Why Mathematical Discourse Is Good for Students

As a new teacher, I remember my principal telling me, “When I walk into a classroom, the person I see doing the most talking is the person doing the most learning.” Her words stuck with me over the years, and I was always mindful of who was talking in my classes.

Now, as Carnegie Learning’s Director of Professional Learning (Jasmine) and Manager of School Partnerships (Tiffany), we get to visit classrooms and train teachers to facilitate robust mathematical discussions. You might be surprised by the impact they can have.

Math in the Old Days

When you think back to your middle and high school days, you’ll probably recall discussions in your ELA classes. But your math class likely consisted of teachers standing at the board solving equations. If you were lucky (or unlucky, depending on your relationship with math), maybe you got to solve a problem at the board now and then. If you were correct, the exercise was over. If you weren’t, hands probably shot upwards, belonging to others hoping for a chance to rectify your mistake.  

Thank goodness this old paradigm is changing because mathematical discourse is invaluable. Here's why you should make discussions a more significant part of your math curriculum.

1. Discussions Empower Students to Take Responsibility for Their Learning  

(Jasmine)

About five years into my teaching career, I ditched the top-down model and empowered students to discover new ideas through dialogue and inquiry-based learning. This switch happened when I moved away from an instructional resource that emphasized direct instruction and started using one that encouraged students to engage in exploration activities, collaboration, and, most importantly, questioning and discourse.

The result? Student learning was more effective and longer-lasting. I could tell from students’ higher test scores and their depth of responses that they were learning at a more meaningful level than before. What’s more, their dispositions toward math began to shift. Many students came to me hating math but learned to enjoy it because of the discussions that were happening every day.

I still treasure the moments when students grew comfortable enough with what they were learning to disagree with me. When students feel this level of agency, they can take responsibility for their own learning, and teachers can facilitate instead of feeding students every new piece of information. This is a win-win for everyone.

2. Discussions Build Confidence 

(Jasmine)

Do you know what a fortunate side effect of all this empowering, self-directed learning is? Confidence! 

Discussions provide a safe landing pad for productive failure. When I visit classrooms, I regularly see that students who are used to discussions that prioritize questions over solutions and discovery over correctness are more comfortable taking risks with more challenging topics. 

This confidence helps even the most unlikely students start thinking of themselves as “math people.” They realize that wrong answers are not the journey's end but rather a launching point for further thought. As students develop confidence by valuing process over product, they’ll be able to take on challenges in your classroom and beyond.

3. Discussions Build Community and Strengthen SEL Skills

(Tiffany)

Discussions are naturally collaborative, and they allow students to connect with and listen to each other. This takes the pressure off individuals to perform singularly, builds camaraderie, and encourages students to learn from their peers. 

The natural connections that happen in discussions can foster SEL competencies, something that is always critical, but even more so as students navigate learning during Covid. Working with others teaches students empathy, compromise, creative problem-solving, negotiation, and active listening, which are crucial 21st-century skills in and outside of math class.

4. Discussions Value Multiple Perspectives

(Tiffany)

Whenever I talk about how mathematical discourse honors multiple perspectives, I think back to my time teaching geometry. We were learning about exterior angles, and, as usual, students were tackling the task at hand differently. Some added the two remote angles. Others calculated all the interior angles and made a linear pair. And others did something pretty wacky that I don’t quite remember but ended up with the correct answer. While there is certainly an easy and efficient way to calculate exterior angles, the students who took other paths weren't wrong. 

When each group discussed their approach, it became apparent that multiple perspectives were both valid and productive for learning. When you can incorporate more experiences and approaches into your classroom, you come closer to establishing a genuinely asset-based education, and everyone benefits from this.  

5. Discussions Foster Critical Thinking 

(Jasmine)

Nationwide, most mathematical standards emphasize the need to let students explain their reasoning and critique the reasoning of others. Discussions go beyond focusing on answers and allow students to talk about process and methodology. And these discussions strengthen critical reasoning skills and metacognition. Discussions also give students the space to argue constructively and disagree respectfully. And, quite honestly, these are skills that will give them a leg up on many adults! 

Anytime I had two or more students disagree on a solution or even the solution pathway, I'd let them "argue” it out. Each side would outline their thinking, explain why it was correct, and explain why the other student was incorrect. Engaging in this type of discourse fostered critical thinking, deepened understanding, and built emotional maturity and mathematical fluency. 

6. Discussions Allow Students to Develop Mathematical Language  

(Jasmine)

Math is its own language, and how can we expect students to learn this language if they never get to practice it? Discussions allow students to familiarize themselves with terms and concepts specific to mathematical discourse and work towards attaining mathematical fluency. 

Mathematics is a discourse community, after all, and when students realize that they can function in a whole new community that was previously off-limits to them, they’ll have a tangible accomplishment to be proud of as well as a set of transferable skills.   

Still Reluctant? You Got This! 

Centering mathematical discourse in your lessons takes some front-end planning, especially if you’re new to facilitating discussions. But trust me, the rewards are innumerable. If you’re unsure of how to start, take small steps. Choose one problem and plan discussion around it by formulating thoughtful questions and anticipating student responses. Many teachers swear by Think, Pair, Share, and this is a good starting point.  

While building a community of math discussants will likely be challenging at first, if you keep at it, things will get easier. And as students self-direct more, you’ll start to guide learning rather than dictate it.

We’re Here to Help

Want to start incorporating more discussions into your math class? MATHbook will help you center mathematical discourse and empower your students to take ownership of their learning. Features including "Question to Support Discourse" will support you as you foster students' critical thinking, confidence, and enthusiasm.