E-Book Overview
Just as athletes stretch their muscles before every game and musicians play scales to keep their technique in tune, mathematical thinkers and problem solvers can benefit from daily warm-up exercises. Jessica Shumway has developed a series of routines designed to help young students internalize and deepen their facility with numbers. The daily use of these quick five-, ten-, or fifteen-minute experiences at the beginning of math class will help build students' number sense. Students with strong number sense understand numbers, ways to represent numbers, relationships among numbers, and number systems. They make reasonable estimates, compute fluently, use reasoning strategies (e.g., relate operations, such as addition and subtraction, to each other), and use visual models based on their number sense to solve problems. Students who never develop strong number sense will struggle with nearly all mathematical strands, from measurement and geometry to data and equations. InNumber Sense Routines, Jessica shows that number sense can be taught to all students. Dozens of classroom examples -- including conversations among students engaging in number sense routines -- illustrate how the routines work, how children's number sense develops, and how to implement responsive routines. Additionally, teachers will gain a deeper understanding of the underlying math -- the big ideas, skills, and strategies children learn as they develop numerical literacy.
E-Book Content
NUMBER SENSE ROUTINES Building Numerical Literacy Every Day in Grades K–3 Jessica F. Shumway Foreword by Lucy West
Stenhouse Publishers www.stenhouse.com Copyright © 2011 by Jessica F. Shumway All rights reserved. Except for the pages in the appendix, which may be photocopied for classroom use, no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, or any information storage and retrieval system, without permission from the publisher. Every effort has been made to contact copyright holders and students for permission to reproduce borrowed material. We regret any oversights that may have occurred and will be pleased to rectify them in subsequent reprints of the work. Credits Page 57: Early Counting Learning Trajectory from Learning and Teaching Early Math: The Learning Trajectories Approach by Douglas H. Clements and Julie Sarama, published by Routledge, an imprint of Taylor & Francis Group. Copyright © 2009. Used with permission. Library of Congress Cataloging-in-Publication Data Shumway, Jessica F. Number sense routines : building numerical literacy every day in grades K–3 / Jessica F. Shumway. p. cm.—(Number sense routines) Includes bibliographical references and index. ISBN 978-1-57110-790-9 (pbk. : alk. paper)—ISBN 978-1-57110-901-9 (e-book) 1. Mathematics—Study and teaching (Primary) 2. Mathematics—Study and teaching (Preschool) I. Title. QA135.53.S57 2011
372.7’2—dc22 2010045397 Cover, interior design, and typeset by Martha Drury Manufactured in the United States of America
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For the students of Bailey’s Elementary School for the Arts and Sciences. I have learned so much from you!
CONTENTS Foreword by Lucy West Acknowledgments Introduction PART I BUILDING NUMBER SENSE THROUGH ROUTINES Chapter 1 Number Sense: What Does It Mean? Chapter 2 Improving Number Sense: Routines That Are Not Routinized PART II NUMBER SENSE ROUTINES Chapter 3 Visual Routines: Seeing and Conceptualizing Quantities Chapter 4 Counting Routines: Understanding Place Value and the Number System Chapter 5 Playing with Quantities: Making Sense of Numbers and Relationships Chapter 6 Calendar and Data Routines: Using Numbers Every Day PART III MORE THAN JUST THE ROUTINE Chapter 7 Learning from Each Other: Building a Strong Com