Five Practices for Orchestrating Productive Mathematics Discussions

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  • Format: Paperback
  • Copyright: 2011-05-13
  • Publisher: Corwin Pr
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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

Prefacep. vii
Introductionp. 1
Successful or Superficial? Discussion in David Crane's Classroomp. 2
Analyzing the Case of David Cranep. 5
Conclusionp. 6
Introducing the Five Practicesp. 7
The Five Practicesp. 7
Anticipatingp. 8
Monitoringp. 9
Selectingp. 10
Sequencingp. 10
Connectingp. 11
Conclusionp. 12
Laying the Groundwork: Setting Goals and Selecting Tasksp. 13
Setting Goals for Instructionp. 13
Selecting an Appropriate Taskp. 15
Conclusionp. 19
Investigating the Five Practices in Actionp. 21
The Five Practices in the Case of Darcy Dunnp. 21
Analyzing the Case of Darcy Dunnp. 26
Evidence of the five practicesp. 27
Anticipatingp. 27
Monitoringp. 27
Selectingp. 27
Sequencingp. 28
Connectingp. 28
Relating the five practices to learning opportunitiesp. 29
Conclusionp. 29
Getting Started: Anticipating Students' Responses and Monitoring Their Workp. 31
Anticipatingp. 31
Analysis of Anticipating in the Case of Nick Bannisterp. 35
Anticipating what students will dop. 35
Planning how to respond to student approachesp. 36
Identifying responses that address mathematical goalsp. 36
Monitoringp. 37
Analysis of Monitoring in the Case of Nick Bannisterp. 40
Conclusionp. 42
Determining the Direction of the Discussion: Selecting, Sequencing, and Connecting Students' Responsesp. 43
Selecting and Sequencingp. 43
Analysis of Selecting and Sequencing in the Case of Nick Bannisterp. 48
Connectingp. 49
Analysis of Connecting in the Case of Nick Bannisterp. 56
Mathematical ideas: The meaning of the point of intersectionp. 57
Mathematical ideas: Functions switch positions at the point of intersectionp. 57
Mathematical ideas: Making connections among representationsp. 58
Conclusionp. 59
Ensuring Active Thinking and Participation: Asking Good Questions and Holding Students Accountablep. 61
Asking Good Questionsp. 62
Exploring questioning in Regina Quigley's classroomp. 63
Analyzing questioning in Regina Quigley's classroomp. 67
Moves to Guide Discussion and Ensure Accountabilityp. 69
Revoicingp. 70
Asking students to restate someone else's reasoningp. 70
Asking students to apply their own reasoning to someone else's reasoningp. 71
Prompting students for further participationp. 72
Using wait timep. 72
Conclusionp. 73
Putting the Five Practices in a Broader Context of Lesson Planningp. 75
Lesson Planningp. 76
Developing thoughtful and thorough lesson plansp. 78
Relationship between the TTLP and the five practicesp. 80
Beyond the five practicesp. 80
Creating a permanent record of the lessonp. 82
Conclusionp. 84
Working in the School Environment to Improve Classroom Discussionsp. 87
Analysis of the Case of Maria Lancasterp. 91
Overcoming Obstaclesp. 91
Working with Othersp. 92
Conclusionp. 94
Referencesp. 95
Professional Development Guidep. 99
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