Mathematical Discourse

Getting students to talk about math is really, really important. It’s the number one vessel to invite students to make conjectures, revise ideas, and develop mindsets that mathematics is open and creative; it’s the teacher’s primary tool for formative assessment. But productive talk and math “show and share” are two different things. Check out the resources below to learn how to make our math discussions valuable for everyone.

Meredith's Must-Know Info

Mathematical discourse, or how students communicate their math ideas, is of utmost importance in every math classroom. When students engage in productive math discourse, they have opportunities to refine their own ideas, to increase their conceptual understanding, and to practice reasoning and justification skills. Math discourse is an important tool for teachers, too. When students start talking about their ideas we can more fully understand what they know and what they are yet to know. Gaps in understanding are more easily revealed through discourse; there are fewer chances to hide misconceptions behind correct answers that may not be grounded in conceptual understanding.

Getting Started with Mathematical Discourse

1. Build a community climate that values all ideas and welcomes mistakes.
   • Talking about math can produce anxiety in some students. Imagine your own learning experiences as a math student… did you tremble at the thought of “being called on?” Did you breathe a sigh of relief when the bell rang and you managed to escape math class unscathed? Students must feel safe in order to express mathematical ideas in a small group or whole group discussion, and we want to establish a community that feels far removed from the anxiety-inducing situations of many traditional classrooms. The Building a Mathematical Community section has some detailed suggestions for community building, but you can start with establishing the norms that everyone’s ideas are valued and everyone has math ideas to contribute for the good of the group. Offering students opportunities to rehearse their ideas with you prior to sharing whole group, engaging students in small group discourse, or inviting students to share ideas with you individually are also effective instructional strategies.
2. Follow the 5 Practices for Orchestrating Discourse Protocol (developed by Margaret S. Smith and Mary Kay Stein).
   • Anticipate: The more we anticipate what students might say and the strategies and misconceptions that might come up, the better prepared we will be with appropriate questions or scaffolding in response.
   • Monitor: Move around the room while students are engaging in the task. Conference with students using purposeful questions that focus learning without removing opportunities to use problem solving skills.
   • Select: While you monitor students working, make intentional selections about the students/ strategies that will be discussed at the whole group discussion at the end of work time.
   • Sequence: Think about the order that you will invite students that you have selected to present their work. This order needs to help you to meet the math goals of the discussion. You can order strategies/ solutions by increasing difficulty or compare and contrast two strategies for efficiency or relationships. Or you could troubleshoot a common mistake together. The sequence is important in helping you to meet the math goals of the discussion.
   • Connect: Although this is the last step of the 5 practices, how you will connect the math ideas of the discussion needs to be considered before you even begin the lesson. What mathematical goals/ concepts/ strategies will you target during the discussion? What questions will you ask to help students to make these connections to the mathematics? What standards of math practice will you target? The connect piece of orchestrating discourse is the part that helps you move the discussion beyond math “show and share” to productive discourse. It’s not to be skipped!

     Note: Orchestrating Discourse Teaching Tool available in Lesson Support

3. Choose a talk-worthy task.
   • Without a rich task, there will not be much to talk about! In order to have a productive discussion, students need opportunities to engage in productive struggle which means we have to choose tasks that offer opportunities for that. If you suspect your tasks may not yet be talk-worthy, check out the resources in Worthwhile Tasks. Some teachers have told me that getting started with mathematical discourse is a little bit scary. Worries include: “I’m not sure about releasing my control to my students.” “What do I do if a student shares a strategy that I don’t understand?” and “I don’t have time for all this talk.” If you have had concerns like these, just pause and breathe. It’s ok to not know a student strategy… that offers an opportunity for you to model growth mindset and you always have the out of saying, “Oh, wow. I’ve never thought about it that way! Let me think more on that tonight and I’ll get back to you tomorrow. Thanks for challenging me!” Then, you can bring that piece of student work to some colleagues and collaborate around how to respond to the student, or invite the student to explain it to you in more depth later in the day. That will honor the student’s thought without derailing the conversation. Also, it’s important that we give ourselves the “space and grace” to learn new instructional strategies just like we want to offer that safe space for students. We will make mistakes. But we will grow and improve. And our students will grow and improve because of our efforts. Finally, I would argue that we don’t have time NOT to engage our students in discourse. We have been given the charge to engage our students in eight standards of mathematical practice and if we do that effectively, we must get students talking about math. We are building critical thinkers, mathematicians, problem solvers. To do that well, let’s start talking!

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