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What is mathematical discourse?

Language specialists use the term “speech community” to describe a group of people who share common language norms that allow them to engage, ask questions, debate answers, and fully participate in the community (Hirsch, 2020). Math classrooms are essentially speech communities, where everyone shares the common language of mathematics. Mathematical discourse is evident within the math community when teachers and learners use their shared language to pose questions about problems and debate different ways to work toward solutions.

Mathematical discourse as the foundation for the math community

Mathematical discourse is more than simply talking about math. It is a set of tools and practices that make both learners’ and teachers’ thinking visible. How learners talk about mathematics reflects in part what they understand about mathematics. Lev Vygotsky (1962) writes that words are tools for building concepts and serve as our social means of thought. Without the vocabulary to question, describe, and debate, our thoughts—mathematical or otherwise—“remain in the shadows.”

Mathematical discourse requires a vocabulary more formal than everyday conversation. As an example, consider drawing as a tool to help you think through a concept. It is a foundational practice in mathematics and should be encouraged. However, as the concepts become deeper, mathematicians do more than draw. They represent, label, diagram, use keys, etc. (Hess, 2014). Think how the discourse matures when learners are challenged to represent the key elements in the problem at hand, rather than simply “draw” them.

One of the surest ways to engage each learner in mathematical discourse is found in small-group, student-led discussions. In one example, grade 9 Algebra students, who could easily identify a line, struggled to describe it mathematically. In focused discussions with peers, “slant” and “straight” matured into “slope” and “linear function” as they talked about the problem-solving task (Cooper, 2017).

Give them something to talk about

If the goal is to foster talking about mathematics, you need to give them something to talk about. For example, rather than asking young learners how many sides a triangle has, ask them to explain how the triangle is different from other polygons (Hill, 2016). Your questions set the stage for rich discourse. Similarly, rather than asking if 0.33 is equal to one-third, ask students to compare the relationships among one-fourth and 25%, one-half and 50%, and one-third and 33%.

To drive even deeper discussions, consider the Inquiry Based Lessons available in Freckle Math. These lessons situate mathematics learning via authentic settings and offer students multiple opportunities to think about the inquiry and debate ways of seeking a resolution. This is the epitome of a mathematics-focused speech community, where a common language and debate—in the form of mathematical discourse—offer multiple pathways to eloquent problem-solving.


Cooper, A. (2017). How personalized learning starts with less teacher talk, more student voice. Retrieved from

Hess, K. (2014). How to go deep to meet the new math standards. Webinar sponsored by Renaissance Learning.

Hirsch, E.D. (2020). How to educate a citizen: The power of shared knowledge to unify a nation. New York: Harper.

Hill, Z. (2016), Mathematical discourse, part 1: Choosing a task to talk about. Retrieved from,-Part-1_-Choosing-a-Task-to-Talk-About/

Vygotsky, L. (1962). Thought and language. Cambridge, MA: MIT Press.

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