MATHEMATICS LEARNING in Early Childhood

Paths Toward Excellence and Equity

Committee on Early Childhood Mathematics

Christopher T. Cross, Taniesha A. Woods, and Heidi Schweingruber, Editors

Center for Education

Division of Behavioral and Social Sciences and Education

NATIONAL RESEARCH COUNCIL OF THE NATIONAL ACADEMIES

THE NATIONAL ACADEMIES PRESS

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MAT HEMAT ICS LEAR NIN G in Early Childhood Paths Toward Excellence and Equity Committee on Early Childhood Mathematics Christopher T. Cross, Taniesha A. Woods, and Heidi Schweingruber, Editors Center for Education Division of Behavioral and Social Sciences and Education

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THE NATIONAL ACADEMIES PRESS 500 Fifth Street, N.W. Washington, DC 20001 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 No. HHSP23320042509X1,TO#10 between the National Academy of Sciences and the U.S. Department of Health and Human Services; by Contracts No. HHSN267200700434P and HHSN267200800606P with the National Institute of Child Health and Human Development; by Contract No. 20070221 with the Ewing Marion Kauffman Foundation; and by the Presi- dent’s Fund of the National Research Council. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the organizations or agencies that provided support for the project. Library of Congress Cataloging-in-Publication Data Mathematics learning in early childhood : paths toward excellence and equity / Christopher T. Cross, Taniesha A. Woods, and Heidi Schweingruber, editors ; Committee on Early Childhood Mathematics, Center for Education, Division of Behavioral and Social Sciences and Education. p. cm. Includes bibliographical references and index. ISBN 978-0-309-12806-3 (hardback) — ISBN 978-0-309-12807-0 (pdf) 1. Mathematics—Study and teaching (Early childhood) 2. Early childhood education. I. Cross, Christopher T. II. Woods, Taniesha A. III. Schweingruber, Heidi A. IV. National Research Council (U.S.). Committee on Early Childhood Mathematics. QA135.6.M384 2009 372.7—dc22 2009033436 Additional copies of this report are available from National Academies Press, 500 Fifth Street, N.W., Lockbox 285, Washington, DC 20055; (800) 624-6242 or (202) 334-3313 (in the Washington metropolitan area); Internet, http://www.nap.edu. Copyright 2009 by the National Academy of Sciences. All rights reserved. Printed in the United States of America Suggested citation: National Research Council. (2009). Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. Committee on Early Childhood Mathematics, Christopher T. Cross, Taniesha A. Woods, and Heidi Schweingruber, Editors. Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: The National Academies Press.

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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 Acad- emy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Ralph J. Cicerone 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 en- gineers. 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 engineer- ing programs aimed at meeting national needs, encourages education and research, and recognizes the superior achievements of engineers. Dr. Charles M. Vest is presi- dent 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 Insti- tute 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 Sci- ences 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. Ralph J. Cicerone and Dr. Charles M. Vest are chair and vice chair, respectively, of the National Research Council. www.national-academies.org

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COMMITTEE ON EARLY CHILDHOOD MATHEMATICS CHRISTOPHER T. CROSS (Chair), Cross & Joftus, LLC, Danville, California OSCAR BARBARIN, School of Social Work, University of North Carolina, Chapel Hill SYBILLA BECKMANN, Department of Mathematics, University of Georgia SUE BREDEKAMP, Council for Early Childhood Professional Recognition, Washington, DC DOUGLAS H. CLEMENTS, Department of Learning and Instruction, The State University of New York at Buffalo KAREN C. FUSON, School of Education and Social Policy, Northwestern University YOLANDA GARCIA, E3 Institute for Advancing Excellence in Early Education, WestEd, San Jose, California HERBERT GINSBURG, Department of Human Development, Teachers College, Columbia University NANCY C. JORDAN, School of Education, University of Delaware SHARON LYNN KAGAN, Teachers College, Columbia University SUSAN C. LEVINE, Department of Psychology, Department of Comparative Human Development, and Committee on Education, University of Chicago KEVIN MILLER, Combined Program in Education and Psychology, University of Michigan, Ann Arbor ROBERT C. PIANTA, Curry School of Education, University of Virginia TANIESHA A. WOODS, Study Director PATRICIA MORISON, Interim Director, Center for Education HEIDI SCHWEINGRUBER, Deputy Director, Board on Science Education MARY ANN KASPER, Senior Program Assistant 

