Book Review - 5 Practices for Orchestrating Productive Mathematics Discussions

03-21-2022 15:10:18

Title:  5 Practices for Orchestrating Productive Mathematics Discussions - 2nd Edition
Author: Margaret S. Smith and Mary Kay Stein

Brief description:
Learn the 5 practices for facilitating effective inquiry-oriented classrooms:

  • Anticipating what students will do--what strategies they will use--in solving a problem
  • Monitoring their work as they approach the problem in class
  • Selecting students whose strategies are worth discussing in class
  • Sequencing those students' presentations to maximize their potential to increase students' learning
  • Connecting the strategies and ideas in a way that helps students understand the mathematics learned


This book presents and discusses a framework for orchestrating mathematically productive discussions that are rooted in student thinking.


The 5 Practices framework identifies a set of instructional practices that will help teachers achieve high-demand learning objectives by using student work as the launching point for discussions in which important mathematical ideas are brought to the surface, contradictions are exposed, and understandings are developed or consolidated. By giving teachers a road map of things that they can do in advance and during whole-class discussions, these practices have the potential for helping teachers to more effectively orchestrate discussions that are responsive to both students and the discipline.

 Includes a Professional Development Guide.

Picture of book: 

Important aspects (quotes): 

This book is a great tool for  ‘book club’ type meetings in which actual case studies are presented and then questions are presented to help analyze the positives and negatives to help participants self-reflect on their own plans.  

 There are many specific tools presented including a Task Analysis guide.

 In the final chapter it summarizes lessons learned and potential benefits of the Five Practices as: 1) High-level cognitively demanding task are a necessary condition for productive discussions; 2) If all students solve a challenging task the same way, lesson reflection can provide clues as to why this may have occurred; 3) Students need time to think independently before working in groups; 4) The goals for the lesson should drive the teacher’s selection of responses to share during a whole-group discussion; 5) If you leave students with advancing questions to pursue, you need to follow up with them to see what progress they have made; and 6) A monitoring chart is an essential tool in orchestrating a productive discussion.


  1.  Introducing the Five Practices
  2. Laying the Groundwork: Setting Goals and Selecting Tasks
  3. Investigating the Five Practices in Action
  4. Getting Started: Anticipating Students’ Responses and Monitoring Their Work
  5. Determining the Direction of the Discussion:  Selecting, Sequencing, and Connecting Students’ Responses
  6. Ensuring Active Thinking and Participation:  Asking Good Questions and HOlding Students Accountable
  7. Putting the Five Practices in a Broader Context of Lesson Planning
  8. Working in the School Environment to IMprove Classroom Discussions
  9. The Five Practices: Lessons Learned and Potential BEnefits;


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