Reading: O’Halloran, Kay (2000). Classroom discourse in mathematics: A multisemiotic analysis. Linguistics and Education 10(3): 359-388.

I got to lead discussion in class today.

At one point I told the story of how I first became interested in systemic functional linguistics. I was working as a teacher and going to teaching conferences, and I went to two or three SFL-related papers. Every time, the presenters would say “SFL is too complicated for me to really explain it to you; I’m just going to sum up the most important bit so you can understand what I’m talking about.” And of course, my contrary self wanted to know, what about the rest of it? What are you leaving out? Are you implying I wouldn’t understand it? Don’t tell me what I can’t do!

Well, today I was the one summing up. I figured, since time is limited, if they’re going to understand O’Halloran 2000 then we can do a five-minute summary of Process, Medium, and rankshift, and that should be enough.

It is a pretty crazy article. She’s talking about math notation, and how it has its own grammar that is deeply dissimilar to the grammar of natural language, expresses meanings that are not available to natural language, but can somehow be analyzed using some of the same analytic tools. And then, considering math class as a whole, you can’t understand what the teacher is saying without the notation, and vice versa. It breaks down like this:

**Notation** *generally* gives complete descriptions of mathematical objects and ideas

**Visuals** *generally* relate those descriptions to our sensory experience of the world

**Language** *generally* puts the notation and visuals in context

But then, of course, she talks about “semiotic metaphor,” which means that any one of those tools can be used for any one of those purposes, at least some of the time. She gives the example “the sum of the squares of two consecutive positive even integers,” which is a linguistic way of expressing *x2 + (x + 2)2*.

For me, all of this raises two key questions:

- What’s the relationship between non-linguistic and linguistic modes of communication?
- How do teachers teach and students learn all of this?

So we looked at some data, and we talked about it. There was a lot of good talk and a lot of good feedback. Notably, for my project as a publicist of SFL among discourse analysts, one colleague suggested that I should compare the process types that students use to those that show up in teacher talk. It’s a good suggestion that I hadn’t even considered, and a likely indicator of how much students have learned to “talk like mathematicians” (or at least, like math teachers).

Given that I was talking about math, and that O’Halloran’s examples come from high school trigonometry, I felt the need to give a disclaimer for the sake of any math-phobic members of the group. Of course, the data that we were looking at was from a 7th grade class, and didn’t seem to aggravate anyone’s phobias. And then later in the afternoon our department held a talk from a postdoc on formal semantics. Talk about math phobia … if you’re not familiar, scroll through this pdf.

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