Improving Instruction In Rational Numbers and Proportionality

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

• ISBN13: 9780807745298
• ISBN10: 0807745294
• Format: Paperback
• Copyright: 2005-01-21
• 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 One is rational numbers and proportionality.

Table of Contents

Acknowledgments	ix
Introduction	xi
Great Expectations for Middle Grades Mathematics	xi
The Materials in This Volume	xii
This Volume and Its Companions	xiv
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 Cases	5	(3)
Connecting Fractions, Decimals, and Percents--The Case of Randy Harris	8	(18)
Opening Activity	8	(1)
Reading the Case	8	(2)
The Case of Randy Harris	10	(13)
Analyzing the Case	23	(1)
Extending Your Analysis of the Case	23	(1)
Connecting to Your Own Practice	24	(1)
Exploring Curricular Materials	24	(1)
Connecting to Other Ideas and Issues	25	(1)
Introducing Ratios and Proportions--The Case of Marie Hanson	26	(18)
Opening Activity	26	(1)
Reading the Case	27	(1)
The Case of Marie Hanson	28	(12)
Analyzing the Case	40	(1)
Extending Your Analysis of the Case	40	(1)
Connecting to Your Own Practice	41	(1)
Exploring Curricular Materials	41	(1)
Connecting to Other Ideas and Issues	42	(2)
Comparing Similar Figures--The Case of Marcia Green	44	(14)
Opening Activity	44	(1)
Reading the Case	45	(1)
The Case of Marcia Green	46	(8)
Analyzing the Case	54	(1)
Extending Your Analysis of the Case	54	(1)
Connecting to Your Own Practice	55	(1)
Exploring Curricular Materials	56	(1)
Connecting to Other Ideas and Issues	56	(2)
Exploring Problems Involving Ratios and Percents--The Case of Janice Patterson	58	(17)
Opening Activity	58	(1)
Reading the Case	58	(2)
The Case of Janice Patterson	60	(9)
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 Randy Harris	81	(7)
Case Analysis	81	(4)
Facilitating the Opening Activity	85	(1)
Facilitating the Case Discussion	86	(1)
Extending the Case Experience	87	(1)
Facilitating Learning from The Case of Marie Hanson	88	(8)
Case Analysis	88	(5)
Facilitating the Opening Activity	93	(1)
Facilitating the Case Discussion	94	(1)
Extending the Case Experience	95	(1)
Facilitating Learning from The Case of Marcia Green	96	(7)
Case Analysis	96	(4)
Facilitating the Opening Activity	100	(1)
Facilitating the Case Discussion	101	(1)
Extending the Case Experience	102	(1)
Facilitating Learning from The Case of Janice Patterson	103	(6)
Case Analysis	103	(3)
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 Randy Harris	109	(5)
Teacher-Generated Solutions to the Opening Activity	109	(1)
Facilitator-Generated List of Supporting and Inhibiting Factors	110	(1)
Teacher-Generated List of Supporting and Inhibiting Factors	110	(4)
Appendix B: Sample Responses to The Case of Marie Hanson	114	(5)
Teacher-Generated Solutions to the Opening Activity	114	(2)
Facilitator- and Teacher-Generated List of Ways in Which Marie Hanson Supported Her Students' Learning of Mathematics	116	(3)
Appendix C: Sample Responses to The Case of Marcia Green	119	(4)
Teacher-Generated Solutions to the Opening Activity	119	(1)
List of Marcia Green's Questions	120	(1)
Teacher-Generated Criteria for Good Questions	120	(3)
Appendix D: Sample Responses to The Case of Janice Patterson	123	(8)
Teacher-Generated Solutions to the Opening Activity	123	(4)
Facilitator-Generated Responses to the Question, ``Did Janice Patterson Really Teach?''	127	(1)
Teacher-Generated Responses to the Question, ``Did Janice Patterson Really Teach?''	127	(4)
References	131	(4)
About the Authors	135	(2)
Index	137