Everyday Mathematics for Parents Everyday Mathematics for Parents What You Need to Know to Help Your Child Succeed The UniversiTy of ChiCago sChool MaTheMaTiCs ProjeCT The University of Chicago Press Chicago and London The University of Chicago Press, Chicago 60637 The University of Chicago Press, Ltd., London © 2017 by The University of Chicago All rights reserved. No part of this book may be used or reproduced in any manner whatsoever without written permission, except in the case of brief quotations in critical articles and reviews. For more information, contact the University of Chicago Press, 1427 E. 60th St., Chicago, IL 60637. Published 2017 Printed in the United States of America 26 25 24 23 22 21 20 19 18 17 1 2 3 4 5 ISBN- 13: 978- 0- 226- 49375- 6 (cloth) ISBN- 13: 978- 0- 226- 26548- 3 (paper) ISBN- 13: 978- 0- 226- 26551- 3 (e- book) DOI: 10.7208/chicago/9780226265513.001.0001 Illustrations created by Bill Dickson, represented by jupiterartists .com. Library of Congress Cataloging- in- Publication Data Names: University of Chicago. School Mathematics Project. Title: Everyday mathematics for parents : what you need to know to help your child succeed / The University of Chicago School Mathematics Project. Description: Chicago ; London : The University of Chicago Press, 2017. | Includes index. Identifiers: LCCN 2016058314 | ISBN 9780226493756 (cloth : alk. paper) | ISBN 9780226265483 (pbk. : alk. paper) | ISBN 9780226265513 (e- book) Subjects: LCSH: University of Chicago. School Mathematics Project. Everyday mathematics. | Mathematics—Study and teaching (Primary)—United States. | Mathematics—Study and teaching (Elementary)—United States. | Mathematics—Study and teaching— Parent participation. Classification: LCC QA16.E84 2017 | DDC 372.70973—dc23 LC record available at https:// lccn .loc .gov / 2016058314 ♾ This paper meets the requirements of ANSI/NISO Z39.48- 1992 (Permanence of Paper). Contents seCTion 1: Why Everyday Mathematics? 1 Because It Is Based on Proven Principles 1 Go Online 5 Because Spiraling Builds a Firm Mathematical Foundation 5 Further Reading 8 Because of What We Know about How Children Learn 9 Because of How Key Content Is Taught 16 Because It Works 17 Further Reading 22 Go Online 22 seCTion 2: Exploring Everyday Mathematics Content 23 Number Stories: The Foundation for Success with Computation 23 Further Reading 30 There’s Nothing “Basic” about Mastering Basic Facts 30 Further Reading 42 Moving On Up . . . Operations with Bigger Numbers 43 Further Reading 53 Algebra in Kindergarten? 53 Further Reading 65 The Trouble with Fractions 65 Further Reading 74 What Happened to Rulers? 75 Further Reading 81 seCTion 3: What to Expect from Everyday Mathematics 83 Linking Math in School to Math at Home 83 Using a Calculator Is NOT Cheating 88 Further Reading 92 Fun and Games: Math Is So Much More than (S)Kill and Drill 93 Go Online 98 What to Expect at Each Grade Level of Everyday Mathematics 99 Kindergarten 100 First Grade 111 Second Grade 124 Third Grade 138 Fourth Grade 153 Fifth Grade 165 Sixth Grade 180 Problem Solving in Everyday Mathematics: How Children Think about Mathematics 196 seCTion 4: How Do I Find Out More about Everyday Mathematics? 205 Index 211 seCTion 1 Why Everyday Mathematics? • Where are my child’s math worksheets? • Why does my child keep talking about math games? • When will my child memorize the basic facts? Where are the timed tests and flash cards? • Why does my child’s homework jump from topic to topic every day? How is my child supposed to learn if the math keeps changing? • Why isn’t my child learning to add and subtract (or multiply and divide) the way that I did? • How can I help my child with homework if it is so different from what I know how to do? Does any of this sound familiar? If you are new to Everyday Mathematics, or just trying to understand it better, you are not alone. Many parents recognize that Everyday Mathematics is not how they learned math. They wonder whether their kids will learn this “new math.” Or they worry that their kids will fall behind stu- dents at other schools. Knowing something about the background and philosophy of Everyday Mathematics will help you under- stand how it works and why it looks different from the way you may remember learning mathematics in school. In this section you will learn the many reasons why so many schools around the world have chosen to adopt Everyday Mathematics as their math curriculum. Because It Is Based on Proven Principles One reason why so many schools select Everyday Mathematics is because it is a pioneering program that has been developed, tested, and refined for over thirty years by teachers and researchers at the University of Chicago School Mathematics Project (UCSMP) to improve mathematics education across the United States. Since 1 its launch in the mid- 1980s, the program has established itself as the leading research-b ased elementary mathematics curriculum in the country. Before embarking on the first edition of their new math curric- ulum, researchers at UCSMP undertook a worldwide study of how mathematics was being taught in schools. They translated and an- alyzed textbooks from top- performing countries and compared them to textbooks from the United States. In addition, the re- searchers wanted to understand exactly how children learn math- ematics. They reviewed scholarly literature that was emerging, and they carried out their own research with teachers and children in classrooms. In one early study, UCSMP authors surveyed incoming kinder- gartners to learn what they knew about mathematics at the start of the school year. They found that children come to school with far more mathematical knowledge than math curricula used at the time seemed to assume. For example, most textbooks at that time expected children to count and know numbers up to 20 by the end of kindergarten. UCSMP researchers found that 46% of children entering kindergarten could already count to 30. It was a startling finding. In fact, many children coming into kindergarten already knew much of the mathematics they were expected to learn during their first year of school. Here are some other UCSMP findings: • U.S. mathematics textbooks at that time focused almost exclusively on paper- and- pencil calculation. The idea of children learning how to use mathematical tools such as calculators was frowned upon. • Most U.S. mathematics textbooks were organized to teach math skills in isolation, without linking the skills to each other or to the underlying mathematical concepts in a way that could make them interesting to children. • Children actually learn mathematics better when they are given the opportunity to connect their everyday experiences to what they are learning. Learning to use mathematics, to apply it to everyday problems they understand, is particularly 2 why everyday mathematics? important— and was largely neglected in textbooks of the time. • And, contrary to widespread expectations at that time, all children can learn mathematics. Girls and underrepresented minorities can learn mathematics as well as anyone if they are given the chance. This research shaped the first edition of Everyday Mathematics by helping the authors establish the following principles to guide them as they wrote a new curriculum: Recognize that children begin school with a great deal of knowledge and intuition on which to build. Research has shown that children begin school with an intuitive knowledge of mathematics and abundant common sense. To be effective, a mathematics curriculum must meet children at their level and build on what they already know. Connect children’s learning of mathematics to their own experiences. A mathematics curriculum must begin with children’s experiences and work to connect those experiences to mathematics. Fortunately, this is easy to do because basic mathematics is such a big part of daily life. Making connections to their everyday experiences gives children another reason for learning mathematics. Emphasize excellent instruction. As with any subject, excellent instruction plays a critical role in children’s success. A good textbook must include features that help teachers provide high- quality instruction and reflect on how they can improve the way they teach. Work with children’s problem- rich environment. Research shows that the school mathematics curriculum should incorporate challenging, interesting, real- world problems from children’s environments in order to nurture higher- order thinking skills. Use distributed practice to build skills. A well- designed program of routine practice spaced out over time helps children build mathematical skills. With solid mathematical beCaUse iT is based on Proven PrinCiPles 3