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"Adding it Up" explores how students in pre-K through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years. The committee identifies five interdependent components of mathematical proficiency and describes how students develop this proficiency. With examples and illustrations, the book presents a portrait of mathematics learning: research findings on what children know about numbers by the time they arrive in pre-K and the implications for mathematics instruction; and details on the processes by which students acquire mathematical proficiency with whole numbers, rational numbers, and integers, as well as beginning algebra, geometry, measurement, and probability and statistics. The committee discusses what is known from research about teaching for mathematics proficiency, focusing on the interactions between teachers and students around educational materials and how teachers develop proficiency in teaching mathematics.
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of Sciences. All rights reserved. of Sciences. All rights reserved. A DDING + IT UP HELPING CHILDREN LEARN MATHEMATICS Mathematics Learning Study Committee Jeremy Kilpatrick, Jane Swafford, and Bradford Findell, editors Center for Education Division of Behavioral and Social Sciences and Education National Research Council National Academy Press Washington, DC of Sciences. All rights reserved. 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 supported by Contract/Grant No. ESI-9816818 between the National Academy of Sciences and 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 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 Adding it up : helping children learn mathematics / Jeremy Kilpatrick, Jane Swafford, and Bradford Findell, editors. p. cm. Includes bibliographical references and index. ISBN 0-309-06995-5 (hardcover) 1. Mathematics—Study and teaching (Elementary)—United States. 2. Mathematics—Study and teaching (Middle school)—United States. I. Kilpatrick, Jeremy. II. Swafford, Jane. III. Findell, Bradford. QA135.5 .A32 2001 372.7—dc21 2001001734 Suggesed citation: National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press. Additional copies of this report are available from National Academy Press, 2101 Constitution Avenue, N.W., Lockbox 285, Washington, DC 20055; (800) 624-6242 or (202) 334-3313 (in the Washington metropolitan area); Internet, http://www.nap.edu Printed in the United States of America. Copyright 2001 by the National Academy of Sciences. All rights reserved. of Sciences. All rights reserved. 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