LEARNING AND UNDERSTANDING

IMPROVING ADVANCED STUDY OF MATHEMATICS AND SCIENCE IN U.S. HIGH SCHOOLS

Committee on Programs for Advanced Study of Mathematics and Science in American High Schools

Jerry P. Gollub, Meryl W. Bertenthal, Jay B. Labov, and Philip C. Curtis, Editors

Center for Education

Division of Behavioral and Social Sciences and Education

National Research Council

NATIONAL ACADEMY PRESS
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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools LEARNING AND UNDERSTANDING IMPROVING ADVANCED STUDY OF MATHEMATICS AND SCIENCE IN U.S. HIGH SCHOOLS Committee on Programs for Advanced Study of Mathematics and Science in American High Schools Jerry P. Gollub, Meryl W. Bertenthal, Jay B. Labov, and Philip C. Curtis, Editors Center for Education Division of Behavioral and Social Sciences and Education National Research Council NATIONAL ACADEMY PRESS Washington, DC

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools NATIONAL ACADEMY PRESS 2101 Constitution Avenue N.W. Washington, DC 20418 NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for the report were chosen for their special competences and with regard for appropriate balance. This study was conducted under an award from the National Science Foundation and the United States Department of Education (Award # ESI-9817042). Any opinions, findings, conclusions, or recommendations expressed in this report are those of the members of the committee and do not necessarily reflect the views of the sponsors. Library of Congress Cataloging-in-Publication Data Learning and understanding : improving advanced study of mathematics and science in U.S. high schools / Committee on Programs for Advanced Study of Mathematics and Science in American High Schools, Center for Education, Division of Behavioral and Social Sciences and Education ; Jerry P. Gollub … [et al.], editors. p. cm. Includes bibliographical references and index. ISBN 0-309-07440-1 1. Mathematics--Study and teaching (Secondary)—United States. 2. Science—Study and teaching (Secondary)—United States. 3. Advanced placement programs (Education) I. Gollub, J. P., 1944- II. National Research Council (U.S.). Committee on Programs for Advanced Study of Mathematics and Science in American High Schools. QA13 .L38 2002 507.1'073--dc21 2002006487 Additional copies of this report are available from National Academy Press 2101 Constitution Avenue, NW Box 285 Washington, DC 20055 800/624-6242 202/334-3313 (in the Washington Metropolitan Area) <http://www.nap.edu> Copyright 2002 by the National Academy of Sciences. All rights reserved. Printed in the United States of America. Suggested citation: National Research Council. (2002). Learning and understanding: Improving advanced study of mathematics and science in U.S. high schools. Committee on Programs for Advanced Study of Mathematics and Science in American High Schools. J.P. Gollub, M.W. Bertenthal, J.B. Labov, and P.C. Curtis, Editors. Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools THE NATIONAL ACADEMIES National Academy of Sciences National Academy of Engineering Institute of Medicine National Research Council The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Bruce M. Alberts is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineering programs aimed at meeting national needs, encourages education and research, and recognizes the superior achievements of engineers. Dr. Wm. A. Wulf is president of the National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Harvey V. Fineberg is president of the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy’s purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Bruce M. Alberts and Dr. Wm. A. Wulf are chairman and vice chairman, respectively, of the National Research Council.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools COMMITTEE ON PROGRAMS FOR ADVANCED STUDY OF MATHEMATICS AND SCIENCE IN AMERICAN HIGH SHOOLS JERRY P. GOLLUB, Cochair, Department of Physics, Haverford College PHILIP C. CURTIS, Jr., Cochair, Department of Mathematics, University of California, Los Angeles CAMILLA BENBOW, Peabody College of Education and Human Development, Vanderbilt University HILDA BORKO, School of Education, University of Colorado, Boulder WANDA BUSSEY, Department of Mathematics, Rufus King High School, Milwaukee, WI GLENN A. CROSBY, Department of Chemistry, Washington State University JOHN A. DOSSEY, Department of Mathematics (retired), Illinois State University DAVID ELY, Department of Biology, Champlain Valley Union High School, Hinesburg, VT DEBORAH HUGHES HALLETT, Department of Mathematics, University of Arizona JOHN K. HAYNES, Department of Biology, Morehouse College VALERIE E. LEE, School of Education, University of Michigan STEPHANIE PACE MARSHALL, President, Illinois Mathematics and Science Academy MICHAEL E. MARTINEZ,* Department of Education, University of California, Irvine PATSY W. MUELLER, Department of Chemistry, Highland Park High School, IL and Regina Dominican High School, Wilmette, IL JOSEPH NOVAK, Department of Education (Emeritus), Cornell University; Institute for Human and Machine Cognition, University of West Florida JEANNIE OAKES, Graduate School of Information Studies, University of California, Los Angeles VERA C. RUBIN, Department of Terrestrial Magnetism, Carnegie Foundation of Washington (through November 2, 2000) ROBIN SPITAL, Science Department, The Bolles School, Jacksonville, FL CONRAD L. STANITSKI, Department of Chemistry, University of Central Arkansas WILLIAM B. WOOD, Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder *   Michael Martinez was an active member of the committee from its inception until August 1, 2001, when he began a position as program officer in the Directorate for Human Resources at the National Science Foundation. National Research Council rules prevented Dr. Martinez from contributing to the final preparation of the report after assuming this position.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools JAY B. LABOV, Study Director, Center for Education MERYL W. BERTENTHAL, Senior Program Officer JOHN SHEPHARD, Research Assistant ANDREW E. TOMPKINS, Senior Project Assistant ALEXANDRA BEATTY, Senior Program Officer (until November 1999) RICHARD J. NOETH (until January 2000) MARILEE SHELTON, Program Officer, Board on Life Sciences (until November 2000)

