Five Practices for Orchestrating Productive Mathematical Discussions

An excellent resource is a book by Margaret S. Smith and May Kay Stein, Five Practices for Orchestrating Productive Mathematics Discussions. [1] This book also includes a Professional Development Guide. The five practices are as follows:

Anticipating

In the Anticipating phase, the teacher predicts during planning how students will respond to a particular mathematic task. He or she considers possible alternative strategies that students may use, as well as potential misconceptions that may surface.

Monitoring

Monitoring occurs as the teacher circulates during the Explore of the lesson in a CMP classroom. He or she listens to student discussions while asking clarifying questions and posing new challenges.

Selecting

This Selecting phase involves choosing the strategies for students that occur during the Explore that will best illustrate and promote the desired understanding of the Focus Question.

Sequencing

In Sequencing, before the Summarize, the teacher plans which students will share their thinking, and in what order, so as to maximize the quality of the discussion.

Connecting

Finally, the Connecting practice which occurs during the Summarize involves posing questions that enable students to understand and use each other’s strategies, and to connect the Problem’s Big Idea to previous learning. Connecting practice may also foreshadow future learning.


References

[1] Margaret S. Smith and May Kay Stein, Five Practices for Orchestrating Productive Mathematics Discussions. NCTM. 2011