Using Cases to Transform Mathematics Teaching and Learning – Volume 1 – Improving Instruction in Rational Numbers and Proportionality (Ways of Knowing in Science and Mathematics)

✍ Scribed by Margaret Schwan Smith, Edward A. Silver, Mary Kay Stein, Melissa Boston, Marjorie A. Henningsen, Amy F. Hillen

• Publisher: Teachers College Press
• Year: 2005
• Tongue: English
• Leaves: 159
• Series: Ways of Knowing in Science and Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

Helping students develop an understanding of important mathematical ideas is a persistent challenge for teachers. In this book, one of a three-volume set, well-known mathematics educators Margaret Smith, Edward A. Silver, and Mary Kay Stein provide teachers of mathematics the support they need to improve their instruction. They focus on ways to engage upper elementary, middle school, and high school students in thinking, reasoning, and problem solving to build their mathematics understanding and proficiency. The content focus of Volume One is rational numbers and proportionality. Using materials that were developed under the NSF-funded COMET (Cases of Mathematics to Enhance Teaching) program, each volume in the set features: * Cases from urban, middle school classrooms with ethnically, racially, and linguistically diverse student populations. Each case illustrates an instructional episode in the classroom of a teacher who is implementing standards-based instruction. * The teachersÂ’ perspective, including their thoughts and actions as they interact with students and with key aspects of mathematical content. * Cognitively challenging mathematics activities that are built around samples of authentic classroom practice. * Facilitation chapters to help professional developers "teach" the cases, including specific guidelines for facilitating discussions and suggestions for connecting the ideas presented in the cases to a teacherÂ’s own practice. As a complete set, this resource provides a basis on which to build a comprehensive professional development program to improve mathematics instruction and student learning.

✦ Table of Contents

Contents......Page 8
Acknowledgments......Page 10
Introduction......Page 12
PART I USING CASES TO ENHANCE LEARNING......Page 20
Using Cases to Learn......Page 22
Connecting Fractions, Decimals, and
Percents—THE CASE OF RANDY HARRIS......Page 27
Introducing Ratios and Proportions—
THE CASE OF MARIE HANSON......Page 45
Comparing Similar Figures—
THE CASE OF MARCIA GREEN......Page 63
Exploring Problems Involving
Ratios and Percents—
THE CASE OF JANICE PATTERSON......Page 77
PART II FACILITATING LEARNING FROM CASES......Page 92
Using Cases to Support Learning About Teaching......Page 94
Facilitating Learning from The Case of Randy Harris......Page 100
Facilitating Learning from The Case of Marie Hanson......Page 107
Facilitating Learning from The Case of Marcia Green......Page 115
Facilitating Learning from The Case of Janice Patterson......Page 122
APPENDIX A Sample Responses to The Case of Randy Harris......Page 128
APPENDIX B Sample Responses to The Case of Marie Hanson......Page 133
APPENDIX C Sample Responses to The Case of Marcia Green......Page 138
APPENDIX D Sample Responses to The Case of Janice Patterson......Page 142
References......Page 150
About the Authors......Page 154
Index......Page 156