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools MEMBERS OF THE DISCIPLINARY CONTENT PANELS* Biology WILLIAM B. WOOD, Committee Liaison and Chair, Department of Molecular, Cellular, and Developmental Biology, University of Colorado, Boulder ROBERT A. BLOODGOOD, Department of Cell Biology, University of Virginia MARY P. COLVARD, Department of Biology, Cobleskill-Richmond High School, NY PATRICK G. EHRMAN, Department of Molecular Biotechnology, University of Washington JOHN JUNGCK, Department of Biology, Beloit College JAMES H. WANDERSEE, Department of Curriculum and Instruction, Louisiana State University Chemistry CONRAD L. STANITSKI, Committee Liaison and Chair, Department of Chemistry, University of Central Arkansas ARTHUR B. ELLIS, Department of Chemistry, University of Wisconsin, Madison PATRICIA METZ, Department of Chemistry, United States Naval Academy JOHN C. OLIVER, Department of Chemistry, Lindbergh High School, St. Louis, MO DAVID PYSNIK, Chemistry Department, Sydney High School, Sydney, NY A. TRUMAN SCHWARTZ, Department of Chemistry, Macalester College GLENDA M. TORRANCE, Chemistry Department, Montgomery Blair High School, Silver Spring, MD Physics ROBIN SPITAL, Committee Liaison and Chair, Science Department, The Bolles School, Jacksonville, FL S. JAMES GATES, JR., Physics Department, University of Maryland, College Park DAVID M. HAMMER, Physics Department, University of Maryland, College Park *   Biographical sketches for members of the four disciplinary content panels are included as an appendix with each panel report.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools ROBERT C. HILBORN, Department of Physics, Amherst College ERIC MAZUR, Department of Applied Physics, Harvard University PENNY MOORE, College of Mathematical and Physical Sciences, Ohio State University ROBERT A. MORSE, Physics Department, St. Albans School, Washington, DC Mathematics DEBORAH HUGHES HALLETT, Committee Liaison and Chair, Department of Mathematics, University of Arizona HAROLD BOGER, Department of Mathematics, Crenshaw High School, Los Angeles, CA MARILYN P. CARLSON, Department of Mathematics, Arizona State University ROGER HOWE, Department of Mathematics, Yale University DANIEL J. TEAGUE, Department of Mathematics, North Carolina School of Science and Mathematics, Durham, NC ALAN C. TUCKER, Department of Applied Mathematics and Statistics, State University of New York, Stony Brook

