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      THE NEW

      Art and Science

      OF TEACHING

      Mathematics

      NATHAN D. LANG-RAAD ROBERT J. MARZANO

      Copyright © 2019 by Solution Tree Press

      Materials appearing here are copyrighted. With one exception, all rights are reserved. Readers may reproduce only those pages marked “Reproducible.” Otherwise, no part of this book may be reproduced or transmitted in any form or by any means (electronic, photocopying, recording, or otherwise) without prior written permission of the publisher.

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      Visit go.SolutionTree.com/instruction to download the free reproducibles in this book.

      Printed in the United States of America

      Library of Congress Cataloging-in-Publication Data

      Names: Lang, Nathan D., author. | Marzano, Robert J., author.

      Title: The new art and science of teaching mathematics / Nathan D. Lang-Raad and Robert J. Marzano.

      Description: Bloomington, IN : Solution Tree Press, [2019] | Includes bibliographical references and index.

      Identifiers: LCCN 2018042848 | ISBN 9781945349652 (perfect bound)

      Subjects: LCSH: Mathematics--Study and teaching. | Mathematics teachers--Training of. | Effective teaching. | Teaching--Aids and devices. | Learning, Psychology of.

      Classification: LCC QA11.2 .L342 2019 | DDC 510.71--dc23 LC record available at https://lccn.loc.gov/2018042848

       Solution Tree

      Jeffrey C. Jones, CEO

      Edmund M. Ackerman, President

       Solution Tree Press

      President and Publisher: Douglas M. Rife

      Associate Publisher: Sarah Payne-Mills

      Art Director: Rian Anderson

      Managing Production Editor: Kendra Slayton

      Senior Production Editor: Suzanne Kraszewski

      Senior Editor: Amy Rubenstein

      Copy Editor: Miranda Addonizio

      Proofreader: Elisabeth Abrams

      Text and Cover Designer: Rian Anderson

      Editorial Assistant: Sarah Ludwig

      I dedicate this book to my husband, Herbie Raad. Your unending support, encouragement, creativity, and love inspires me to aim higher than I ever could have on my own. You kept me on schedule, edited and proofed, and gave me the best advice. Thank you for being you. I love you so.

      —Nathan Lang-Raad

      Visit go.SolutionTree.com/instruction to download the free reproducibles in this book.

      Table of Contents

       About the Authors

       Introduction

       The Overall Model

       The Need for Subject-Specific Models

       About This Book

       Part I: Feedback

       1 Providing and Communicating Clear Learning Goals

       Element 1: Providing Scales and Rubrics

       Element 2: Tracking Student Progress

       Element 3: Celebrating Success

       Summary

       2 Using Assessments

       Element 4: Using Informal Assessments of the Whole Class

       Element 5: Using Formal Assessments of Individual Students

       Summary

       Part II: Content

       3 Conducting Direct Instruction Lessons

       Element 7: Processing Content

       Element 8: Recording and Representing Content

       Summary

       4 Conducting Practicing and Deepening Lessons

       Element 9: Using Structured Practice Sessions

       Element 10: Examining Similarities and Differences

       Element 11: Examining Errors in Reasoning

       Summary

       5 Conducting Knowledge Application Lessons

       Element 12: Engaging Students in Cognitively Complex Tasks

       Element 13: Providing Resources and Guidance

       Element 14: Generating and Defending Claims

       Summary

       6 Using Strategies That Appear in All Types of Lessons

       Element 15: Previewing Strategies

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