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Preface Early childhood education has risen to the top of the national policy agenda with recognition that ensuring educational success and attainment must begin in the earliest years of schooling. There is now a substantial body of research to guide efforts to support young children’s learning. Over the past 15 years, great strides have been made in supporting young children’s literacy. This report summarizes the now substantial literature on learning and teaching mathematics for young children in hopes of catalyz- ing a similar effort in mathematics. The need for this study was recognized and championed by the Na- tional Research Council’s (NRC’s) Mathematical Sciences Education Board following the publication in 2001 of Adding It Up: Helping Children Learn Mathematics. The tireless efforts of board member Sharon Griffin and then board director David Mandel led the design of this project, which is a comprehensive examination of the evidence base that can guide math- ematics education (teaching and learning) for children ages 2 through 6. It represents the further extension of a portfolio of NRC reports focused on mathematics learning and teaching that includes Adding It Up: Help- ing Children Learn Mathematics (2001); Eager to Learn: Educating Our Preschoolers (2001); How Students Learn: Mathematics in the Classroom (2005); and On Ealuating Curricular Effectieness: Judging the Quality of K-12 Mathematics Ealuations (2004). The majority of support for this study was provided by the U.S. De- partment of Health and Human Services, Administration for Children and Families, Office of Head Start. In particular, we thank Frank Fuentes, deputy director of the Office of Head Start, Administration for Children ii

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iii PREFACE and Families; Amanda Bryans, director of the Educational Development and Partnership Division, Office of Head Start, Administration for Children and Families; and Michele Plutro, education specialist, Office of Head Start, Administration for Children and Families. Additional funding was provided by the Office of Planning, Research, and Evaluation in the Administration for Children and Families, under the leadership of Mary Bruce Webb. Other sponsors who contributed to the project include the Ewing Marion Kauffman Foundation, under the guidance of Margo Quiriconi and Karen Norwood, and the National Institute of Child Health and Human Development, under the leadership of Daniel Berch and James Griffin. In addition, the National Academies President’s Fund provided partial support for the study. Our work was also advanced by the contributions of able consul- tants and staff and the input of outside experts. Throughout the study process, the committee benefited from presentations or written input by individuals with a range of perspectives: W. Steven Barnett, National Insti- tute for Early Education Research, Rutgers, The State University of New Jersey; Linda Bevilacqua, Core Knowledge Foundation; Toni Bickart, Creative Curriculum, Teaching Strategies; Bruce D. McCandliss, Sackler Institute for Developmental Psychobiology, Weill Medical College of Cornell University; Holly Rhodes, consultant; Elisa Rosman, consultant for the Georgetown University Center for Child and Human Develop- ment; Lawrence Schweinhart, High/Scope Educational Research Founda- tion; Catherine Snow, Harvard Graduate School of Education; and Prentice Starkey, Graduate School of Education, University of California, Berkeley. The committee also thanks those who wrote papers that were invalu- able to our discussions: Sarah Archibald, Consortium for Policy Research in Education, University of Wisconsin-Madison; Kathryn Bouchard Chval, College of Education, University of Missouri; Jason Downer, Center for the Advanced Study of Teaching and Learning, University of Virginia; Shalom Fisch, MediaKidz Research and Consulting; Michael Goetz, University of Wisconsin, Madison; Bridget K. Hamre, Curry School of Education, Uni- versity of Virginia; Marilou Hyson, National Association for the Educa- tion of Young Children and George Mason University; Carolyn R. Kilday, Graduate Student, Curry School of Education, University of Virginia; Pat McGuire, Graduate Student Curry Leadership Foundations and Policy, School of Education, University of Virginia; Barbara Reys, Department of Learning, Teaching, and Curriculum, University of Missouri; Catherine Scott-Little, Human Development and Family Studies Department, Uni- versity of North Carolina, Greensboro; and John Switzer, Department of Learning, Teaching, and Curriculum, University of Missouri. 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 Report Review Committee of the NRC. The