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Preface The United States has compiled a remarkable record of excellence and leadership in science, mathematics, and technology over the past half century. Effective mathematics and science education at the advanced high school level is critical if this record is to continue. In addition, quality science and mathematics education is important in preparing students to succeed in higher education and to be informed citizens. This report is the product of a 2-year study of programs for advanced science and mathematics education in U.S. high schools. Recent research on learning and program design served as the basis for the analysis. This emerging knowledge was used to evaluate the Advanced Placement (AP) and International Baccalaureate (IB) programs and to examine specific ways in which these and other programs of advanced study can be made more effective and more accessible to all students who might benefit from them. The study committee comprised professional educators, teachers with experience in the AP and IB programs, university scientists and mathematicians, experts in learning and talent development, and authorities on access and equity in education. Their diverse perspectives resulted in an interdisciplinary approach to the analysis and assessment of programs for advanced study. We appreciate the cooperative efforts of the study committee to achieve a balance among these different perspectives. This study was particularly complex for several reasons. First, the committee was charged by the National Research Council (NRC) to consider advanced study in depth in four disciplines: biology, chemistry, physics, and mathematics (with an emphasis on calculus). The committee therefore convened diverse panels of experts in each of these fields, and their extensive reports form an important part of the study results, grounding the analysis in the classroom practice of advanced study programs.1 A second source of complexity in the study was the fact that the AP and IB programs must be 1   The four panel reports are available online as pdf files 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 examined in the context of the entire system of education in the United States. These programs have important effects on school curricula and staffing starting in the middle-school years, and they also influence and are shaped by trends in higher education. A third source of complexity was the dilemma of how to deal with extensive disparities in access to advanced study that have the effect of excluding many students, especially minorities and residents of impoverished communities, while continuing to ensure that traditionally advantaged students are served effectively. All members of the committee contributed generously to the study, both to discussions held during and between meetings, and, by providing draft text or comments, to the process of preparing this report. Four committee members also served as panel chairs, drafted the respective panel reports, and responded to reviews: William Wood, biology panel; Conrad Stanitski, chemistry panel; Robin Spital, physics panel; and Deborah Hughes Hallett, mathematics panel. Their exceptional efforts contributed substantially to the success of this project. We also acknowledge important scholarly work on access and equity by Valerie Lee and Jeannie Oakes. In addition, we note the central contributions of Camilla Benbow, Hilda Borko, John Dossey, Stephanie Pace Marshall, Michael Martinez, and Joseph Novak, who as a group developed the material presented in Chapters 6 and 7 and guided the analyses of Chapters 8 and 9. We thank David Ely, Patsy Mueller, Robin Spital, and Wanda Bussey, the members of the committee who are teachers of the AP and IB programs, for helping the committee understand today’s high school settings. Finally, we acknowledge Glenn Crosby’s contributions to our discussions of teacher education and professional development. The NRC’s Center for Education provided exceptional support for this project. Project director Jay Labov and senior program officer Meryl Bertenthal worked tirelessly to seek out the extensive information required by the study committee and to help overcome obstacles to achieving consensus. They also contributed substantially to the process of drafting this report and guiding the panel reports successfully through the stringent NRC review process. We appreciate as well the capable efforts of John Shephard and Andrew Tompkins, our research and project assistants. Leslie Ann Pierce, an experienced AP and IB teacher, served as consultant to the committee and contributed to the report. Program officer Marilee Shelton and consultant Billy Goodman assisted in the early phases of the project. We acknowledge the helpfulness of the staff of the AP and IB, who provided the committee with extensive information. Their commitment to the long-term improvement of these programs and their receptiveness to the committee’s ideas were evident. Although this report constitutes a strong critique in many respects, its recommendations should not be regarded either as questioning the importance of these programs or as conflicting with improvement efforts already in progress. The active collaboration of many

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools different groups will be required to implement the recommendations of this study. This study is part of a major commitment by the NRC to use its expertise in the service of science and mathematics education. The committee anticipates that the report will be useful to all those concerned with improving educational quality and equity, including program developers, science and mathematics teachers, university scientists, policymakers, school administrators, and parents. Jerry W. Gollub and Philip C. Curtis, Cochairs

