Every student has had a different journey through math learning before becoming a member of your classroom. How can we draw on these different experiences as we strive to build a community of math thinkers, of students who feel capable of tackling learning challenges as they further their understanding?

Encouraging math discourse has incredible benefits for each member of a classroom. When we provide opportunities for students to talk with one another and share their thinking, we as teachers can discover so much about them. How deep is this student’s level of understanding? What misconceptions might be getting in the way? What is this student’s style of learning? Which students explain their thinking better verbally rather than by showing work on paper? Which students are less confident in their explanations and could use additional encouragement or scaffolding?

Beginning with a high-quality contextual question allows an entry point for every student - we can all at least draw a picture to model what the question is about. After allowing for some individual think time, start by giving students a chance to pair with a partner or small group (even while social distancing) to build confidence in sharing their thinking. By providing some sentence starters such as “I started by drawing a picture but then I got stuck,” “First I tried…” or “My strategy is similar to/different than yours because…” students have a chance to connect one strategy to another, expand on each others’ thinking, or try out someone else’s idea and discover that it helps them to find their own path to a solution. All of this occurs with no more than a few words or questions from the teacher. By structuring a classroom that encourages student voice and discussion, I’ve seen even the least confident students with significant gaps in learning flourish. They jump at the chance to share their thinking with their whole class of peers, taking pride in the model they created or the way that they tried out someone else’s idea and found new understanding.

It’s truly magical to see a student’s synapses fire before our eyes. We always talk about that light bulb of understanding going off but it’s so incredibly powerful for a student to see that they were the reason that a friend now “gets it;” that the connections they made and their willingness to share ideas led to someone else furthering their understanding. It’s truly empowering for a kid to have that kind of impact on their peers.

A classroom rich with math discourse has many incredible benefits to students. New learning is more meaningful to them when they build connections to their previous learning and students become more invested when they are making connections to others’ strategies. When students have repeated opportunities to explain their thinking to others, to use mathematical language, and to find connections between strategies or models, they’re becoming math thinkers, not just math “do-ers.”

Building a classroom environment that not only encourages student discourse but relies on it as an essential tool allows us to naturally attend to our Mathematical Practice Standards. As students share and discuss their thinking, they make sense of problems while communicating their understanding and reasoning with others. Through their discussions, they notice and attend to their own and others’ precision of communication, reasoning, regular use of math vocabulary, and the connections between multiple strategies and approaches to problem solving. When asked to support their thinking, more opportunities exist for students to slow down, to consider the reasonableness of their solutions, and further develop their mathematical thinking skills and understanding.

Student discourse is integral to students seeing themselves as capable mathematicians and as part of a classroom community that works together to build understanding. As teachers pull away from seeing themselves as the “keepers of math knowledge” and instead see themselves as facilitators of mathematical thinking, truly incredible learning takes place.