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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 supported by Contract/Grant No. ESI-9816818 between the National Academy of Sciences and the ExxonMobil Foundation. Additional support was also provided by the U.S. Department of Education and the National Science Foundation. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the organizations or agencies that provided support for the project.
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Library of Congress Catalog Control Number: 2002106187
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Copyright 2002 by the National Academy of Sciences. All rights reserved.
Suggested citation: National Research Council. (2002). Helping Children Learn Mathematics. Mathematics Learning Study Committee, J.Kilpatrick and J.Swafford, Editors. Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
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MATHEMATICS LEARNING STUDY COMMITTEE
JEREMY KILPATRICK, Chair,
University of Georgia
DEBORAH LOEWENBERG BALL,
University of Michigan
HYMAN BASS,
University of Michigan
JERE BROPHY,
Michigan State University
FELIX BROWDER,
Rutgers University
THOMAS P.CARPENTER,
University of Wisconsin-Madison
CAROLYN DAY,
Dayton Public Schools
KAREN FUSON,
Northwestern University
JAMES HIEBERT,
University of Delaware
ROGER HOWE,
Yale University
CAROLYN KIERAN,
University of Quebec, Montreal
RICHARD E.MAYER,
University of California, Santa Barbara
KEVIN MILLER,
University of Illinois, Urbana-Champaign
CASILDA PARDO,
Albuquerque Public Schools
EDGAR ROBINSON,
ExxonMobil Corporation (Retired)
HUNG HSI WU,
University of California, Berkeley
JANE SWAFFORD, Study Director
BRADFORD FINDELL, Program Officer
BRIAN McQUILLAN, Senior Project Assistant
CAROLE LACAMPAGNE, Director,
Mathematical Sciences Education Board
Acknowledgments
In preparing this book, we had the good fortune of working with a number of people who shared our enthusiasm for the project, and we are indebted to them for the insights and assistance they provided. The entire Mathematics Learning Study Committee contributed valuable ideas, but we particularly acknowledge the members of the subcommittee who conceptualized and shaped the book: Thomas Carpenter, James Hiebert, Casilda Pardo, and Edgar Robinson. We are grateful to them for their inspiration, hard work, and guidance. During the outlining and preliminary drafting of the book, we benefited from the views and prose provided by Pat McNees, a writer consultant. And we are especially indebted to Steve Olson, who took our rough drafts and sketchy ideas and turned them into this final product. Without his expert editorial assistance, the project might never have been completed.
We would like to thank our sponsor for this book, the ExxonMobil Foundation, for seeking to engage a much broader audience in discussion and action. In particular, we thank Edward Ahnert, president of the Foundation, and Joe Gonzales, program officer, for their support and interest. We also want to thank the sponsors of the Mathematics Learning Study, the National Science Foundation and the U.S. Department of Education, for their continued support during the production of the book.
This book has been reviewed by individuals chosen for their diverse perspectives and technical expertise, in accordance with procedures approved by the National Research Council’s (NRC) 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 book as sound as possible and to ensure that the book 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 thank the following individuals for their review of this book: Arthur J.Baroody, Department of Curriculum and Instruction, University of Illinois; Keith Devlin, Center for the Study of Language and Information, Stanford University; Nancy A.Doorey, Brandywine School District, Delaware; Andrew M.Gleason, Department of Mathematics, Harvard University; Nancy Larson, West Haven Schools, Connecticut; Mike Riley, Bellevue School District, Washington; Zalman P. Usiskin, Department of Education, University of Chicago; and Carrie L.Valentine, Madison Metropolitan School District and University of Wisconsin.
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 book before its release. The review of this book was overseen by Alfred Manaster, University of California at San Diego, and Patrick Suppes, Stanford University. Appointed by the NRC, they were responsible for making certain that an independent examination of this book was carried out in accordance with institutional procedures and that all review comments were carefully considered. Responsibility for the final content of this book rests solely with the authoring committee and the NRC.
Finally, we extend our sincere thanks to a number of individuals at the NRC who made significant contributions to our work: Michael J.Feuer, director of the Center for Education (CFE), for providing key advice; Kirsten Sampson Snyder, reports officer for CFE, for guiding us through the report review process; Bradford Findell, former program officer, for his contributions to several drafts; Patricia Morison, senior program officer, for shepherding this project through its final stages; Sally Stanfield and Francesca Moghari, National Academy Press, for making our book look so nice; Carole Lacampagne for her wise advice during late stages; and Dionna Williams and Yvonne Wise for help with production. Last, we would like to express our appreciation to Brian McQuillan, senior project assistant, who provided a wealth of logistical support during the project.
Jeremy Kilpatrick, Chair
Jane Swafford, Study Director
Mathematics Learning Study Committee