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools of North America (IBNA), for providing program materials and data throughout the study. They attended several committee meetings and workshops as invited guests, organized presentations to the committee, and answered ongoing questions about their respective programs. Their cooperation was critical to our efforts. When this study began, the IB program was less familiar than the AP program to most committee members. We thank the many individuals who provided the committee with in-depth information about the IB program. David Roylance, IB coordinator, Jeb Stuart High School in Fairfax, Virginia, presented an overview of the IB program model. The committee obtained insight into the structure, organization, and goals of IB science and mathematics curricula, instructional models, assessment, and professional development opportunities from Jonathan Knopp, Rufus King High School, Milwaukee, Wisconsin; Ken Fox, Smoky Hill High School, Aurora, Colorado; Arden Zipp, State University of New York at Courtland; and IBNA associate director Paul Campbell. We acknowledge as well the ongoing help received from IBNA staff members George Pook, Roger Brown, Jeff Thompson, and Helen Drennen. Individually and collectively, members of the committee benefited from discussions with experts in a variety of fields. We especially thank James Pellegrino, University of Illinois at Chicago, and José Mestre, University of Massachusetts at Amherst, who helped expand our understanding of the relevance of research on human cognition to the design and evaluation of advanced study programs. Their advice helped the committee conceptualize the model presented in this report for the design and evaluation of advanced study programs. Results from the Third International Mathematics and Science Study (TIMMS) contributed to the motivation for this study. We wish to thank Michael Martin, TIMSS international deputy study director, and Patrick Gonzales, National Center for Education Statistics, U.S. Department of Education, for helping the committee understand the TIMMS results. Many individuals aided the committee’s work by participating in a series of information-gathering workshops that were held in conjunction with several of the committee’s meetings. The following individuals participated in a committee workshop addressing the design and development of AP programs and assessments in mathematics and science: Dr. John Smarrelli, chair, AP Biology Committee, Loyola University, Chicago; Dr. Robert Cannon, chief faculty consultant, AP Biology, University of North Carolina at Chapel Hill; Dr. Thomas P. Dick, chair, AP Calculus Committee, Oregon State University; Dr. Larry Riddle, chief faculty consultant, AP Calculus, Agnes Scott College; Dr. William H. Ingham, chair, AP Physics Committee, James Madison University; Patrick Polley, chief faculty consultant, AP Physics, Beloit College; Beth Nichols, assessment specialist, Educational Testing Service; Chancey Jones,

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools assessment specialist, Educational Testing Service; Ann Marie Zolandz, assessment specialist, Educational Testing Service; and Rick Morgan, measurement statistician, Educational Testing Service. Howard Everson, The College Board vice-president for Teaching and Learning, was also instrumental in helping the committee understand the mission and goals of the AP program. Bernard L. Madison, professor of mathematics, University of Arkansas, Fayetteville, and a member of the College Board’s Commission on the Future of the Advanced Placement Program, provided the committee with an overview of the commission’s findings and recommendations. Three individuals—Peter O’Donnell, president of the O’Donnell Foundation in Dallas, Texas; Carolyn Bacon, executive director of the Foundation; and Gregg Fleisher, president, Advanced Placement Strategies—spoke with the committee about an innovative program that engages students, teachers, and schools in an effort to increase the number of traditionally underrepresented Texas students who take AP courses and succeed on AP examinations. We also acknowledge several consultants who contributed significantly to the project. Carolyn Callahan, University of Virginia, helped the committee understand the roles of AP and IB in meeting the needs of gifted and talented students. Karen Boeschenstein, Office of Undergraduate Admission at the University of Virginia, assisted the committee in interpreting data that was gathered through an informal survey of deans of admission (see Chapters 2 and 10). Bert Green, The Johns Hopkins University, helped the committee with an independent evaluation and interpretation of the College Board’s AP validity studies (see Chapter 10). Julie Heifetz, Moss Rehabilitation Center in Philadelphia, Pennsylvania, interviewed AP and IB students from different schools. Many individuals within the National Research Council (NRC) assisted the committee. We are grateful for the support of Bruce Alberts, president of the National Academy of Sciences, who took a particular interest in this study and provided support and encouragement along the way. Alexandra Beatty drafted the original proposal for the project, and Richard Noeth was study director in the early months of the project. We thank Michael Feuer, director of the Center for Education, for his support and encouragement, and Kirsten Sampson Snyder, who shepherded the four panel reports and the main committee report through the NRC review process, and Yvonne Wise for processing the report through final production. Genie Grohman gave valuable assistance in thinking about the organization of this report, and Judy Koenig contributed to the assessment sections of the report. Rona Briere capably edited the final version. Naomi Chudowsky, study director of the Cognitive Foundations of Assessment Committee, shared with us early drafts of her committee’s report and consulted with us about our conceptual model for the design and evaluation of advanced study programs. Brenda

