Alfred S. Posamentier - What Successful Math Teachers Do, Grades 6-12: 80 Research-Based Strategies for the Common Core-Aligned Classroom

To Barbara for her support, patience, and inspiration.
To my children and grandchildren, David, Lauren, Lisa, Danny, Max, Sam, and Jack, whose futures are unbounded.
And in memory of my dear parents, Alice and Ernest, who never lost faith in me.

Alfred S. Posamentier

To my Mom and Dad, whose unceasing love and support, and examples of integrity and hard work have converged to allow me a life limited only by my imagination.

Terri L. Germain-Williams

To my wife, Tae Jin, who has made every sacrifice to ensure my happiness and success.
To my children, Jennifer and Rebecca, who are an eternal source of pride and joy, and in memory of my parents, Stanley and Beatrice, who were always there for me.

Daniel Jaye

Copyright 2013 by Corwin

All rights reserved. When forms and sample documents are included, their use is authorized only by educators, local school sites, and/or noncommercial or nonprofit entities that have purchased the book. Except for that usage, no part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher.

National Council of Teachers of Mathematics (NCTM) standards throughout the book are reprinted with permission by NCTM. They are quoted from Curriculum and Evaluation Standards for School Mathematics (1989), Professional Standards for Teaching Mathematics (1991), Handbook of Research on Mathematics Teaching and Learning (1992), Assessment Standards for School Mathematics (1995), Principles and Standards for School Mathematics (2002), and Research Companion to Principles and Standards for School Mathematics (2003). All rights reserved. Standards are listed with the permission of NCTM. NCTM does not endorse the content or validity of these alignments.

All trade names and trademarks recited, referenced, or reflected herein are the property of their respective owners who retain all rights thereto.

Printed in the United States of America

Library of Congress Cataloging-in-Publication Data

Posamentier, Alfred S.
What successful math teachers do, grades 612 : 80 research-based strategies for the common corealigned classroom. Second edition / Alfred S. Posamentier, Terri L. Germain-Williams, Daniel Jaye.

pages cm
Includes bibliographical references and index.

ISBN 978-1-4522-5913-0 (pbk.)

1. MathematicsStudy and teaching (Secondary) StandardsUnited States. I. Germain-Williams, Terri L. II. Jaye, Daniel. III. Title.

QA13.P67 2013
510.712dc23 2013011072

This book is printed on acid-free paper.

13 14 15 16 17 10 9 8 7 6 5 4 3 2 1

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Prologue

A s a direct result of federal pressure on the states to continuously improve their instructional program and ensure that all students are being reached in the teaching process, teachers are being called on to meet professional standards and base their work on research-proven methods of teaching. Educational research, often conducted at universities or on educational sites by university researchers, is reported in educational journals and is most often read by other researchers. All too often, the style in which research reports or articles on research findings are reported is not friendly or appealing to the classroom teacher. The very communityclassroom teachersthat could benefit enormously from the findings of many of these educational initiatives rarely learns about these endeavors. It is the objective of this book to bring some of the more useful research findings to the classroom teacher. In our quest for the most salient research findings, we were guided by the Common Core State Standards and the National Council of Teachers of Mathematics standards. Rather than merely presenting the research findings that support these standards, we have attempted to convert them into useful classroom strategies, thus capturing the essence of the findings and at the same time putting them into a meaningful context for the practicing mathematics teacher.

This book is to serve as a resource for mathematics teachers. It should provide a portal to access the many worthwhile findings resulting from educational, psychological, and sociological research studies done in Europe and in the United States. Heretofore, teachers have had very few proper vehicles for getting this information, short of combing through the tomes of research reports in the various disciplines. This book is designed to provide an easy way for the classroom teacher to benefit from the many ideas embedded in these academic exercises.

The book is designed to be an easy and ready reference for the mathematics teacherboth preservice and inservice. It consists of 11 chapters, each with a theme representing one aspect of the typical instructional program and each guided by the Common Core Standards. Each chapter presents a collection of teaching strategies, concisely presented in a friendly format:

The Strategy

This is a simple and crisp statement of the teaching strategy we recommend.

What the Research Says

This offers a discussion of the research project that led to the strategy. This section should give the teacher some confidence in, and a deeper understanding of, the principle being discussed as a teaching strategy.

Teaching to the National Council of Teachers of Mathematics Standards

Here we present the salient National Council of Teachers of Mathematics standard that we are supporting with the strategy.