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Meaningful Discussion Is the Glue to a Student-Centered Math Class
By John SanGiovanni, Elementary Mathematics Supervisor, Howard County, MD
Meaningful discussion is not about what we tell students but what they tell us.
Even more importantly, it’s what they tell one another.
Here’s why: those doing the talking are also those doing the thinking.
Mathematical discourse helps cement learning because discussion exposes students’ ideas to us and their classmates, opening the door to feedback and refinement. Discussion helps students sharpen their thinking while learning to communicate clearly and precisely. Most importantly, discourse exposes students to the strategies and reasoning of others, causing them to think more deeply about ideas while also acquiring different perspectives and approaches to add to their own knowledge.
A New Kind of Math Classroom
This is probably different from the math learning experiences many of us had as students. In those classrooms, the teacher explained what the students were supposed to do, and the students were to do it — no questions asked.
The teacher would ask a question here and there. Those questions were often closed, low-level questions. Students who could raise their hands the fastest were called on. Sometimes students were asked if they agreed with the teacher or a classmate, but typically, no one was ever brave enough to disagree.
And there were also occasions where the teacher publicly interviewed a student asking what they did and why. They might call for student demonstrations. In both cases, classmates sat by passively. In short, math class was expected to be relatively quiet, orderly, and somewhat rigid rather than what learning math should be.
Math should be interesting, engaging, and challenging. It isn’t about teacher understanding but rather centered on student understanding and reasoning.
Talking About Mathematics
The third standard for mathematical practice, Construct Viable Arguments and Critique the Reasoning of Others, calls for a student-centered math class, where talking about mathematics is a focal point. Discussion should be a vibrant exchange of ideas in which students get to share their thinking first.
In other words, math discussion is not done to students but rather with students.
This doesn’t happen by randomly calling on names written on popsicle sticks or calling on someone we think has tuned out. It is an intentional instructional practice. Effective math discussions develop through thoughtful planning. It starts with building trust, establishing a safe environment, and co-creating discussion norms. It takes time to train and practice with persistence and patience. Some things to consider for meaningful math discussions include:
- Anticipate (1): Taking a few moments to anticipate what students will do helps us prepare for math. It’s like a rehearsal for the lesson and our discussions. It can help us think about their strategies and possible misunderstandings.
- Do the task: To anticipate what our students will do, we have to take a few moments to also do the main task for the lesson. This helps us anticipate and it might help us recognize our own bias or preference toward solving a problem (2).
- Partner discussions: Turn-and-talk or “think-pair-share” are easy ways to get students engaged in discussion. The only problem is that often students don’t know exactly how to talk with each other about math. Some of the sentence starters and discussion prompts collected over the years and posted below can help.
- Checklist: Our students are still learning to craft arguments. Providing a checklist for them to frame their messages helps. It might include ideas like, my argument is clear, I included my reasoning (justification), I used the right words (precision), I included drawings or calculations.
- Listen Fors: Sentence starters help frame what a student is saying. Listen fors are a collection of reminders that help guide students on what to listen for. They sound like guidance for crafting statements but in reverse. We also have to take time to teach what it means to listen well and reinforce those expectations repeatedly throughout the year.
- Tools and Representations: Effective arguments often incorporate visual aids like diagrams, graphs, or symbolic expressions to support reasoning. They have to be a daily feature of our instruction if we expect our students to use them in their discussions.
- Community: The math class must be a place where discussion is safe. Classroom norms must feature respect and acceptance. Work to build a productive math class starts on day one but we must continually reinvest in it throughout the year (3).
Math discussion isn’t always easy, and it may feel clunky sometimes. It takes time, practice, and persistence — sometimes discussions feel awkward, and they won’t always go as planned. What matters most is consistently positioning students as leaders of the conversation. Rich mathematical discourse, held in a student-first format, doesn’t mean that we never tell them, show them, or explain to them how something works in mathematics. We do. But first, we let them talk about it to share their observations, attempts, setbacks, and questions. We use their ideas to craft the message that we want to ultimately deliver. We sometimes find that students will harness the mathematics and make it their own before we ever need to tell them a thing. Granted, we might need to help them polish those ideas, but we can be confident that they won’t have trouble remembering someone else’s way to do math because through discussion, they have made the mathematics their own.
Problem-solving is at the center of all we do in teaching and learning math. Meaningful math talk, however, is the glue that holds it together and moves us forward.
Questions to Ask Your Partner (During Turn-and-Talk)
- What is your answer?
- What did you do first?
- What did you do next?
- How did you solve it?
- Why did you ___?
- What made you think to ___?
- How did you know to ___?
Starters and Frames for Talking About Your Thinking
- I noticed …
- I know the problem is asking me to ____ because ______
- The strategy I used was …
- I selected this strategy because …
- When I checked my work, I noticed …
- I used ____ to help me find the answer.
Starters and Frames for Responding to Others
- I agree/disagree with _____ because
- Your reasoning makes sense because …
- I like _____ answer, but I solved the problem in a different way. I solved the problem by …
- My strategy is similar to/different from _____ because …
- I made a connection with what ____ said because ____
- Another strategy you could use is ….
Constructing viable arguments and critiquing the reasoning of others is the third of eight mathematical practices that build on one another to develop deep conceptual and procedural understanding. You can learn more about why these math practices are so important by reading Dr. SanGiovanni’s blog, here:
Our TK-12 math program for California teachers, California Reveal Math, offers persistent opportunities for meaningful math talk and teacher guidance to facilitate classroom discourse, to help teachers address important elements of the 2023 California Math Framework. To learn more about California Reveal Math, visit mhecalifornia.com/reveal.
Learn more about our national PreK-12 math program, Reveal Math, at revealmath.com. Classroom discourse and all eight math practices are a central component of Reveal Math’s instructional design.
John SanGiovanni is an elementary mathematics supervisor in Howard County, MD, where he oversees mathematics curriculum, digital learning, assessment, and professional development. He is the coauthor of the best-selling Putting the Practices Into Action and the Mastering the Basic Math Facts series. He is an adjunct instructor and coordinator of the Elementary Mathematics Instructional Leader graduate program at McDaniel College as well as a national consultant for curriculum and professional development.
References
(1) Smith, M. S., & Stein, M. K. (2011). 5 Practices for orchestrating productive mathematics discussions. National Council of Teachers of Mathematics.
(2) SanGiovanni, J., Katt, S., Rivera, G., & Knighten, L. (2023). Answers to your biggest questions about teaching elementary math. Corwin.
(3) SanGiovanni, J., Katt, S., & Dykema, K. (2020). Productive math struggle: A six-point action plan for fostering perseverance. Corwin.