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Buchbinder managed the finances of the project, and Viola Horek, administrative officer for the Center for Education, provided important assistance. This report has been reviewed in draft form by individuals chosen for their diverse perspectives and technical expertise, in accordance with procedures approved by the NRC’s Report Review Committee. The purpose of this independent review is to provide candid and critical comments that will assist the institution in making the published report as sound as possible and to ensure that the report meets institutional standards for objectivity, evidence, and responsiveness to the study charge. The review comments and draft manuscript remain confidential to protect the integrity of the deliberative process. We wish to thank the following individuals for their participation in the review of this report: Jo Boaler, Stanford University Stephen B. Dunbar, University of Iowa Martin L. Johnson, University of Maryland Joel J. Mintzes, University of North Carolina at Wilmington Carolyn J. Morse, University of North Carolina at Chapel Hill Harris Sokoloff, University of Pennsylvania Patsy Wang-Iverson, Research for Better Schools James A. Watts, Southern Regional Education Board Although the reviewers listed above have provided many constructive comments and suggestions, they were not asked to endorse the conclusions or recommendations nor did they see the final draft of the report before its release. The review of this report was overseen by Royce W. Murray and Melvin C. George. Appointed by the NRC, they were responsible for making certain that an independent examination of this report was carried out in accordance with institutional procedures and that all review comments were carefully considered. Responsibility for the final content of this report rests entirely with the authoring committee and the institution. In addition, the following individuals served as reviewers for the four panel reports included as supporting documentation in this volume: Biology: Neil A. Campbell, University of California, Riverside Warren Hunnicutt, St. Petersburg Junior College, FL Charles Lytle, North Carolina State University Randy McGonegal, Palm Harbor University High School, Palm Harbor, FL Duncan MacQuarrie, Tacoma Public Schools, Tacoma, Washington

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Chemistry: William R. Robinson, Purdue University Keith Sheppard, Columbia University Myra Thayer, Fairfax County Public Schools, Virginia David Thissen, University of North Carolina at Chapel Hill Physics: Susan A. Agruso, Charlotte-Mecklenburg School District, North Carolina Arthur Eisenkraft, Foxlane High School, Bedford, NY Mark Headlee, United World College, Montezuma, NM William H. Ingham, James Madison University Kris Whelan, Plano Independent School District, Plano, TX Mathematics: John R. Brunsting, Hinsdale Central High School, Hinsdale, IL Miriam Clifford, Caroll College, Waukesha, WI Renee Fish, Palm Harbor University High School, Palm Harbor, FL Michael J. Kolen, University of Iowa Thomas W. Tucker, Colgate University Although the reviewers listed above have provided many constructive comments and suggestions, they were not asked to endorse the conclusions or recommendations of the panel reports, nor did they see the final drafts of the reports before their release. The review of these reports was overseen by Philip C. Curtis. Appointed by the NRC, he was responsible for making certain that an independent examination of these reports was carried out in accordance with institutional procedures and that all review comments were carefully considered. Responsibility for the final content of these reports rests entirely with the authoring panels and the institution. As a final note, we would like to acknowledge that when copyright permissions were being sought from various sources, the IBO pointed out several inaccuracies in our listing of their programs. Since this report was already in the final stages of printing when these errors were noted, we correct them here for the entire report and extend our apologies to the IBO: The “program guides” to which we refer throughout the main report as well as the content panel reports should instead be labeled as “subject guides” in specific disciplines (e.g., Chemistry guide). The IB Diploma Programme is one of three academic programs. The IBO is now using the U.S. spelling of “Organization” as part of its official name rather than “Organisation” that is presented throughout this report. Finally, it also should be noted that permission to reprint AP materials does not constitute review or endorsement by the Educational Testing Service or the College Board of this publication as a whole or of any questions or testing information it may contain.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Contents     EXECUTIVE SUMMARY   1 1.   INTRODUCTION   17      Background,   18      Brief Overview of the Programs,   20      What Is Advanced Study?,   22      The Student Clientele for Advanced Study,   23      Study Charge and Approach,   24      Audiences for the Report,   26      Overview and Structure of the Report,   26 2.   CONTEXT OF ADVANCED STUDY   28      Policy Context,   29      Educational Context,   36      Disparities in Opportunities to Pursue and Succeed in Advanced Study,   47      Connections Between Advanced Study and Higher Education,   51      Epilogue,   63 3.   THE ADVANCED PLACEMENT PROGRAM   64      Overview,   64      AP Curriculum,   66      AP Instruction,   71      AP Assessment,   75      AP Professional Development,   79

