My Kids Can: Making Math Accessible to All Learners, K-5

240 Pages·2009·1.53 MB·English

by  Judith Storeygard

My Kids Can
Making Math Accessible to All Learners, K–5
Edited by Judy Storeygard
HEINEMANN
Portsmouth, NH
Heinemann
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Portsmouth, NH 03801–3912
www.heinemann.com
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© 2009 by Technical Education Research Centers, Inc.
All rights reserved. No part of this book may be reproduced in any form or by any electronic or mechanical
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except by a reviewer, who may quote brief passages in a review.
“Dedicated to Teachers” is a trademark of Greenwood Publishing Group, Inc.
The authors and publisher wish to thank those who have generously given permission to reprint borrowed
material:
Figures 18–1, 18–2, and excerpts from Investigations in Number, Data, and Space by S. J. Russell,
K. Economopoulos, and L. Wittenberg. Copyright © 2008 by Pearson Education, Inc. or its affiliate(s). Used by
permission. All rights reserved.
This material is based upon a work supported by the National Science Foundation under Grant
No. HRD-0435017. Any opinions, findings, and conclusions or recommendations expressed in
this material are those of the authors and do not necessarily reflect the views of the National
Science Foundation or other funders.
Library of Congress Cataloging-in-Publication Data
My kids can : making math accessible to all learners, K–5 / edited by Judy Storeygard.
p. cm.
Includes bibliographical references.
ISBN-13: 978-0-325-01724-2
ISBN-10: 0-325-01724-7
1. Mathematics—Study and teaching (Elementary). 2. Effective teaching.
3. Mathematics teachers—Anecdotes. I. Storeygard, Judy.
QA135.6.M95 2009
372.7—dc22 2009000232
Editor: Victoria Merecki
Production: Sonja S. Chapman
Cover design: Susan Paradise
Cover photograph: Christina Myren
DVD production: Sherry Day
Typesetter: Aptara Inc.
Manufacturing: Steve Bernier
Printed in the United States of America on acid-free paper
13 12 11 10 09 VP 1 2 3 4 5
To Jacob Matthew, with love.
May you have teachers as dedicated and knowledgeable
as those who contributed to these resources.
Accompanying Video
Video footage of teachers in the classroom, demonstrating key teaching
moves and modeling effective classroom language, can be accessed at
http://www.heinemann.com/ebooks/my_kids_can.aspx.
iv
Contents
Acknowledgments vii
Foreword by Deborah Schifter viii
Introduction x
Making Mathematics Explicit 1
1 Are We Multiplying or Dividing? Being Explicit in Teaching
Mathematics Ana Vaisenstein 5
2 What Comes Next? Being Explicit About Patterns Laura Marlowe 18
3 You Can’t Build a Sand Castle on a Classmate’s Head:
Being Explicit in Kindergarten Math Lisa Seyferth 26
4 Double or Nothing: Guided Math Instruction Michelle Perch 32
5 Focused Instruction on Quick Images: A Guided Math
Group Video featuring Michael Flynn Arusha Hollister 38
6 Solving Multiplication Problems: Purposeful Sharing of Strategies
Video featuring Heather Straughter Arusha Hollister 43
Linking Assessment and Teaching 47
7 Assessing and Supporting Students to Make Connections:
Developing Flexibility with Counting Ana Vaisenstein 51
8 The Pieces Get Skinnier and Skinnier: Assessing Students’ Ideas
About Fractions Marta Garcia Johnson 60
9 After One Number Is the Next! Assessing a Student’s Knowledge
of Counting Maureen McCarty 69
10 Assessing and Developing Early Number Concepts: Working
with Kristen Anne Marie O’Reilly 77
11 How Many Children Got off the Bus? Assessing Students’
Knowledge of Subtraction Video featuring Ana Vaisenstein
Arusha Hollister 88
v
CONTENTS
12 Get to 100: Assessing Students’ Number Sense
Video featuring Michael Flynn Arusha Hollister 93
Building Understanding Through Talk 99
13 What’s Another Way to Make 9? Building Understanding Through
Math Talk Christina Myren 103
14 Lightbulbs Happen: Making Connections Through Math Talk
Nikki Faria-Mitchell 113
15 Talking About Square Numbers: Small-Group Discussion of
Multiples and Factors Dee Watson 126
16 Kindergartners Talk About Counting: The Counting Jar
Video featuring Lillian Pinet Arusha Hollister 136
17 What Do We Do with the Remainder? Fourth Graders Discuss
Division Video featuring Dee Watson Arusha Hollister 140
Taking Responsibility for Learning 145
18 Becoming a Self-Reliant Learner: The Story of Eliza
Kristi Dickey 149
19 Getting “Un-Stuck”: Becoming an Independent Learner
Mary Kay Archer 158
20 Tasha Becomes a Learner: Helping Students Develop
Confidence and Independence Candace Chick 169
Working Collaboratively 181
21 Collaborative Planning: It’s More Than One-on-One
Michael Flynn 185
22 A Double Dose of Math: Collaborating to Support Student
Learning Marta Garcia Johnson 194
23 Planning Guided Math Groups: A Collaboration Between
Classroom Teachers and Title 1 Staff John MacDougall with
Marta Garcia Johnson and Karen Joslin 202
References 217
Contributors 221
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Acknowledgments
This collection is the culmination of a long strand of work. I have been very for-
tunate to work with a group of dedicated teachers and colleagues. I could never
have edited these resources without their intellect and commitment to the work.
My colleague, Cornelia Tierney, and I began thinking about students who
struggle with mathematics ten years ago. Her vision and passion about equity
shaped the projects that we initiated. Our project officer at the National Science