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ix PREFACE purpose of this independent review is to provide candid and critical com- ments 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 thank the following individuals for their review of this report: Arthur Baroody, Curriculum and Instruction, University of Illinois, Urbana- Champaign; Elena Bodrova, Mid-continent Research for Education and Learning, Lakewood, CO; Karen S. Cook, Department of Sociology, Insti- tute for Research in the Social Sciences, Stanford University; Sharon A. Griffin, Department of Education, Clark University; Jacqueline A. Jones, Division of Early Childhood Education, New Jersey Department of Edu- cation; Constance Kamii, Curriculum and Instruction, University of Alabama; Michèle M. M. Mazzocco, Psychiatry and Behavioral Sciences, Johns Hopkins School of Medicine and Math Skills Development Project, Kennedy Krieger West Campus, Baltimore, MD; Sally Moomaw, College of Education, Criminal Justice, and Human Services, University of Cincinnati; Donald G. Saari, Institute for Mathematical Behavioral Sciences, Univer- sity of California, Irvine; Maria Shea Terrell, Department of Mathematics, Cornell University; and Karen L. Worth, Center for Science Education, Education Development Center, Inc., Newton, MA. 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 Jeremy Kilpatrick, Department of Mathematics and Science Education, University of Georgia, Athens, and Charles (Randy) Gallistel, Rutgers University, Rutgers Center for Cognitive Science, The State University of New Jersey. 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. Re- sponsibility for the final content of this report rests entirely with the author- ing committee and the institution. We are also grateful to the work of others at the NRC, including Christine McShane, senior editor, Division of Behavioral and Social Sci- ences and Education (DBASSE), whose work greatly improved the text of the report; Kirsten Sampson Snyder, DBASSE reports officer, who worked with us through several revisions of the report; and Yvonne Wise, DBASSE production editor, who managed the report through final publication. As well, we are thankful to those who assisted committee members with lit- erature searches or background research, including Patricia Harvey, Julie Shuck, and Matthew Von Hendy, at the National Academies. The committee appreciates the support provided by the Center for

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x PREFACE Education, under the leadership of Patricia Morison. Taniesha Woods, the study director, provided invaluable support and guidance to the commit- tee throughout the study. We could not have asked for a better colleague. Senior program assistant Mary Ann Kasper masterfully handled all the logistical aspects of this project, including our four committee meetings. We are also grateful for the leadership and support of Heidi Schweingruber, deputy director of the Board on Science Education, who provided much thoughtful counsel throughout this process and contributed substantially to editing the report in the final stages. Christopher T. Cross, Chair Committee on Early Childhood Mathematics

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Contents Summary 1 PART I: INTRODUCTION AND RESEARCH ON LEARNING 1 Introduction 7 2 Foundational Mathematics Content 21 3 Cognitive Foundations for Early Mathematics Learning 59 4 Developmental Variation, Sociocultural Influences, and Difficulties in Mathematics 95 PART II: TEACHING-LEARNING PATHS 5 The Teaching-Learning Paths for Number, Relations, and Operations 127 6 The Teaching-Learning Paths for Geometry, Spatial Thinking, and Measurement 175 PART III: CONTEXTS FOR TEACHING AND LEARNING 7 Standards, Curriculum, Instruction, and Assessment 225 8 The Early Childhood Workforce and Its Professional Development 289 PART IV: FUTURE DIRECTIONS FOR POLICY, PRACTICE, AND RESEARCH 9 Conclusions and Recommendations 331 xi

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xii CONTENTS APPENDIXES A Glossary 351 B Concepts of Measurement 359 C Biographical Sketches of Committee Members and Staff 363 Index 371