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools 4.   THE INTERNATIONAL BACCALAUREATE PROGRAMME   83      Overview,   83      IB Curriculum,   86      IB Instruction,   92      IB Assessment,   94      IB Professional Development,   100 5.   OTHER OPPORTUNITIES AND APPROACHES TO ADVANCED STUDY   103      Alternatives for Providing College-Level Learning in High School,   103      Enrichment Activities,   113      Conclusion,   116 6.   LEARNING WITH UNDERSTANDING: SEVEN PRINCIPLES   117      Seven Principles of Human Learning,   118      Conclusion,   129     ANNEX 6-1 Characteristics of High-Ability Learners and Implications for Curriculum and Instruction,   130 7.   DESIGNING CURRICULUM, INSTRUCTION, ASSESSMENT, AND PROFESSIONAL DEVELOPMENT   134      Curriculum,   135      Instruction,   137      Assessment,   141      Teacher Professional Development,   146      From Framework to Advanced Study Programs,   152 8.   ANALYSIS OF THE AP AND IB PROGRAMS BASED ON LEARNING RESEARCH   154      Principled Conceptual Knowledge,   156      Prior Knowledge,   160      Metacognition,   164      Differences Among Learners,   166      Motivation,   168      Learning Communities,   170      Learning in Context,   172      Concluding Remarks,   174

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools 9.   ANALYSIS OF AP AND IB CURRICULUM, INSTRUCTION, ASSESSMENT, AND PROFESSIONAL DEVELOPMENT   176      Curriculum,   176      Instruction,   178      Assessment,   180      Professional Development,   183      Conclusion,   184 10.   USES, MISUSES, AND UNINTENDED CONSEQUENCES OF AP AND IB   185      High Stakes,   185      Quality Control,   188      Access and Equity,   191      College Credit and Placement,   192      Conclusion,   196 11.   RECOMMENDATIONS   197     Recommendation 1:  The Primary Goal of Advanced Study,   197     Recommendation 2:  Access and Equity,   198     Recommendation 3:  Learning Principles,   199     Recommendation 4:  Curriculum,   199     Recommendation 5:  Instruction,   200     Recommendation 6:  Assessment,   201     Recommendation 7:  Qualified Teachers and Professional Development,   201     Recommendation 8:  Alternative Programs,   202     Recommendation 9:  The Secondary–College Interface,   202     Recommendation 10:  Changes in the AP and IB Programs,   203     REFERENCES   206 APPENDIX A:   Overview of Panel Findings and Recommendations   229 APPENDIX B:   Biographical Sketches of Committee Members   253

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools APPENDIX C:   Statement of Task   259     INDEX   261     CONTENT PANEL REPORTS*     Biology   273     Chemistry   337     Physics   393     Mathematics   483 *   Content Panel Reports are not printed in this volume but are available online. Go to http://www.nap.edu and search for Learning and Understanding.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools LEARNING AND UNDERSTANDING

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