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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools 11 Recommendations Chapters 6 and 7 of this report present a framework for examining programs of advanced study. This framework is based on extensive research on student learning and the implications of that research for the design and integration of curriculum, instruction, assessment, and professional development. In Chapters 8 and 9 this framework is used to analyze the Advanced Placement (AP) and International Baccalaureate (IB) programs; areas in which there is alignment with the principles of learning are highlighted, as are aspects of the programs that deviate from those principles. Chapter 10 provides further analysis through an examination of the uses, misuses, and unintended consequences of the AP and IB programs and examination results. The present chapter presents a set of recommended actions that could significantly improve existing programs for and approaches to advanced study and serve as the basis for the design of alternatives. Italic type is used to highlight particular groups to which the recommendations are directed. However, given the diversity and decentralized nature of the educational system in the United States, the committee leaves specific implementation strategies to local and state education agencies. Similarly, program developers must also decide how to execute our recommendations within the unique structures of their respective organizations. The committee’s first and most important recommendation articulates a principle concerning the goals of advanced study and is addressed to all those involved in developing or teaching advanced study courses. 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
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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools 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. It is not enough for students to achieve familiarity with factual content alone; they need to understand the central ideas of the discipline in order to build a conceptual framework for further learning and apply what they have learned to new situations and to other disciplines. A consequence of this principle is that accelerating students’ exposure to college-level material, while appropriate as a component of some secondary advanced study programs, is not by itself a sufficient goal. Except for a small number of highly able students, courses that pursue acceleration as the sole objective may proceed too quickly for many students to develop deep conceptual understanding. 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. Many additional students could benefit from participation in advanced study given improved preparation in earlier years and wider program availability. As documented in Chapter 2, certain racial and ethnic groups (including African American and Hispanic students) are substantially underrepresented among matriculants in advanced courses and among AP test takers, though the causes for this are unclear. A coherent plan that extended across grade levels and schools within a district could enable a higher proportion of potentially qualified students to benefit from advanced study. By treating all students as potential participants while in grades 6–10, schools could help even those who do not eventually enroll in advanced study to emerge with strong foundations in mathematics and science. The positive effects on student achievement of a high school curriculum that stresses high levels of academic learning for all students have been demonstrated empirically (Lee, 2001; Lee, Burkam, Chow-Hoy, Smerdon, and Geverdt, 1998; Lee, Croninger, and Smith, 1997). The committee therefore recommends that high schools eliminate low-level, “dead-end” math-
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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools ematics and science courses,1 which do not afford students the opportunity to prepare adequately for advanced study. Additional support will be needed to make this recommended action work for some students. Access to advanced study is currently limited in many schools, especially those that are located in rural areas, urban centers, and other localities that enroll large proportions of low-income and minority students. States, school districts, and program developers (those who design courses for advanced study) must work to expand these opportunities to all schools. Finally, districts, with the support of advanced study programs, must provide substantial professional development opportunities for teachers, invest appropriately in laboratory facilities and materials, and develop academic support systems for those students who need them. 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. Program developers should collaborate with discipline experts, researchers in pedagogy and cognitive science, and master teachers to examine existing programs and develop new ones. They should ensure that the components of their programs (curriculum, instruction, assessment, and professional development) are consistent with what is known about how people learn and work together to foster students’ conceptual understanding. 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 infor- 1 The committee chose not to cite such courses specifically by name because (1) the decentralized nature of U.S. education means that school districts title their courses in accordance with their own unique curriculum structure, and labeling conventions making it difficult to name with accuracy all the possible courses to which we refer; and (2) similarly titled courses offered in different school districts could be very different (for example, a course called “general chemistry” could provide adequate preparation for advanced study in one district but not in another). The committee chose, therefore, to define low-level courses as those that leave a student unprepared for further study in the discipline.
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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools mation on which those concepts and principles are based. Because science and technology progress rapidly, frequent review of course content is essential. Curricula should be focused on a reasonable number of concepts that can be studied in depth during the time allotted. Integration of the advanced study curriculum with earlier courses is essential, because building on earlier experiences can contribute to achieving both breadth of knowledge and depth of understanding over a period of years. It may sometimes make sense for advanced courses to extend over multiple school years to allow sufficient time for this process, as occurs in the IB program. Identifying organizing principles and structuring them appropriately for advanced learners is labor-intensive and requires varied expertise. Therefore, effective curriculum development must be a collaborative effort conducted by teams of experienced teachers working with curriculum specialists and experts in the disciplines, in cognitive theory, and in pedagogy. The teams need to use a systematic approach to the development process that is aligned with the principles of learning set forth in this report and that involves repeated cycles of design, trial teaching with students, evaluation, and revision. 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. While the quality of instruction depends on the knowledge, creativity, and sensitivity of teachers, program developers can do much to suggest possible strategies, and school administrators need to provide both material resources and opportunities for professional development if high-quality teaching is to be achieved. Effective ways to use the Internet and other electronic resources should be encouraged and evaluated. In general, the committee recommends careful alignment of instruction with the National Science Education Standards (NRC, 1996) and the standards proposed by the National Council of Teachers of Mathematics (NCTM, 1991) and the National Board for Professional Teaching Standards (NBPTS, 2001).
