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Orchestrating mathematical discourse to enhance student learning

This post is sponsored by Curriculum Associates.

The importance of engaging students in meaningful mathematical discussion has long been identified as an essential component of students’ mathematics learning. With the new requirement by the Common Core Standards for Mathematical practice, it has become even more crucial that students reflect on their own understanding while making sense of and critiquing the ideas of others in a collaborative and supportive learning environment. When students share and exchange their ideas, both they and their teachers benefit. Here, Gladis Kersaint, professor of mathematics education at the University of South Florida, addresses questions about how educators can create successful classroom environments where every student participates in rigorous discussions.

What is mathematical discourse and why is it important?

Mathematical discourse is spoken and written communication about mathematics in the classroom, specifically around the ways in which teachers and students strategically work together to represent, think and talk about math. There are several important benefits of mathematical discourse:

  • Classroom discussion ultimately reveals a student’s understanding of the concepts presented by asking them to show both how a problem was solved and why a particular method was chosen.
  • Students learn to engage in mathematical reasoning and debate, developing the mathematical language skills needed for productive discourse and learning.
  • Students learn to constructively critique their own and others’ ideas while seeking out efficient mathematical solutions, a skill transferable to other areas of their lives.

What strategies can teachers use to facilitate “productive talk” and encourage full student participation in their classrooms?

Teachers need to be intentional about how they begin mathematical discourse, recognizing that students are not immediately prepared for this type of conversation. This means establishing classroom norms right away and continually modeling and reinforcing specific behaviors, such as appropriate ways to engage in a disagreement with a peer. Instead of attacking a peer’s answer to an issue, students should be taught to focus on attacking the issue itself.

Providing the correct language to use is especially important at certain grade levels. Middle school students in particular benefit from this guidance. By consistently using certain responses themselves (and calling attention to the use of these responses), teachers can facilitate the desired classroom productivity and participation levels. This can be done through strategic questions designed to support instructional processes as well as direct/redirect student focus, such as:

  • “Would you please repeat that? I heard you say x, but I think you meant y.”
  • “Do you agree with Julie’s reasoning?”
  • “Did anyone do the problem a different way?”
  • “Can someone explain Caitlin’s approach in another way?”
  • “What assumptions did you make when you solved this problem?”

How do students benefit from having their answers evaluated by their peers?

Having their answers evaluated by peers encourages students to think about things from someone else’s perspective. While listening to their peers, students learn to pay careful attention to subject matter so they can decide whether they agree or disagree with the given answer and why. This process reveals alternative approaches to solving problems that they hadn’t thought of before and can then adopt because they make more sense. It also reinforces the need to think about what they say and how they say it.

How can teachers help students feel more comfortable about making mistakes, especially those they make “out loud?”

Teachers are responsible for creating a learning environment where it’s acceptable to make mistakes as mirrored through their own responses to errors. When students are encouraged to make conjectures and explore, they may reach erroneous conclusions. When they make mistakes and participate in classroom discussions around mistakes, they begin to see them as simply part of the math learning process. As a result, teachers can recognize and reinforce errors as natural occurrences that enhance learning rather than a reason to be embarrassed in front of peers.

In addition, school administration can help support teachers in the creation of this learning environment by visiting and viewing a classroom during discourse and reinforcing positive student engagement as it happens.

What are some best practices for teachers to keep in mind when planning to facilitate mathematical discourse in their classroom?

The five process standards—problem solving, reasoning and proof, communication, connections and representation—shared in Margaret Schwan Smith and Mary Kay Stein’s book on mathematical discourse—are excellent best practices to follow when approaching the task of planning and facilitating an effective inquiry-oriented classroom. Such practices include:

  • Anticipating the strategies students will use in solving a problem
  • Monitoring students’ work as they approach the problem
  • Highlighting students’ strategies that should be shared with the classroom
  • Organizing students’ sharing that will be beneficial to the class
  • Connecting the strategies and ideas in a way that helps students understand that, even though different approaches may be used, the underlying math is the same.

Learn more about Ready® Mathematics, the rigorous instruction and practice program that supports a rich classroom environment in which mathematical reasoning, mathematical discourse, and the mathematical practices all thrive. Its comprehensive teacher support makes it powerfully simple for teachers to implement.

Dr. Gladis Kersaint is a respected scholar in mathematics education. She has published books, chapters and journal articles on teacher education, effective teaching of at-risk students and the use of technology in teaching and learning. She is an author of Curriculum Associates’ Ready® Mathematics program.