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Mathematics Learning in Early Childhood. INSTITUTION National Council of Teachers of Mathematics, Inc., Washington, D.C

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Mathematics Learning in Early Childhood. INSTITUTION National Council of Teachers of Mathematics, Inc., Washington, D.C DOCUMENT RESUME ED 107 534 SE 019 342 AUTHOR Payne, Joseph N., Ed. TITLE Mathematics Learning in Early Childhood. INSTITUTION National Council of Teachers of Mathematics, Inc., Washington, D.C. PUB DATE 75 NOTE 300p.; NCTM 37th Yearbook AVAILABLE FROM National Council of Teachers of Mathematics, Inc., 1906 Association Drive, Reston, VA 22091 ($11 for NCTM members, single copy only; $12 to general public; 2-9 copies, 10 percent off the list price; 10 or more copies, 20 percent off the list price) EDRS PRICE MF-$0.76 HC Not Available from EDES. PLUS POSTAGE DESCRIPTORS Activity Learning; *Curriculum; Elementary Education; *Elementary School Mathematics; Geometry; Instruction; *Learning; Literature Reviews; *Mathematics Education; Measurement; Number Concepts; Problem Solving; *Yearbooks IDENTIFIERS *National Council of Teachers of Mathematics;NCTM ABSTRACT This yearbook presents many aspects of mathematics learning by children between the ages of threeand eight. Addressed to teachers of primary school children, the book begins withchapters discussing learning and cognition, the primary curriculum,and research on mathematics learning at thisage level. Eight subsequent chapters deal with the teaching of specific mathematicscontent: problem solving; mathematical experiences; numberand numeration; operations on whole numbers; fractional numbers;geometry; measurement; and relations, number sentences, and other topics. The final chapter discusses curricular change. Amajor theme throughout the bookis the importance of experience to learning,and the building of new knowledge on the foundation theseexperiences provide. The book is designed to provideeasy reference to both general information, such as answers to researchquestions, and suggested classroom activities related to specific topics.Many illustrations, the use of two-color printing, anda detailed index aid the user in this. regard, (SD) U.S. OEPARTMENT OF HEALTH. EOUCATION A WELFARE NATIONAL INSTITUTE OF EOUCATION THIS DOCUMENT HAS BEEN REPRO DUCED EXACTLY AS RECEIVED FROM THE PERSON OR ORGANIZATION ORIGIN ATING IT POINTS OF VIEW OR OPINIONS STATED DO NOT NECESSARILY REPRE SENT OFFICIAL NATIONAL INSTITUTE OF EDUCATION POSITION 07 POLICY PERMISSION TO REPRODUCE THIS COPYRIGHTED MATERIAL BY MICRO. FICHE ONLY HAS BEEN GRANTED BY _G11arles_R-11urica N.0 .T .M. TO ERIC 7ND-OFTGANQATIONS OPERAT THE NA ING UNDER AGREEMENTS WITH TIONAL INSTITUTE OF EDUCATION FURTHER R REPRODUC T ION OU TSIDE THE ERIC SYSTEM REOUIR ES PERMIS SION OF THE COPYRIGHT OWNER NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS I mathema=tics learning in early childhood thirty-seventh yearbook national council ,1 teachers of mathematics 1975 r editor joseph n. payne, university of michigan editorial panel mary folsom, university of miami (florida) e. glenadine gibb, university of texas 1. doyal nelson, university of alberta edward c. rathmell, university of northern iowa caul r. trafton, national college of education design and artwork irene b. tejuda, university of michigan joanna c. payne, stephens college nctm staff james d. gates charles r. hucka charles c. e. clement:: Copyright CI 1975 by THE NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS. INC. 1906 Association Drive. Reston. Virginia 22091 All rights reserved Library of Congress Cataloging in Publication Data: Main entry under title: Mathematics learning in early childhood. (37th YearbookNational C_ ouncil of Teachers of Mathematics) Includes bibliographies and index. 1. MathematicsStudy and teaching (Preschool) 2. MathematicsStudy and teaching (Primary) I. Payne. Joseph Neal. II. Title. III. Series: Na- tional Council of Teachers of Mathematics. Yearbook; 37th. QA1.N3 37th(QA135.5J510'.7s(372.7J75-6631 Printed in the United States of America contents ABOUT THE BOOK v 1 learning and' cognition 1 harold w. stevenson, university of michigan 2 the curriculum 15 pawl r. trafton, national college of education 3 research on mathematics learning 43 marilyn n. suydam, ohio state university j. fred weaver, university of wisconsin 4 problem solving 69 I. doyal nelson, university of alberta joan kirkpatrick, university of alberta 5 experiences for young children 95 e. glenadine gibb, university of texas alberta m. castaneda, university of texas 6 number and numeration 125 Joseph n. payne, university of michigan edward c. rathmell, university of northern Iowa 7 operations on whole numbers 161 mary folsom, university of miami (florid# 8 fractional numbers 191 arthur 1. coxford, university of michigan lawrence w. ellerbruch, eastern michigan university iii iv CONTENTS 9 geometry 205 g. edith robinson, university