Using Cases to Transform Mathematics Teaching And Learning

by Smith, Margaret Schwan; Silver, Edward A.; Stein, Mary Kay; Boston, Melissa; Henningsen, Marjorie A.

• ISBN13: 9780807745311
• ISBN10: 0807745316
• Format: Paperback
• Copyright: 2005-02-21
• Publisher: Teachers College Pr

Summary

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.

Author Biography

Margaret Schwan Smith holds a joint appointment at the University of Pittsburgh as an associate professor in the Department of Instruction and Learning in the School of Education, and at the Learning Research and Development Center (LRDC) as a Research Scientist Edward A. Silver is Professor of Education and Mathematics at the University of Michigan Mary Kay Stein holds a joint appointment at the University of Pittsburgh as an associate professor in the Administrative and Policy Department of the School of Education, and at the LRDC as a Research Scientist

Table of Contents

Acknowledgments	ix
Introduction	xi
Great Expectations for Middle Grades Mathematics	xi
The Materials in This Volume	xii
Why Geometry and Measurement?	xiv
This Volume and Its Companions	xv
PART I: USING CASES TO ENHANCE LEARNING
Using Cases to Learn	3	(5)
The Cases	3	(1)
The Cases as Learning Opportunities	4	(1)
Using the Case Materials	5	(3)
Reasoning About Units for Linear and Area Measure---The Case of Barbara Crafton	8	(13)
Opening Activity	8	(1)
Reading the Case	9	(9)
The Case of Barbara Crafton	10	(8)
Analyzing the Case	18	(1)
Extending Your Analysis of the Case	18	(1)
Connecting to Your Own Practice	19	(1)
Exploring Curricular Materials	19	(1)
Connecting to Other Ideas and Issues	20	(1)
Exploring Area and Perimeter---The Case of Isabelle Olson	21	(18)
Opening Activity	21	(1)
Reading the Case	21	(14)
The Case of Isabelle Olson	23	(12)
Analyzing the Case	35	(1)
Extending Your Analysis of the Case	35	(1)
Connecting to Your Own Practice	36	(1)
Exploring Curricular Materials	36	(1)
Connecting to Other Ideas and Issues	37	(2)
Exploring Volume and Surface Area---The Case of Keith Campbell	39	(17)
Opening Activity	39	(1)
Reading the Case	40	(12)
The Case of Keith Campbell	41	(11)
Analyzing the Case	52	(1)
Extending Your Analysis of the Case	52	(1)
Connecting to Your Own Practice	53	(1)
Exploring Curricular Materials	53	(1)
Connecting to Other Ideas and Issues	54	(2)
Estimating and Calculating Volume--The Case of Nancy Upshaw	56	(19)
Opening Activity	56	(1)
Reading the Case	56	(13)
The Case of Nancy Upshaw	58	(11)
Analyzing the Case	69	(1)
Extending Your Analysis of the Case	69	(1)
Connecting to Your Own Practice	70	(1)
Exploring Curricular Materials	70	(1)
Connecting to Other Ideas and Issues	71	(4)
PART II: FACILITATING LEARNING FROM CASES
Using Cases to Support Learning About Teaching	75	(6)
Why Cases?	75	(1)
Learning from Cases	76	(1)
What Can Be Learned from Our Cases	77	(1)
Preparing for and Facilitating Case Discussions	78	(2)
Putting the Pieces Together	80	(1)
Facilitating Learning from The Case of Barbara Crafton	81	(6)
Case Analysis	81	(3)
Facilitating the Opening Activity	84	(1)
Facilitating the Case Discussion	85	(1)
Extending the Case Experience	86	(1)
Facilitating Learning from The Case of Isabelle Olson	87	(7)
Case Analysis	87	(3)
Facilitating the Opening Activity	90	(2)
Facilitating the Case Discussion	92	(1)
Extending the Case Experience	93	(1)
Facilitating Learning from The Case of Keith Campbell	94	(8)
Case Analysis	94	(4)
Facilitating the Opening Activity	98	(2)
Facilitating the Case Discussion	100	(1)
Extending the Case Experience	101	(1)
Facilitating Learning from The Case of Nancy Upshaw	102	(7)
Case Analysis	102	(4)
Facilitating the Opening Activity	106	(1)
Facilitating the Case Discussion	107	(1)
Extending the Case Experience	108	(1)
Appendix A. Sample Responses to The Case of Barbara Crafton	109	(3)
Teacher-Generated Solutions to the Opening Activity	109	(1)
Teacher-Generated Responses to the ``Analyzing the Case'' Activity	110	(2)
Appendix B. Sample Responses to The Case of Isabelle Olson	112	(6)
Teacher-Generated Solutions to the Opening Activity	112	(4)
Teacher-Generated Responses to the ``Analyzing the Case'' Activity	116	(2)
Appendix C. Sample Responses to The Case of Keith Campbell	118	(3)
Teacher-Generated Solutions to the Opening Activity	118	(1)
Teacher-Generated Responses to the ``Analyzing the Case'' Activity	119	(2)
Appendix D. Sample Responses to The Case of Nancy Upshaw	121	(4)
Teacher-Generated Solutions to the Opening Activity	121	(2)
Teacher-Generated Responses to the ``Analyzing the Case'' Activity	123	(2)
References	125	(4)
About the Authors	129	(2)
Index	131