Five Practices for Orchestrating Productive Mathematics Discussions

by Margaret S. Smith

• ISBN13: 9781452202907
• ISBN10: 1452202907
• Format: Paperback
• Copyright: 2011-05-13
• Publisher: Corwin Pr

Summary

This book's 5 manageable practices have the power to connect students' approaches with the underlying mathematics and put teachers in control of productive classroom discussions.  

Table of Contents

Preface	p. vii
Introduction	p. 1
Successful or Superficial? Discussion in David Crane's Classroom	p. 2
Analyzing the Case of David Crane	p. 5
Conclusion	p. 6
Introducing the Five Practices	p. 7
The Five Practices	p. 7
Anticipating	p. 8
Monitoring	p. 9
Selecting	p. 10
Sequencing	p. 10
Connecting	p. 11
Conclusion	p. 12
Laying the Groundwork: Setting Goals and Selecting Tasks	p. 13
Setting Goals for Instruction	p. 13
Selecting an Appropriate Task	p. 15
Conclusion	p. 19
Investigating the Five Practices in Action	p. 21
The Five Practices in the Case of Darcy Dunn	p. 21
Analyzing the Case of Darcy Dunn	p. 26
Evidence of the five practices	p. 27
Anticipating	p. 27
Monitoring	p. 27
Selecting	p. 27
Sequencing	p. 28
Connecting	p. 28
Relating the five practices to learning opportunities	p. 29
Conclusion	p. 29
Getting Started: Anticipating Students' Responses and Monitoring Their Work	p. 31
Anticipating	p. 31
Analysis of Anticipating in the Case of Nick Bannister	p. 35
Anticipating what students will do	p. 35
Planning how to respond to student approaches	p. 36
Identifying responses that address mathematical goals	p. 36
Monitoring	p. 37
Analysis of Monitoring in the Case of Nick Bannister	p. 40
Conclusion	p. 42
Determining the Direction of the Discussion: Selecting, Sequencing, and Connecting Students' Responses	p. 43
Selecting and Sequencing	p. 43
Analysis of Selecting and Sequencing in the Case of Nick Bannister	p. 48
Connecting	p. 49
Analysis of Connecting in the Case of Nick Bannister	p. 56
Mathematical ideas: The meaning of the point of intersection	p. 57
Mathematical ideas: Functions switch positions at the point of intersection	p. 57
Mathematical ideas: Making connections among representations	p. 58
Conclusion	p. 59
Ensuring Active Thinking and Participation: Asking Good Questions and Holding Students Accountable	p. 61
Asking Good Questions	p. 62
Exploring questioning in Regina Quigley's classroom	p. 63
Analyzing questioning in Regina Quigley's classroom	p. 67
Moves to Guide Discussion and Ensure Accountability	p. 69
Revoicing	p. 70
Asking students to restate someone else's reasoning	p. 70
Asking students to apply their own reasoning to someone else's reasoning	p. 71
Prompting students for further participation	p. 72
Using wait time	p. 72
Conclusion	p. 73
Putting the Five Practices in a Broader Context of Lesson Planning	p. 75
Lesson Planning	p. 76
Developing thoughtful and thorough lesson plans	p. 78
Relationship between the TTLP and the five practices	p. 80
Beyond the five practices	p. 80
Creating a permanent record of the lesson	p. 82
Conclusion	p. 84
Working in the School Environment to Improve Classroom Discussions	p. 87
Analysis of the Case of Maria Lancaster	p. 91
Overcoming Obstacles	p. 91
Working with Others	p. 92
Conclusion	p. 94
References	p. 95
Professional Development Guide	p. 99
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