of georgia 10 measurement 227 g. edith robinson, university of georgia michael I. mahaffey, university of georgia I. doyal nelson,,university of alberta 11 relations, number sentences, and other topics 251 henry van engen, emeritus, university of wisconsin douglas grouws, university of rnissouri 12 directions of curricular change 273 alan r. osborne, ohio state university william h. nibbelink, university of iowa INDEX 295 os. about the book Children, ages three to eight: their mathematics, theirlearning, their teacher, their achievement, assessing their knowledge and givingguidance to their thoughts, planning their experiences, and cultivating their ability ... to solve problems ... to learn mathematics .. to be successful with mathematica ... to see uses of mathematics ... to have fun and satisfaction with mathematics that's what this yearbook is about. It is a book for teachersfor teachers ofyoung childrendesigned to help them in making important decisions about teaching andabout curriculum. It was planned to bea source of knowledge and a source of activities. Knowledge about children's general cognitive development,about the way they learn mathematics, and about curriculum design is reflected inchapters 1, 2, and 3. In these early chapters''s established a general framewOrkfor learning,and for curriculum. Knowledge about learning and teach.ng specific mathematicalcontent is found in chapters 4 through 11 Knowledge special curriculum projects and direction for change areoutlined in chapter 12. Activities for children permeate the "content"chapters, chapters 4 through 11. These activities are designed to engage children andto elicit thoughtful responses to produce effective learning. Most will stimulate teachersto go further in designing their own activities. Three themes are stressed: problem solving, relatingmathematics to the real world of the child, and a developmental point of view towardlearning. "Problem Solvingwas deliberately placed firstamong the content chapters. This prime placement suggests both the importance of problemsolving as a major goal and the use of problem solving in all the contentareas. Relating mathematics to the real world of the childrequires at least two things: (1) relating the mathematics to be learned to that whicha child already knows; and (2) relating the mathematics to be learned to the child'sown perceptions and views of concrete manipulative objects and situations in the real world.All content chapters stress the need to begin with concrete objects. Questionsare then asked about the features of the objects, leading to the abstraction of the mathematical idea.Suggestions are given for helping children relate symbols and verbal languageto the mathematical ideas in a meaningfulway. The developmental nature of learning should beevident throughout the book. Each author took seriously the charge to try to show how givencontent relates to, and grows from, that which a child already knows. A careful analysis ofeach child's learning is emphasized. The teacher is viewed as a planner ofexperiencesexperiences executed with a balance between teacher direction and child initiation. Incidentalexperiences are to be used, but they are not to be the only learning experience. The informality of the learning atmosphere is reflectedin the activities and in the suggestions to teachers. Furthermore, itwas a major factor considered in the overall design of the book. The design, the large pages, theuse of a second color all should combine to V vi ABOUT THE BOOK reflect an attractive and inviting atmosphere, which should be sought with children in the classroom. The variety of the content chapters suggests a wide range of objectives for children aged three to eight. These chapters contain a careful analysis of familiar ideas as well as fresh views of some content areas. Special concern was noted for the mathematics learning of children at an early age. To give emphasis to this concern, chapter 5 was devoted to mathematics experiences for young children. Most of the other content chapters also have specific suggestions that are useful with young children. What should be striking to the reader of chapter 5 and the other chapters is that the mathematics learning of very young children is much more that, just counting (too often the only goal of early childhood education). The book is designed to be used by teachers on an independent basis, by teachers engaged in continuing education, by preservice teachers in courses on teaching mathematics to children, and by graduate students in seminars on mathematics learning. The book should be helpful to school systems active in curriculum development at the primary school level and to preschool programs such as Head Start. It is a hope that the practical suggestions will make the book of continuing use to a teacher in the classroom. Further, it is hoped that the research and the theoretical work will be of continuing
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