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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools 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). Since end-of-course assessments strongly influence instruction, program staff must ensure that these assessments measure students’ depth of understanding and their ability to transfer knowledge to unfamiliar situations. Programs should report the results of their end-of-year assessments in sufficient detail so the results are useful to students in evaluating what they have learned, to colleges in advising students accurately on their course options, and to schools and teachers in improving their advanced study courses and programs. Combining the results of several different indicators instead of relying solely or primarily on the results of a single high-stakes examination can provide a more accurate picture of student achievement. Program staff should assist teachers in developing formative assessments that measure student progress toward desired learning outcomes. While classroom assessment is primarily the responsibility of teachers, programs can favorably affect student progress and increase teacher effectiveness by suggesting appropriate strategies and providing examples. 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. Professionals in most demanding fields require continuing education to maintain and improve their knowledge over time. The same applies to teachers. Professional development should emphasize deep understanding of content and discipline-based methods of inquiry, provide multiple perspectives on students as learners, and develop teachers’ subject-specific pedagogical knowledge and skills. It should treat teachers as active learners,
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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools build on their existing knowledge, and take place in professional communities where colleagues have the opportunity to discuss ideas and practices. Many groups can contribute effectively to teacher professional development. Discipline-based professional associations should help identify the knowledge and skills required for excellent teaching. Researchers should investigate the effects of different levels of teacher professional development on student learning and achievement in advanced study. University and college science and mathematics departments and schools of education must work collaboratively to develop discipline-specific approaches to teacher preparation and continuing professional development. States, in monitoring the quality of local education, should collect and report data on the qualifications of teachers of advanced study. National programs of advanced study should assume greater responsibility for assisting schools, districts, and states in developing professional development programs and in upgrading their own programs in the ways suggested in this report. 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. Some small-scale alternatives are described in Chapter 5. However, there is much room for new ideas. Funding and research agencies should encourage the development of additional advanced study options and should collect and disseminate information about existing alternatives that might become national models. Little has been said in this report about the special needs of very high-ability students (the top few percent in mathematics and science). However, the committee urges funding agencies to sponsor research related to the learning needs of these exceptional students and to support educators in the development of innovative strategies for meeting those needs. 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.
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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Legislatures should avoid imposing laws or regulations requiring public colleges and universities to award credit for specified minimum scores on AP or IB examinations. Offices of college admissions should emphasize that taking advanced study courses without doing well in them or without taking the exams is insufficient. Program developers should clearly discourage any-one from using their programs and assessment results to draw inappropriate inferences about teachers, schools, and communities. 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. It is still common in some introductory college science and mathematics courses to cover large numbers of topics relatively superficially and with little connection to the world in which the topics are applied, thereby encouraging memorization at the expense of developing deep understanding of concepts and principles. These courses need to be brought into alignment with Recommendations 4 through 6, in part because teachers’ ideas about how to teach science and mathematics come from their own college experiences. Many students who participate in secondary advanced study later enroll in introductory college courses. Therefore, these college courses need to evolve so that they will continue to be appropriate for audiences with diverse preparation. RECOMMENDATION 10: CHANGES IN THE AP AND IB PROGRAMS 10(a): The College Board should abandon its practice of designing AP courses in most disciplines primarily to replicate typical introductory college courses. The committee endorses recent moves by the College Board in this direction. As noted in particular in the report prepared by the calculus panel for this study, the College Board now bases AP calculus on expected outcomes and emerging best practices in college and university courses, rather than on lists of topics to be covered and tested. This approach, embraced by most of the mathematics professional communities, can serve as a model for revisions in other subject areas. 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
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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools 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.2 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. This research should address such questions as the following: What is the preparation of teachers in these programs? What instructional strategies are actually used in practice, as indicated by classroom observation? How effective are the AP and IB professional development activities? How do the programs affect other school offerings and the curricula of the preceding years? How do students who participate in the AP and IB programs fare in college as compared with students lacking this experience? How are their choices of college courses affected? How do students fare who take the 2 The committee notes that the College Board has used this strategy in the past. For example, in 1997 the National Task Force on Minority High Achievement was convened to assist the College Board in outlining recommendations for substantially increasing the number of African American, Latino, and Native American undergraduates who achieve high levels of academic success.
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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools courses but not the exams? What is the impact on colleges of the large numbers of students earning credit through advanced study? Answers to such questions are urgently needed if the programs are to improve. Given the large and growing investment in this segment of secondary education, a substantial research effort is justified. Both public and private agencies should be prepared to assist in sponsoring this research. The various parties, including the agencies and the programs, should consider how to ensure independent review of the results. The College Board and the IBO should develop ways to incorporate the results of this recommended research systematically into the ongoing improvement of their programs.
Representative terms from entire chapter: