Engaging your students in meaningful math conversations doesn’t just happen. It requires planning and orchestrating discourse in ways that support understanding. But how do you facilitate this?
Just preparing the content of a math lesson isn't enough—you need to select specific mathematical tasks that provide opportunities for your students to ask questions to promote learning.
When your students take the time to think, share, and compare strategies, you have greater insight into their thought processes and can plan classroom conversations and anticipate possible solutions.
Fostering Rich Classroom Discussions
As part of a well-designed plan, the following best practices based on “Orchestrating Productive Mathematical Discussions: Five Practices for Helping Teachers Move Beyond Show and Tell” by math educators Margaret Smith and Mary Kay Stein will strengthen your students’ understanding of complex mathematical practices:
“Actively envision how students might approach the mathematics task they will work on,” Smith and Stein write.
For example, consider the following questions:
• “How might your students interpret the problem?”
• “What different strategies might they use?”
• “What specific aspects of the subject matter do you 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 you walk around the room to observe and interact with your students, note which students use expected or unexpected strategies and when they use them. This helps you keep track of which student or group produces solutions and which ideas you should 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, you 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 and the steps for getting there.
“Help students draw connections between their solution and other students’ solutions as well as the key mathematical ideas in the lesson.”
For example, try asking 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 you orchestrate mathematical discourse in meaningful ways. Although it’s not possible to anticipate every strategy your students might present, these 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.
Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313–340.