367 spotlight on yc exploring math

Spotlight on Young Children:

Exploring Math

Contents 2 Introduction / Amy Shillady 4 The Patterns of Music: Children Birth

Derry Koralek, Chief Publishing Officer Amy Shillady, Editor Catherine Cauman, Associate Editor Mabel Yu, Assistant Editor Patrick Cavanagh, Design and Production Coordinator Copyright © 2012 by the National Association for the Education of Young Children, except as noted. All rights reserved. Printed in the United States of America.

Photo credits: Front cover (clockwise from top right): see pp. 6, 50, 26, 12, 31, 10. Back cover (clockwise from top right): see pp. 15, 46, 15, 44, 33.

Illustrations by Patrick Cavanagh.

National Association for the Education of Young Children 1313 L Street NW, Suite 500 Washington, DC 20005-4101 202-232-8777 or 800-424-2460 www.naeyc.org Through its publications program, the National Association for the Education of Young Children (NAEYC) provides a forum for discussion of major issues and ideas in the early childhood field, with the hope of provoking thought and promoting professional growth. The views expressed or implied are not necessarily those of the Association.

NAEYC thanks the contributors to this volume.

ISBN 978-1-928896-85-2 NAEYC #367 Library of Congress Control Number: 2012939767

through 5 Learning Mathematics through Beat, Rhythm, and Melody / Kamile Geist, Eugene A. Geist, and Kathleen Kuznik

10 Five Strategies for Creating Meaningful Mathematics Experiences in the Primary Years / Megan Burton

15 Mathematics and Social Justice in Grade 1: How Children Understand Inequality and Represent It / M. Shaun Murphy

21 Second and Third Grade Mathematical Pattern Hunters / Phyllis Whitin and David J. Whitin

28 Encouraging Preschoolers’ Emerging Mathematics Skills / Andrew M. Tyminski and Sandra M. Linder

34 Math Is Everywhere! Tips for Mathematizing Preschool Settings / Amy Shillady

36 Mathematics and Poetry in Grades 2 and 3: The Right Connection / David J. Whitin and Michelle Piwko

42 Teaching Mental Computation Strategies in the Primary Grades / Ann Margaret Heirdsfield

49 More, All Gone, Empty, Full: Math Talk with Infants and Toddlers—Every Day, in Every Way / Jan Greenberg

52 Books Count! Children’s Books with Mathematics Themes / Holly Bohart

57 Resources for Teaching and Learning about Math with Young Children

60 Reflecting, Discussing, and Exploring: Questions and Follow-Up Activities On the opening page of several articles, ® 2, 3 NAEYC’s logo and the numbers indicate which of the 10 NAEYC Early Childhood Program Standards those articles address—information for programs for young children seeking NAEYC Accreditation or improving program quality.

© Sample photo copyright

The following are the selections published previously in Young Children, NAEYC’s award-winning journal, and the issues in which they appeared: D.J. Whitin & M. Piwko, “Mathematics and Poetry: The Right Connection,” March 2008; M.S. Murphy, “Mathematics and Social Justice in Grade 1: How Children Understand Inequality and Represent It,” May 2009; M. Burton, “Five Strategies for Creating Meaningful Mathematics Experiences in the Primary Years,” November 2010; A.M. Heirdsfield, “Teaching Mental Computation Strategies in Early Mathematics,” March 2011; P. Whitin & D.J. Whitin, “Mathematical Pattern Hunters,” May 2011; K. Geist, E.A. Geist, & K. Kuznik, “The Patterns of Music: Young Children Learning Mathematics through Beat, Rhythm, and Melody,” January 2012; and J. Greenberg, “More, All Gone, Empty, Full: Math Talk Every Day in Every Way,” May 2012.

Math2 TOC.indd 1

5/24/2012 1:26:56 PM

Spotlight on Young Children

Exploring Math All early childhood teachers—those working with infants and toddlers through the primary grades—play an important role in laying a foundation for children’s future success in math. Promoting children’s math skills is easier than many think given that young children have an inherent understanding of mathematics (just think of the last time you gave a disproportionate number of treats to children— I’m sure the children let you know who had fewer and who had more!). Building off this natural mathematical inclination is a great starting point. However, research shows that for children to be successful in future math endeavors, this isn’t enough. It is important for teachers to actively incorporate mathematics into the daily curriculum.

Educators can help young children build the math skills they need to do well in school and life by providing in-depth experiences in a logical sequence for key math concept areas: number and operations, geometry, measurement, and data analysis (NAEYC & NCTM 2010). This allows children to develop, construct, use, and reflect on their mathematical understandings over time. With some planning, teachers can create these experiences to extend children’s mathematics learning.

While diapering, Ms. Ramirez promotes baby Margot’s spatial awareness: “I’m going to lift up your legs now. I put a clean diaper underneath you. Now let’s bring your legs back down.”

Mr. Johnson helps the preschoolers sort the leaves they found on their nature walk by size—small, medium, and large. Later he suggests that the children sort the leaves by another characteristic—color.

