses designed to meet the needs of special education students.
Recommendation 3: Learning Principles
Programs of advanced study in science and mathematics must be made consistent with findings from recent research on how people learn. These findings include the role of students’ prior knowledge and misconceptions in building a conceptual structure, the importance of student motivation and self-monitoring of learning (metacognition), and the substantial differences among learners.
Recommendation 4: Curriculum
Curricula for advanced study should emphasize depth of understanding over exhaustive coverage of content. They should focus on central organizing concepts and principles and the empirical information on which those concepts and principles are based. Because science and technology progress rapidly, frequent review of course content is essential.
Recommendation 5: Instruction
Instruction in advanced courses should engage students in inquiry by providing opportunities to experiment, analyze information critically, make conjectures and argue about their validity, and solve problems both individually and in groups. Instruction should recognize and take advantage of differences among learners by employing multiple representations of ideas and posing a variety of tasks.
Recommendation 6: Assessment
Teachers of advanced study courses should employ frequent formative assessment of student learning to guide instruction and monitor learning. External, end-of-course examinations have a different purpose: they certify mastery. Both types of assessment should include content and process dimensions of performance and evaluate depth of understanding, the primary goal of advanced study (see Recommendation 1).
Recommendation 7: Qualified Teachers and Professional Development
Schools and districts offering advanced study must provide frequent opportunities for continuing professional development so teachers can improve their knowledge of both content and pedagogy. National programs for advanced study should clearly specify and monitor the qualifications
expected of teachers. Professional development activities must be adequately funded and available to all teachers throughout their teaching careers.
Recommendation 8: Alternative Programs
Approaches to advanced study other than AP and IB should be developed and evaluated. Such alternatives can help increase access to advanced study for those not presently served and result in the emergence of novel and effective strategies.
Recommendation 9: The Secondary–College Interface
9(a): When awarding credit and advanced placement for courses beyond the introductory college level, institutions should base their decisions on an assessment of each student’s understanding and capabilities, using multiple sources of information. National examination scores alone are generally insufficient for these purposes.
9(b): College and university scientists and mathematicians should modify their introductory courses along lines similar to those proposed in this report for high school advanced study. Departments should carefully advise undergraduates about the benefits and costs of bypassing introductory courses.
Recommendation 10: Changes in the AP and IB Programs
The following substantial changes in the AP and IB programs are recommended:
10(a): The College Board should abandon its practice of designing AP courses in most disciplines primarily to replicate typical introductory college courses.
10(b): The College Board and the IBO should evaluate their assessments to ensure that they measure the conceptual understanding and complex reasoning that should be the primary goal of advanced study. Programs of validity research should be an integral part of assessment design.
10(c): Both the College Board and the IBO should take more responsibility for ensuring the use of appropriate instructional approaches. Specifying the knowledge and skills that are important for beginning teachers and providing models for teacher development are likely to advance teacher effectiveness.
10(d): The College Board should exercise greater quality control over the AP trademark by articulating standards for what can be labeled an AP
course, desirable student preparation for each course, strategies for ensuring equity and access, and expectations for universal participation in the AP examinations by course participants. When necessary, the College Board should commission experts to assist with these tasks.3 These standards should apply whether AP is offered in schools or electronically.
10(e): The College Board and the IBO should provide assistance to schools in their efforts to offer high-quality advanced courses. To this end, the College Board should provide more detailed curriculum, information about best practices for instruction and classroom assessment, and strategies for enhancing professional development opportunities.
10(f): The College Board and the IBO should offer more guidance to educators, policymakers, and the general public concerning proper uses of their examination scores for admission, placement, and teacher evaluation. They should also actively discourage misuse of these scores.
10(g): The College Board and the IBO should develop programs of research on the implementation and effectiveness of their programs.