Listening, Math, and Mathematical Questions

A friend of mine has been working to improve her middle school math students’ listening. They are focusing not just on “paying attention,” or listening to the teacher, but on listening to one another as well. It is challenging and important work. Listening is not just a matter of good manners and a calmer classroom (though what teacher wouldn’t welcome those?) but a way to allow better processing of content. In order to think deeply about math, students need to be able to talk about math, problem solve together, think flexibly about options, and compare ideas. They need to engage in mathematical discourse. And that requires listening.

Perhaps when she has time, my friend will share some of her mini-lessons on listening (or maybe your have some good ideas?). In the meantime, I can share a good resource for mathematical discussions: 100 Questions that Promote Mathematical Discourse. I downloaded it from Curriculum Associates.  Just scroll down to the bottom to find the download option. I don’t know anything about the rest of their products (so, clearly, this is not an endorsement) but this lovely freebie is a good place to start.

So many of these questions bring to mind basic creative thinking processes, particularly in the section titled Help Students Learn to Conjecture, Invent, and Solve Problems:

What would happen if….?

Do you see a pattern here?

Is there another possible answer? If so, explain.

What else would you like to know?

How did you think about the problem?

It strikes me that this kind of conversation has multiple benefits. Of course it promotes deeper mathematical thinking and understanding. It can help students practice flexible thinking in approaching mathematics. Coupled with discussions about listening to one another, it can also help build a classroom atmosphere in which students’ ideas, opinions, and processes matter. Such classrooms make it safe to ask questions, explore ideas, and take risks. That is the kind of place in which learning can flourish–and creativity, too!

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