What is mathematical discourse?

Discourse in the classroom refers to the language teachers and students use to communicate thoughts through written words or conversation.

Mathematical discourse encourages students to reveal their understanding of math concepts as they engage in mathematical reasoning and
debate. Through rich mathematical conversations with teachers and peers, students become fully involved in questioning, conjecturing, defining, and explaining.

What are the benefits of mathematical discourse?

Productive mathematical discussions lead to deeper conceptual understanding, allowing students to develop their thinking in an open, supportive environment. Students who share ideas, construct arguments, and listen to perspectives of their peers develop strong verbal and mathematical reasoning skills.

Facilitated mathematical discourse also gives students tremendous insight into the world of mathematics, leading to a growth mindset as students become more eager to tackle new problems.

How do I work mathematical discourse into my lessons?

Establishing routine mathematical discourse in your classroom is no easy feat. Often, productive discussions begin with students explaining their reasoning and making their thinking visible to others. Encourage all students to share their ideas while valuing the contributions of their classmates, even if it does not lead to debate. Discuss your own mathematical thinking to encourage similar behavior in students.

What it takes and how to do it

During a recent Renaissance webinar Mathematical Discourse: What It Takes & How to Do It, Margaret (Peg) Smith identifies why it can be difficult to facilitate productive mathematical discourse. The author or coauthor of more than 75 books and articles, including 5 Practices for Orchestrating Productive Mathematics Discussion (co-authored with Mary Kay Stein), Smith outlines four key strategies for successful math discourse.

  1. Select the right task. Choose tasks that align to the goal of the lesson and require students to think for themselves, rather than follow previously learned material.
  2. Ask “good” questions and predict responses. Anticipate approaches students might take and create open-ended questions that make thinking public.
  3. Monitor groups as they work. Select and sequence groups to engage in discussions. Start with solutions that all students understand and build to more complex strategies.
  4. Hold students accountable for listening. As students make sense of solutions that are different from their own, they come to understand that others value their thinking.

If you missed Peg Smith’s webinar, check out the on-demand recording.

Resources and further reading

(2015) Talking Math: How to Engage Students in Mathematical Discourse. Retrieved from

(2017) 4 strategies to help students carry out successful mathematical discourse. Retrieved from

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