Foundation (NSF), Dr. Larry Scadden, understood and championed our efforts.
The teachers from our Accessible Mathematics project began this work with us. I
am grateful to all of them: Candace Chick, Heather Straughter, Eileen Backus,
Lisa Nierenberg, Karin Olson-Shannon, MaryKay Resnick, Lisa Davis, Andrea
Cerda, Susan Fitzgerald, Leslie Kramer, Karen Ravin, Somchay Edwards, Lauretta
Medley, Michelle Anderson, and Lauren Grace.
More recently, the Educational Research Collaborative at the Technical
Education Research Center (TERC) provided me with funding to pursue publication.
My colleagues, Andee Rubin and Myriam Steinback, have provided unlimited sup-
port and wisdom. I am grateful for and humbled by their generosity. Arusha Hollister
made major contributions to these resources, in writing the workshops and video con-
text pieces and by imparting her knowledge about primary-grade mathematics.
Keith Cochran, Beth Perry-Brown, and Karen Mutch-Jones have given me
thoughtful ideas and comments about several of the essays. Amy Brodesky, Nancy
Horowitz, and Heather Straughter were very astute reviewers. The insights of
Nicole Feret were incredibly valuable in shaping the writing. David Smith lent
his creativity and patience in producing the DVD.
I was also privileged to have a wise group of colleagues from the Professional
Development Study Group. Deborah Schifter generously offered to write the
Foreword, and members of the group read several entries and provided excellent
feedback and encouragement.
Victoria Merecki at Heinemann has provided me with gentle, intelligent
guidance and encouragement throughout.
vii
Foreword
All teachers of mathematics face the challenge of reaching the range of students
in their classroom. Many teachers feel especially daunted by the task of helping
students who are struggling as learners. Faced with a student who lacks confi-
dence, doesn’t know how to interpret a task, and loses focus, what is a teacher to
do?My Kids Canis an important resource for teachers who are ready to tackle this
challenge.
The most important message in this book is that allchildren, given appropri-
ate supports, can learn mathematics for understanding. This may come as a surprise
to those who were taught that the best way to work with struggling students is to
break mathematical tasks into small chunks to be memorized. Instead, the key is
to find where a student is on solid ground and provide tasks that will help him or
her move forward. The examples presented here demonstrate the progress stu-
dents can make.
My Kids Can devotes each chapter to a broad principle: assessing students’
understanding as a way of making decisions about how to proceed, making the
mathematics explicit, helping students become independent learners. Within
each chapter, through written narratives and video cases, individual teachers con-
vey their own stories, illustrating how they worked with their students. That is,
readers can see the broad principles enacted within the constraints of day-to-day
classroom life: how teachers found time to conduct one-on-one interviews and to
keep records of students’ progress, which assessments were particularly useful, and
what kinds of accommodations were made to make the tasks accessible to stu-
dents while keeping the important mathematics intact. Readers learn about the
kinds of supports that made students who struggle feel confident enough to work
with classmates and to speak up in whole-group discussions. We are shown the
variety of representations students used to make sense of the mathematics and the
connections that students were able to make. And we witness the collaborations
forged between classroom teachers and special educators.
Although not explicitly stated, the knowledge these teachers bring to their
practice shines through each narrative and video case. They understand deeply
viii
FOREWORD
the mathematics content they are responsible for teaching and how students learn
it. They identify the central mathematical concepts, recognize how concepts are
related to each other, and understand how these concepts build from content
covered in earlier grades. They situate these concepts in a variety of representa-
tions and contexts familiar to students from their daily lives. They assess the cor-
rectness of students’ reasoning as students explain their solutions to a problem;
furthermore, if a solution is incorrect, the teachers analyze that reasoning to
determine what is correct about the students’ process and where the thinking has
gone awry. All of this knowledge—together with a deep sense of care and respect
for their students—is applied to the goal of having each student make sense of the
mathematics.
A reader might ask, “How can I put so much effort into one or two or a hand-
ful of students when I am responsible for so many?” The answer: The knowledge
exhibited by the teachers in this volume and many of the techniques they speci-
fy and elucidate enhance the learning of all of their students. When a teacher is
explicit about the mathematics of a lesson, provides additional representations,
and helps students figure out how to participate in whole-group discussion, it
serves every student in the classroom.
Indeed, the challenge of reaching the range of learners in a classroom isgreat.
There is much to learn and much to do. But, as illustrated by My Kids Can, the
rewards are even greater.
Deborah Schifter
Education Development Center, Inc.
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