Why should students talk to each other in math class anyway? I was asked this question recently and I’m trying to avoid a tautological answer (eg. it’s important because it’s important).

In a classroom where students speak to each other about mathematics, the ideas of those students are valued instead of ignored or potentially marginalized. This gives students agency in their learning. It also allows new ideas the students learn to extend from the existing ways they understand the world.

Supporting students speaking to each other means that mathematics is much more likely to become a way of knowing and being rather than just a body of existing knowledge (although the value of mathematics as a set of tools that have been developed over time should not be marginalized). As students develop their understanding of what mathematics is and what it is useful for, they are more likely to insert themselves in the role of the mathematician rather than imagining this to be someone else, potentially from another culture. They can see themselves being part of a mathematical community.

In order to completely understand the language we know, we have to use it, either in writing or ideally in conversation, and hear other people using the same language. So from a practical perspective, students need to talk in order to develop their use of language (mathematical or otherwise), and rather than students talking in serial, one at a time mediated through a teacher, it is far more efficient for them to talk in parallel, to each other.

We remember what we think about. When students construct ideas and communicate them to each other, they necessarily have to think about these ideas, which means that they are building memories. While this occurs no matter what students do, the focus is more likely to be on the thinking with student discourse rather than the activity (eg. completing a task).

Finally, students talking and writing to each other also provides their teachers with more information about the ways they are thinking which makes it easier for the teacher to orchestrate productive whole group discussions and to plan activities that respond to the ways students are actually thinking. It is difficult to plan lessons that build off of student knowing if you don’t know how and why students think the way that they do. When students talk to each other, their teacher can gather formative assessment information about not only **what** they understand but ideally **how** they understand it.

This should not diminish the importance of students having *independent time* to work quietly on mathematical problems *by themselves*. Students are better positioned to work together when they have had time to think about ideas themselves first. Also, some students find working with other students really difficult for a variety of reasons, so in some cases the benefits of students working together may be outweighed by the challenges some students face with this activity.

What would you add as reasons students should talk to each other in a mathematics classroom?

Both independent and students pair/group work allows students to exchange ideas and strategies. It also creates an opportunity for the teacher to check in on a more individual basis which also helps to develop personal relationships with students.

When I saw the title yesterday (without reading it fully first because it got broken before I could), I immediately thought of two main things. Both of which relate to generalizing what “talking to each other” means in a classroom context.

The first is about communicating mathematics. Similar to what you wrote here:

“When students construct ideas and communicate them to each other, they necessarily have to think about these ideas, which means that they are building memories.”

This is important. This means creating a need to communicate the mathematics that they are in the process of understanding – in turn helps them understand it!

The second thing I thought of, was actually not one that you’ve explicitly mentioned – although I have a feeling you will agree with. The second thing is listening. Listening does not come easy. Listening to others is one of the most important thing I value in my daily happenings. Conversations aren’t one way streets. It is an important aspect for students to understand. In addition, listening-to-the-reasonings-of-others are valuable opportunities for better understanding. How many of us teachers believe that we learn from our students? I would say most of us. Did we do this through talking at them? Likely not. It is an invaluable experience that we would be providing students.

So these two were the main ones I was thinking of yesterday (before the site went down). Just now I had more of a chance to stare at the question again, and I would agree with Brian Lawler’s short comment about citizenship. Except more specifically, I would begin with the social relationships within the classroom. Relationships built under the tyranny of the all-powerful speaker in front, would be very different from ones built from a cooperative classroom. And so from a different standpoint, the talking classroom would not only provide examples for talking about strategies and working towards solutions, it would also provide a statement for the power relationships within the classroom. Doesn’t this kind of classroom classroom provide a wonderful opportunity for classroom discussions regardless of race, gender, and religion? And depending on how we facilitate the group discussions, we can even provide power to those who don’t feel they have it.

These, along with the other reasons that you have suggested, would be my current thoughts towards answering the question.