|
Items in cart [4] |
Questions? Call 888-624-8373 |
| Copyright © 2009. National Academy of Sciences. All rights reserved. Terms of Use and Privacy Statement |
Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page R1
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
OCR for page R2
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.
OCR for page R3
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
OCR for page R4
OCR for page R5
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
OCR for page R6
OCR for page R7
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
OCR for page R8
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
OCR for page R9
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
OCR for page R10
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
OCR for page R11
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
OCR for page R12
xii CONTENTS
APPENDIXES
A Glossary 351
B Concepts of Measurement 359
C Biographical Sketches of Committee Members and Staff 363
Index 371
