Teaching K-6 Mathematics

336 Pages·2003·22.62 MB·English

by  Douglas K. Brumbaugh

Teaching K-6 Mathematics
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Teaching K-6 Mathematics
Douglas K. Brumbaugh
David Rock
Linda S. Brumbaugh
Michelle L. Rock
LAWRENCE ERLBAUM ASSOCIATES, PUBLISHERS
2003 Mahwah, New Jersey London
Copyright © 2003 by Lawrence Eribaum Associates, Inc.
All rights reserved. No part of this book may be reproduced in
any form, by photostat, microform, retrieval system, or any other
means, without the prior written permission of the publisher.
Lawrence Eribaum Associates, Inc., Publishers
10 Industrial Avenue
Mahwah, New Jersey 07430
Cover design by Kathryn Houghtaling
Library of Congress Cataloging-in-Publication Data
Teaching K-6 Mathematics, by Douglas K. Brumbaugh, David Rock,
Linda S. Brumbaugh, and Michelle L. Rock / (ISBN: 0-8058-3268-8: pbk.)
Cataloging-ln-Publication Data for this volume can be obtained by
contacting the Library of Congress.
Books published by Lawrence Eribaum Associates are printed on acid-free paper,
and their bindings are chosen for strength and durability.
Printed in the United States of America
10 9 8 7 6 5 4 3 21
In loving memory of Pat and Web Brumbaugh, and J. Z Schmidt
To Shawn, Mike, and Laura, Linda and Doug's kids
To Lucile "Grandma" Schmidt, Linda's mom
To Barbara and Jerry, David's parents
To Ruth and Ken, Michelle's parents
To Carly, Kyle, and Katelyn, Michelle and David's kids who
keep us on our toes each and everyday
To April, David's sister, and Mark and Chris, Michelle's brothers
To Judy Rosenstock and Francis Duvall, the principals who
gave David and Michelle their first teaching positions
To all our teachers
To all our students: past, present, and future
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Contents in Brief
Preface xi
About the Authors xv
As a Teacher of Mathematics: An Introduction 1
1 Guiding Principles for School Mathematics 3
2 Number and Operations 43
3 Algebra in the Elementary Classroom 153
4 Geometry in the Elementary Classroom 165
5 Measurement in the Elementary Classroom 181
6 Data Analysis and Probability 199
7 Problem Solving 213
8 Reasoning and Proof 223
9 Communication 229
10 Connections 233
11 Representation 237
Index 239
Solutions Manual SM-1
Tag Activities TA-1
Tag Solutions Manual TSM-1
vii
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Contents
Preface xi
About the Authors xv
As a Teacher of Mahematics: An Introduction 1
What Makes an Effective Teacher of Mathematics? 1
1 Guiding Principles for School Mathematics 3
Beginnings 3
Curriculum 12
Planning 21
Assessment 27
Using Technology to Teach Mathematics 32
Manipulatives 39
2 Number and Operations 43
Early Childhood 43
Number Sense 50
Whole Number Operations 56
Fraction Operations 92
Decimal Operations 118
Integer Operations 732
Number Notation 146
3 Algebra in the Elementary Classroom 153
When Does Algebra Begin? 755
Laying the Foundation for Algebra 756
Integrating Algebra in the Elementary Classroom 758
Formulas 760
Formulas for Elementary Mathematics 762
4 Geometry in the Elementary Classroom 165
Building a Foundation 765
Manipulatives and Geometry 766
Integrating Technology Into Geometry 769
ix