5 Practices for Orchestrating Productive Mathematics Discussions

The book 5 Practices for Orchestrating Productive Mathematics Discussions, by Margaret Smith and Mary Kay Stein, provides concrete guidance on how to create more powerful discussions in math classes. The ideas are briefly summarized here.  

Facilitating productive discussions about mathematics is very challenging for any teacher. Some lessons can end effectively with a “share and summarize.” At other times, though, a more purposeful discussion is needed to bring out the key mathematics of a lesson.

A key component of productive discussion is teacher facilitation. This facilitation is not accidental and cannot, generally, happen on the fly.

Here are 5 concrete steps that can help improve the quality of mathematics discussion in your class.

1. Anticipating likely student responses to mathematical tasks. 
   Involves envisioning potential student responses, strategies (correct or incorrect), representations, procedures, and interpretations.
2. Monitoring students’ actual responses to the tasks. 
   Involves paying close attention to students’ mathematical thinking as they work on a problem. Commonly done by circulating around the classroom during group work.
3. Selecting student response to feature during the discussions.
   Involves choosing particular students to present their work because of the mathematical responses. These responses need not be chosen solely because they are correct, but rather because they emphasize different approaches to the problem. In fact, it may be advantageous to choose incorrect responses to highlight how and why they are incorrect. This choice can highlight a variety of responses or strategies for a task, or it can show a progression from simple to complex representation. Make sure over time that all students feel they are authors of mathematical ideas.
4. Sequencing student responses during the discussions.
   Involves purposeful ordering of the featured student responses in order to make the mathematics accessible to all students. This also helps build a mathematically coherent story line during whole class discussion.
5. Connecting student responses during the discussions.
   Involves encouraging students to make mathematical connections between different student responses. This helps ensure that key mathematical ideas remain the focus of the lesson debrief.

The 5 Practices for Orchestrating Mathematical Discourse were adapted from the Japanese model of Teaching Through Problem-Solving.