Using Cases to Transform Mathematics Teaching And Learning: Improving Instruction in Geometry And Measurement (Ways of Knowing in Science and Mathematics (Paper))

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 Three is geometry and measurement. 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 teachers?’ 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 teacher?’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. Contents......Page 8 Acknowledgments......Page 10 Great Expectations for Middle Grades Mathematics......Page 12 The Materials in This Volume......Page 13 Why Geometry and Measurement?......Page 15 This Volume and Its Companions......Page 16 PART I: USING CASES TO ENHANCE LEARNING......Page 18 The Cases......Page 22 The Cases as Learning Opportunities......Page 23 Using the Case Materials......Page 24 Opening Activity......Page 27 Reading the Case......Page 28 THE CASE OF BARBARA CRAFTON......Page 29 Extending Your Analysis of the Case......Page 37 Exploring Curricular Materials......Page 38 Connecting to Other Ideas and Issues......Page 39 Reading the Case......Page 40 THE CASE OF ISABELLE OLSON......Page 42 Extending Your Analysis of the Case......Page 54 Exploring Curricular Materials......Page 55 Connecting to Other Ideas and Issues......Page 56 Opening Activity......Page 58 Reading the Case......Page 59 THE CASE OF KEITH CAMPBELL......Page 60 Extending Your Analysis of the Case......Page 71 Exploring Curricular Materials......Page 72 Connecting to Other Ideas and Issues......Page 73 Reading the Case......Page 75 THE CASE OF NANCY UPSHAW......Page 77 Extending Your Analysis of the Case......Page 88 Exploring Curricular Materials......Page 89 Connecting to Other Ideas and Issues......Page 90 PART II: FACILITATING LEARNING FROM CASES......Page 92 Why Cases?......Page 94 Learning from Cases......Page 95 What Can Be Learned from Our Cases......Page 96 Preparing for and Facilitating Case Discussions......Page 97 Putting the Pieces Together......Page 99 Case Analysis......Page 100 Facilitating the Opening Activity......Page 103 Facilitating the Case Discussion......Page 104 Extending the Case Experience......Page 105 Case Analysis......Page 106 Facilitating the Opening Activity......Page 109 Facilitating the Case Discussion......Page 111 Extending the Case Experience......Page 112 Case Analysis......Page 113 Facilitating the Opening Activity......Page 117 Facilitating the Case Discussion......Page 119 Extending the Case Experience......Page 120 Case Analysis......Page 121 Facilitating the Opening Activity......Page 125 Facilitating the Case Discussion......Page 126 Extending the Case Experience......Page 127 Teacher-Generated Solutions to the Opening Activity......Page 128 Teacher-Generated Responses to the “Analyzing the Case” Activity......Page 129 Teacher-Generated Solutions to the Opening Activity......Page 131 Teacher-Generated Responses to the “Analyzing the Case” Activity......Page 135 Teacher-Generated Solutions to the Opening Activity......Page 137 Teacher-Generated Responses to the “Analyzing the Case” Activity......Page 138 Teacher-Generated Solutions to the Opening Activity......Page 140 Teacher-Generated Responses to the “Analyzing the Case” Activity......Page 142 References......Page 144 About the Authors......Page 148 C......Page 150 M......Page 151 T......Page 152 W......Page 153 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 Schwan 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 Three is geometry and measurement.Using materials that were developed under the NSF-funded COMET (Cases of Mathematics Instruction 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 teachers' 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 teacher'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. I: Using cases to enhance learning 1. Using cases to learn 2. Reasoning about units for linear and area measure the case of Barbara Crafton 3. Exploring area and perimeter the case of Isabelle Olson 4. Exploring volume and surface area the case of Keith Campbell 5. Estimating and calculating volume the case of Nancy Upshaw II: Facilitating learning from cases 6. Using cases to support learning about teaching 7. Facilitating learning from the case of Barbara Crafton 8. Facilitating learning from the case of Isabelle Olson 9. Facilitating learning from the case of Keith Campbell 10. Facilitating learning from the case of Nancy Upshaw. Margaret Schwan Smith, Edward A. Silver, Mary Kay Stein, With Marjorie A. Henningsen And Melissa Boston. Includes Bibliographical References (p. 125-127) And Index.