Five Practices for Orchestrating Productive Mathematics Discussions

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Overview

Anticipating students' solutions to a mathematics task

Monitoring students' in-class, "real-time" work on the task

Selecting approaches and students to share them

Sequencing students' presentations purposefully

Connecting students' approaches and the underlying mathematics

These 5 manageable practices have the power to put teachers in control of productive classroom discussions.

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Editorial Reviews

Catherine Martin
"5 Practices for Orchestrating Productive Mathematics Discussions provides teachers with concrete guidance for engaging students in discussions that make the mathematics in classroom lessons transparent to all. These instructional practices are extremely timely in light of the focus on Standards for Mathematical Practice in the Common Core State Standards for Mathematics,
and they will support teachers and students in engaging in these standards. This book will serve as a valuable foundation in our upcoming professional development."
Frederick Dillon
"Ensuring that students have the opportunity to reason mathematically is one of the most difficult challenges that teachers face. A key component is creating a classroom in which discourse is encouraged and leads to better understanding. Productive discourse is not an accident, nor can it be accomplished by a teacher working on the fly, hoping for a serendipitous student exchange that contains meaningful mathematical ideas. While acknowledging that this type of teaching is demanding, Smith and Stein present five practices that any teacher can use to implement coherent mathematical conversations. By using the five practices, teachers will learn to teach effectively in this way."
Lori Lovato
"As a veteran teacher, I found that the book diagnosed several problems that I had unknowingly created for my students' classroom discussions. I now have a prescription for curing these problems."
Teaching Children Mathematics Magazine, August 2012 - Maria Lamattina
"This book is a must-have for educators who are working toward having 'acountable talk.' I found it to be a welcome and thought-provoking addition to my professional library."
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Product Details

  • ISBN-13: 9781452202907
  • Publisher: Corwin Press
  • Publication date: 5/13/2011
  • Edition description: New Edition
  • Pages: 104
  • Product dimensions: 6.80 (w) x 9.90 (h) x 0.30 (d)

Table of Contents

Preface vii

Introduction 1

Successful or Superficial? Discussion in David Crane's Classroom 2

Analyzing the Case of David Crane 5

Conclusion 6

Chapter 1 Introducing the Five Practices 7

The Five Practices 7

Anticipating 8

Monitoring 9

Selecting 10

Sequencing 10

Connecting 11

Conclusion 12

Chapter 2 Laying the Groundwork: Setting Goals and Selecting Tasks 13

Setting Goals for Instruction 13

Selecting an Appropriate Task 15

Conclusion 19

Chapter 3 Investigating the Five Practices in Action 21

The Five Practices in the Case of Darcy Dunn 21

Analyzing the Case of Darcy Dunn 26

Evidence of the five practices 27

Anticipating 27

Monitoring 27

Selecting 27

Sequencing 28

Connecting 28

Relating the five practices to learning opportunities 29

Conclusion 29

Chapter 4 Getting Started: Anticipating Students' Responses and Monitoring Their Work 31

Anticipating 31

Analysis of Anticipating in the Case of Nick Bannister 35

Anticipating what students will do 35

Planning how to respond to student approaches 36

Identifying responses that address mathematical goals 36

Monitoring 37

Analysis of Monitoring in the Case of Nick Bannister 40

Conclusion 42

Chapter 5 Determining the Direction of the Discussion: Selecting, Sequencing, and Connecting Students' Responses 43

Selecting and Sequencing 43

Analysis of Selecting and Sequencing in the Case of Nick Bannister 48

Connecting 49

Analysis of Connecting in the Case of Nick Bannister 56

Mathematical ideas: The meaning of the point of intersection 57

Mathematical ideas: Functions switch positions at the point of intersection 57

Mathematical ideas: Making connections among representations 58

Conclusion 59

Chapter 6 Ensuring Active Thinking and Participation: Asking Good Questions and Holding Students Accountable 61

Asking Good Questions 62

Exploring questioning in Regina Quigley's classroom 63

Analyzing questioning in Regina Quigley's classroom 67

Moves to Guide Discussion and Ensure Accountability 69

Revoicing 70

Asking students to restate someone else's reasoning 70

Asking students to apply their own reasoning to someone else's reasoning 71

Prompting students for further participation 72

Using wait time 72

Conclusion 73

Chapter 7 Putting the Five Practices in a Broader Context of Lesson Planning 75

Lesson Planning 76

Developing thoughtful and thorough lesson plans 78

Relationship between the TTLP and the five practices 80

Beyond the five practices 80

Creating a permanent record of the lesson 82

Conclusion 84

Chapter 8 Working in the School Environment to Improve Classroom Discussions 87

Analysis of the Case of Maria Lancaster 91

Overcoming Obstacles 91

Working with Others 92

Conclusion 94

References 95

Professional Development Guide 99

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