To engage students in productive mathematical conversations, teachers must plan, initiate, and orchestrate discourse in ways that encourage student learning. Just preparing the content of a math lesson is not enough. Teachers must select worthwhile mathematical tasks that provide opportunities for students to engage in rich mathematics discussions.
Five Practices That Promote Math Discourse
Research shows there are best practices that can be used to create a classroom environment that fosters rich classroom discussions. In the second edition of their seminal book 5 Practices for Orchestrating Productive Mathematics Discussions, researchers Margaret S. Smith and Mary Kay Stein describe five specific practices teachers can use to plan and lead productive math discussions. The five practices are viewed as critical components of a well-designed plan to make purposeful and thoughtful decisions that ultimately strengthen students’ understanding of robust mathematics.
“Actively envision how students might approach the mathematics task they will work on,” Smith and Stein write. For example, teachers can consider the following questions:
- “How might students interpret the problem?”
- “What different strategies might they use?”
- “What specific aspects of the subject matter do I want them to understand?”
- “What errors or misconceptions might they make?”
“[Pay] close attention to students’ mathematical thinking and solution strategies as students work the task,” individually or in small groups. For example, as teachers walk around the room to observe and interact with students, they can use a tablet to note which students use expected or unexpected strategies and when they use them. This helps teachers keep track of which student or group produces solutions and which ideas to emphasize during the whole class discussion.
“Select particular students to share their work with the rest of the class to get specific mathematics into the open for examination.” The selected students can be alerted in advance to give them time to gather and organize their thoughts.
“By identifying, sharing, and discussing the causes of errors, students learn to avoid potential pitfalls and misconceptions that may interfere with their reasoning and understanding.”
“Make decisions regarding how to sequence the student presentation.” The goal is to maximize connections between and among ideas. For example, a teacher may first call on a student or group with an incorrect thought or answer to highlight a common misconception before the class discusses the correct answer.
“Help students draw connections between their solution and other students’ solutions as well as the key mathematical ideas in the lesson.” For example, they can ask the following questions:
- “How are these two ideas similar?”
- “How are they different?”
- “How does this second idea build on or extend the idea we just heard?”
These five practices build on each other to help teachers orchestrate mathematical discourse in meaningful ways. Although it is not possible to anticipate every strategy a student might present, the five practices provide a way to capture, make sense of, and organize mathematical discourse in ways to maximize learning.
This post has been adapted from Selecting and Sequencing Student Solutions: Facilitating Productive Mathematics Discussions in the Classroom and Orchestrating Mathematical Discourse to Enhance Student Learning. To learn about using mathematical discourse in your classroom, download the whitepapers.
Smith, M., & Stein, M. (2011). 5 Practices for Orchestrating Productive Mathematics Discussions (2nd Ed.). Reston, VA: National Council of Teachers of Mathematics.
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