Ms. Myers asks the second-graders about ways they can determine how fast the classroom plants grow. The children work together to measure the plant stems with rulers and decide to measure and represent stem growth in a bar chart over the course of a month.

© Sample photo copyright

I hope the articles in this book help inspire you to provide in-depth, meaningful, and engaging mathematics activities for young children.

2

Math2 Intro.indd 2

The book opens with “The Patterns of Music: Children Birth through 5 Learning Mathematics through Beat, Rhythm, and Melody” by Kamile Geist, Eugene A. Geist, and Kathleen Kuznik. The authors describe how music elements possess mathematical principles, which help young children—from birth to 5—understand concepts such as spatial properties, sequencing, and counting. Additionally, using music in mathematical activities builds on children’s natural interests, which helps promote children’s positive attitude toward mathematics.

Megan Burton, author of “Five Strategies for Creating Meaningful Mathematics Experiences in the Primary Years,” describes specific math activities for kindergarten through third grade classrooms. Teachers can promote children’s problem solving through everyday activities such as graphing classroom data, creating alternate ways to present a designated “number of the day,” and playing math games.

Young children gain confidence in their math skills while working with peers and in small groups.

Spotlight on Young Children: Exploring Math

5/24/2012 1:23:00 PM

In “Mathematics and Social Justice in Grade 1: How Children Understand Inequality and Represent It,” author M. Shaun Murphy shares how he encourages first-graders to think of themselves as mathematicians. After reading an allegorical book about European colonists in Australia destroying the Aborigines’ traditional culture, Murphy asks the children to represent their comprehension mathematically. He is amazed by how children show their understanding of both math and social justice using Cuisinaire rods to represent the power struggle between the two groups.

“Second and Third Grade Mathematical Pattern Hunters,” by Phyllis Whitin and David J. Whitin, describes how teachers use a children’s book to help children focus on mathematical patterns and relationships through reading, talking, writing, and drawing. By posing key questions that invite close examination and exploration, teachers help children learn to identify, understand, and represent patterns in a variety of ways.

Andrew M. Tyminksi and Sandra M. Linder’s “Encouraging Preschoolers’ Emerging Mathematics Skills” shares specific strategies that preschool teachers can use to promote children’s mathematical understandings, which support their later success in math. By engaging with materials such as board games, manipulatives, and blocks, children learn about patterns, counting, and number sense and gain spatial awareness. Teachers can further build children’s skills through talk—narrating, asking open-ended questions, and revoicing—while children are engaged with materials and activities.

In Amy Shillady’s “Math Is Everywhere! Tips for Mathematizing Preschool Settings,” readers gain ideas about building math concepts into the daily preschool curriculum. Learn about offering specific materials that can help promote children’s mathematical understanding, engaging in small group work with children to promote their learning, and supporting math play at centers.

David J. Whitin and Michelle Piwko’s “Mathematics and Poetry in Grades 2 and 3: The Right Connection” emphasizes that reading, writing, and mathematics are best learned by children in meaningful, integrated experiences.

A study guide follows the articles in this Spotlight book. Readers can use the guide alone, with colleagues, or as participants in a class or workshop led by a facilitator. It offers a series of questions and follow-up activities, beginning with “Recalling Your Own Early Experiences,” which asks readers to reflect on their experiences learning mathematics in school.

The section “Expanding on Each Article” includes a brief summary of each article in the book, as well as specific questions and activities. In the last section, “Making Connections,” readers consider the big picture, examine their curriculum and ways to improve their teaching practices, plan ways to involve families, and identify next steps.

In an engaging project combining math and literacy, primary grade children in Michelle Piwko’s classroom follow the framework of verses from a classic children’s book to structure their own writing about geometric forms. Children brainstorm geometric attributes, interview their families about geometric shapes, and organize, write about, and illustrate the information.

“Teaching Mental Computation Strategies in the Primary Grades” by Ann Margaret Heirdsfield describes how primary grade teachers use a concept map for determining which math problem-solving models to teach children. By using the empty number line and the 99 chart and 100 chart models, children gain a stronger understanding of number that increases their math reasoning processes.

Jan Greenberg’s “More, All Gone, Empty, Full: Math Talk with Infants and Toddlers—Every Day, in Every Way” emphasizes how teachers can promote math understanding during their everyday interactions with infants and toddlers. The author shares tips for teachers to “talk math”— making math that occurs in daily life concrete and visible to very young children. This helps infants and toddlers build a positive attitude toward math learning.

“Books Count! Children’s Books with Mathematics Themes,” by Holly Bohart, provides a list of books teachers of children birth to 8 can use to promote children’s understanding of key math concepts. Through listening and follow-up activities, children can learn about counting, geometry, patterns, estimating, time measurement, fractions, and more!

—Amy Shillady, Editor

Reference NAEYC & NCTM (National Council of Teachers of Mathematics).

2010. “Early Childhood Mathematics: Promoting Good Beginnings.”

Joint position statement. Washington, DC: NAEYC. www.naeyc.org/ positionstatements/mathematics.

Spotlight on Young Children: Exploring Math

Math2 Intro.indd 3

3

5/29/2012 2:09:28 PM