Talking Circles and Math

Strange things happen when you go into a classroom and talk about something of which you’re very passionate. Sometimes, people take away something you had no intention of discussing. The same principle applies when giving a talk at a convention apparently.

When I was at NCTM talking about what I tried in my stats class, one of the slides I showed became an instant hit. It was posted on Twitter I think 5 times, making it one of the most popular tweets of all time.

So Geoff at Emergent Math asked me for a follow up explanation of tracking conversations. He flattered me, and I’ll oblige.

Last year around this time, I began to read Nate Silver’s The Signal and the Noise. As I read, I became more and more convinced that the narrative behind the book could drive my AP Statistics class. I set an intention to integrate the learning objectives of the stats class by reading parts of the the Signal and the Noise. For example, instead of introducing confidence intervals with a definition or an example, I really wanted to take the story of a flood plain in North Dakota to introduce the idea. This idea is what I presented at NCTM.

When I decided that I would assign actual reading to my class, I had an idea of how it would go. I would assign a reading, then at the next class I would begin a class with a simple question, “What did you LEARRRRNNNNN?” all mystical like, as if I was in one of those hoity-toity movies about … reading or whatever.

It turns out that when I framed the discussion this way, I didn’t exactly get the result that I was looking for. But, hey, this is coming from the guy who invented General Mutant Pancake Theory – no problem. I’ll just walk down the hall to my friends in the English and History departments and steal all of their ideas. One idea they had for me was tracking conversations.

The basic structure is this: Before class starts, I have students read and I give them some leading questions. Questions like:

  • What are the differences between an observation and an experiment?
  • How were correlation and causation discussed?
  • What is a lurking variable that came up?
  • How do we “prove” causation?

During class, students sit in a circle. We put up all the names on the board. Either a student or I are in charge of “tracking the conversation”. My job is to listen and ask questions. Their job is to make the conversation awesome.

In the diagram below, A(dam) makes a point about how causation can be confused with correlation, then D(enise) follows up with something she heard on NPR that relates to the pregnancy study. F(reddie) asks how one can prove causation and then A(dam) reminds him of a problem in which we talked about proving causation. C(eara) asks another questions about how this relates to confidence intervals, and the conversation continues.

image

We don’t really need arrow heads for any of these lines, we just need to see who’s involved and to what degree. G(reg), E(than) and B(etsy) haven’t chimed in yet, but everyone sees that, and at times I might direct the conversation at one of them if they still have no lines connecting them to the rest of the conversation. But usually, another student will call them out, which I think is super empowering.

What makes this work? First, no matter how advanced the students are, they are still amateurs in the subject area. Even though they may be great symbol manipulators or really understand what we’ve done so far, I intentionally gave them material that is new and just outside of their knowledge base.

Second, by taking myself out of the circle and being a guide, it takes the sense of agency away from me and gives it to them – again, then idea that I’m trying to empower them. I rarely correct any incorrect interpretation, but if it seems to pervade the conversation, I might ask some clarifying questions.

Caveat: this system probably isn’t working if you have a class of 30. I have only tried it with ~15. However, it’s totally possible to break the kids into smaller subgroups and do the same kind of thing.

I’ve been interested in Socratic-seminar-like conversations in math class for a long period of time. All knowledge is socially constructed, so when I see students being active agents in that process, it models what learning outside of the false environment of school looks like. Not to get all Vygotsky on you, but constructing a situation like this makes different neurons fire in young brains than just having them work independently.