Using Cases to Transform Mathematics Teaching And Learning

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

• ISBN13: 9780807745304
• ISBN10: 0807745308
• Format: Paperback
• Copyright: 2004-12-23
• 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 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 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., and 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.

Table of Contents

Acknowledgments	ix
Introduction	xi
Great Expectations for Middle-Grades Mathematics	xi
The Materials in This Volume	xii
Why Patterns and Functions in Algebra?	xiv
This Volume and Its Companions	xv
PART I: USING CASES TO ENHANCE LEARNING
Using Cases to Learn	3	(5)
The Cases	3	(2)
The Cases as Learning Opportunities	5	(1)
Using the Case Materials	6	(2)
Examining Linear Growth Patterns---The Case of Catherine Evans and David Young	8	(24)
Opening Activity	8	(1)
Reading the Case	8	(2)
The Case of Catherine Evans	10	(9)
The Case of David Young	19	(9)
Analyzing the Case	28	(1)
Extending Your Analysis of the Case	28	(1)
Connecting to Your Own Practice	29	(1)
Exploring Curricular Materials	29	(1)
Connecting to Other Ideas and Issues	30	(2)
Examining Nonlinear Growth Patterns---The Case of Ed Taylor	32	(18)
Opening Activity	32	(1)
Reading the Case	32	(2)
The Case of Ed Taylor	34	(13)
Analyzing the Case	47	(1)
Extending Your Analysis of the Case	47	(1)
Connecting to Your Own Practice	48	(1)
Exploring Curricular Materials	48	(1)
Connecting to Other Ideas and Issues	48	(2)
Comparing Linear Graphs--The Case of Edith Hart	50	(14)
Opening Activity	50	(1)
Reading the Case	50	(2)
The Case of Edith Hart	52	(8)
Analyzing the Case	60	(1)
Extending Your Analysis of the Case	60	(1)
Connecting to Your Own Practice	61	(1)
Exploring Curricular Materials	61	(1)
Connecting to Other Ideas and Issues	62	(2)
Interpreting Graphs of Time versus Speed--The Case of Robert Carter	64	(21)
Opening Activity	64	(1)
Reading the Case	64	(2)
The Case of Robert Carter	66	(13)
Analyzing the Case	79	(1)
Extending Your Analysis of the Case	79	(1)
Connecting to Your Own Practice	80	(1)
Exploring Curricular Materials	80	(1)
Connecting to Other Ideas and Issues	80	(5)
PART II: FACILITATING LEARNING FROM CASES
Using Cases to Support Learning About Teaching	85	(6)
Why Cases?	85	(1)
Learning from Cases	86	(1)
What Can Be Learned from Our Cases	87	(1)
Preparing for and Facilitating Case Discussions	88	(2)
Putting the Pieces Together	90	(1)
Facilitating Learning from The Case of Catherine Evans and David Young	91	(9)
Case Analysis	91	(4)
Facilitating the Opening Activity	95	(3)
Facilitating the Case Discussion	98	(1)
Extending the Case Experience	99	(1)
Facilitating Learning from The Case of Ed Taylor	100	(7)
Case Analysis	100	(3)
Facilitating the Opening Activity	103	(2)
Facilitating the Case Discussion	105	(1)
Extending the Case Experience	106	(1)
Facilitating Learning from The Case of Edith Hart	107	(8)
Case Analysis	107	(3)
Facilitating the Opening Activity	110	(2)
Facilitating the Case Discussion	112	(2)
Extending the Case Experience	114	(1)
Facilitating Learning from The Case of Robert Carter	115	(8)
Case Analysis	115	(4)
Facilitating the Opening Activity	119	(1)
Facilitating the Case Discussion	120	(1)
Extending the Case Experience	121	(2)
Appendix A. Sample Responses to The Case of Catherine Evans and David Young	123	(3)
Sample Solutions to the Opening Activity	123	(2)
Teacher-Generated Solutions to the ``Case Analysis'' Activity	125	(1)
Appendix B. Sample Responses to The Case of Ed Taylor	126	(7)
Sample Solutions to the Opening Activity	126	(5)
Teacher-Generated Solutions to the ``Case Analysis'' Activity	131	(2)
Appendix C. Sample Responses to The Case of Edith Hart	133	(4)
Sample Solutions to the Opening Activity	133	(2)
Teacher-Generated Solutions to the ``Case Analysis'' Activity	135	(2)
Appendix D. Sample Responses to The Case of Robert Carter	137	(4)
Sample Solutions to the Opening Activity	137	(2)
Teacher-Generated Solutions to the ``Case Analysis'' Activity	139	(2)
References	141	(4)
About the Authors	145	(2)
Index	147