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Improving Mathematics Education: Resources for Decision Making

Committee on Decisions That Count

Steve Leinwand and Gail Burrill, editors

Mathematical Sciences Education Board

Center for Education

Division of Behavioral and Social Sciences and Education

National Research Council


National Academy Press
Washington, DC
2001



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Page i Improving Mathematics Education: Resources for Decision Making Committee on Decisions That Count Steve Leinwand and Gail Burrill, editors Mathematical Sciences Education Board Center for Education Division of Behavioral and Social Sciences and Education National Research Council National Academy Press Washington, DC2001

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Page ii NATIONAL ACADEMY PRESS 2101 Constitution Avenue, NW 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. The study was supported by Contract/Grant No. ESI 9618770, between the National Academy of Sciences and the National Science Foundation. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the view of the organizations or agencies that provided support for this project. International Standard Book Number 0-309-08300-1 Additional copies of this report are available from National Academy Press , 2101 Constitution Avenue, NW , Lockbox 285, Washington, DC 20418 . Call (800) 624–6242 or (202) 334–3313 (in the Washington metropolitan area). This report is also available online at http://www.nap.edu Copyright 2001 by the National Academy of Sciences . All rights reserved. Suggested citation: National Research Council. (2001). Improving Mathematics Education: Resources for Decision Making. Committee on Decisions That Count, Steve Leinwand and Gail Burrill (Eds.). Mathematical Sciences Education Board, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.

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Page iii THE NATIONAL ACADEMIES Advisers to the Nation on Science, Engineering, and Medicine 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. Kenneth I.Shine 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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Page iv

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Page v Committee on Decisions That Count Joan R.Leitzel, Chair, University of New Hampshire Jere Confrey, Vice-Chair, University of Texas at Austin Deborah Loewenberg Ball, University of Michigan Richelle Blair, Lakeland Community College, Ohio Jan de Lange, Freudenthal Institute, The Netherlands Joan Ferrini-Mundy, Michigan State University Dan Kennedy, The Baylor School, Chattanooga, Tennessee Thomas L.Moore, Grinnell College, Grinnell, Iowa Marge M.Petit, National Center for the Improvement of Educational Assessment, Portsmouth, New Hampshire William Steenken, GE Aircraft Engines, Hamilton, Ohio Jerry Uhl, University of Illinois at Urbana-Champaign Staff Gail Burrill, Director, Mathematical Sciences Education Board Brian McQuillan, Senior Project Assistant, Mathematical Sciences Education Board

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Page vi Mathematical Sciences Education Board Joan R.Leitzel, Chair, University of New Hampshire Jere Confrey, Vice Chair, University of Texas at Austin Judy Ackerman, Montgomery College, Rockville, Maryland Richard A.Askey, University of Wisconsin-Madison Deborah Loewenberg Ball, University of Michigan Richelle Blair, Lakeland Community College, Kirtland, Ohio Ingrid Daubechies, Princeton University Jan de Lange, Freudenthal Institute, The Netherlands Keith Devlin, St. Mary's College of California, Moraga, California Karen Economopoulos, TERC, Cambridge, Massachusetts Susan Eyestone, National Parent Teacher Association, Minneapolis, Minnesota Joan Ferrini-Mundy, Michigan State University Arthur M.Jaffe, Harvard University Dan Kennedy, The Baylor School, Chattanooga, Tennessee Karen Longhart, Flathead High School, Kalispell, Montana Miriam Masullo, IBM Corporation, Yorktown Height, New York Thomas L.Moore, Grinnell College, Grinnell, Iowa Debra Paulson, Hornedo Middle School, El Paso, Texas Marge M.Petit, The National Center for the Improvement of Educational Assessment, Portsmouth, New Hampshire Anthony Scott, Chicago Public Schools, Illinois William Steenken, GE Aircraft Engines, Hamilton, Ohio Lee V.Stiff, North Carolina State University James W.Stigler, University of California, Los Angeles Jerry Uhl, University of Illinois at Urbana-Champaign

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Page vii ACKNOWLEDGMENTS The Mathematical Sciences Education Board gratefully acknowledges the National Science Foundation for its financial support of Improving Mathematics Education: Resources for Decision Making. Any opinions expressed herein are those of the authors and do not reflect those of the funders. We would especially like to acknowledge Brian McQuillan at the Center for Education for his effort in providing administrative support for the report. We also thank the authors, editors, and those responsible for developing the eight documents cited in this report for reviewing the text we selected for inclusion and for their input in making sure the right messages were highlighted. 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 its 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 review of this report: Henry L.Alder, University of California, Davis Francis Fennell, University of Western Maryland DeAnn Huinker, University of Wisconsin-Milwaukee Jeane Joyner, North Carolina Department of Public Instruction Pamela Matthews, National Education Association Jackie Mitchell, Maine Department of Education Sharon Stenglein, Minnesota Department of Education 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 Edward A.Silver, University of Michigan, and William G.Howard, Jr., Independent Consultant, Scottsdale, Arizona. Appointed by the National Research Council, 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.

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Page viii

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Page ix CONTENTS 1     Introduction 1 2     What Should We Teach? 5     • Principles and Standards for School Mathematics, developed by the National Council of Teachers of Mathematics, 2000 3     How Should We Teach? 10     • Adding It Up: Helping Children Learn Mathematics, developed by the National Research Council's Mathematics Learning Study Committee, 2001     • How People Learn: Brain, Mind, Experience, and School, developed by the National Research Council's Committee on Developments in the Science of Learning and the Committee on Learning Research and Educational Practice, 2000 4     What Preparation and Support Do Teachers Need? 19     • Before It's Too Late: A Report to the Nation from the National Commission on Mathematics and Science Teaching for the 21 st Century, chartered by the United States Secretary of Education, 2000     • Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millennium, developed by the National Research Council's Committee on Science and Mathematics Teacher Preparation, 2001     • The Mathematical Education of Teachers, developed by the Conference Board of the Mathematical Sciences, 2001 5     How Do We Know That What We Are Doing Is Working? 30     • High Stakes: Testing for Tracking, Promotion, and Graduation, developed by the National Research Council's Committee on Appropriate Test Use, 1999 6     What Must Change? 35     • Every Child Mathematically Proficient: An Action Plan of the Learning First Alliance, 1998

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Page x 7     Conclusion 40 Securing Copies of the Resources Summarized 47 References 48