Lately I’ve been emailing with Bryan Meyer (@doingmath) about theories of learning and where you draw the line between learning and indoctrination. Bryan is a math educator, researcher, and radical constructivist, so when I was writing about students undergoing a process of socialization — which entails “becoming like” senior members of the community — he pushed back on this. He asked whether education can be considered to lead students to “become” something without necessarily “becoming like” their teacher or some other model. I asked what he meant, and he suggested I look at this article by Rochelle Gutierrez (PDF). Here’s my response:

Hi Bryan –

I finally got around to reading this – it’s an interesting article, thanks for sending it. I ought to set aside some time to read more deeply in the math education literature.

Reading this article has me thinking a lot about her claim that “inner city students must be subjected to a kind of ‘parking their identity at the door’ in order to learn rigorous mathematics” (p. 44) – I’d always thought of that idea as being in some way separate from the actual math content. Math isn’t like literature – it’s important to see yourself in the books you’re reading in English class, because that sends a message that school is a place for people like you, but times tables / cosines / integrals are the same for everyone; the idea that “math people” tend to be poorly dressed white or Asian males is an ideology that gets overlaid on the actual practice of mathematics. But now, reading Gutierrez, I wonder if that’s me speaking from a place of privilege and assuming that what I’m used to is in some sense universal. (Although if it isn’t, and every cultural group has their own mathematics, then what should be taught in math class? Should standards / curriculum depend on classroom demographics? Am I in Nepantla yet?)

As far as situated learning, she seems to use the phrase “community of practice” in a technical sense that I’m not familiar with. She does say this, which caught my eye:

Most often, the goal in mathematics teaching is to try to get the student to become a legitimate participant (Lave & Wenger, 1991; Lampert, 1990) in the community of mathematicians, thereby subsuming their identity within the currently sanctioned way of communicating in the field. (p. 38)

That word “subsuming” is not in line with what I understand situated learning theory to be, and maybe this gets to your previous question. Whenever anyone learns anything, it’s a process of identity navigation. I’m taking an ASL class this summer, and I’m going to have to develop some sense of who I am as an ASL speaker. As I join the community, that changes me, but it changes the community as well. Now this isn’t really a good comparison for underprivileged students taking high school math – I don’t need ASL, and there are no structural boundaries preventing me from getting access – so then, as I think about the theory, the question becomes how to incorporate sociological ideas of privilege into a situated learning framework. For me, the way I’ve done it, is I’ve noticed that students tend to have a mental image of who the central community member is, and for various reasons they may conclude that they can’t or don’t want to become that person.

So, it’s thought-provoking stuff – thanks for sharing. I’m curious to learn your take on it.

*The conversation continues on Bryan’s blog: “Must schooling require ‘becoming like’?”*

So… I would be interested in an articulation of a specific cultural group’s mathematics–a description that is as developed to the level of delicacy and application that “the Discipline” has been. And a comparative description would be even more interesting. For instance, what is the difference between Greek math and Icelandic math, or, in my own region, between Kentuckian math and Hoosier math. Or perhaps even closer–how do Indiapolisians do math differently from Lafayetteans? Is there the same level of delicacy with math as there is in language–is there an idiolect version of mathematics? Is Ginsberg math different than Maune math? Are there different semiotic systems realizing different mathematical meanings? Are Ginsberg math meanings incommensurable with Maune math meanings? And then… since machine-readable languages only understand the dominant mathematical dialect, does that mean computers are built prejudiced?

I can’t decide if all that I wrote was tongue-in-cheek or in earnest. Because if there really is a culturally-defined mathematics that is fundamentally and categorically different than the weaker notion that people use a universal semiotic system and universally agreed-upon set of mathematical meanings to do different things–meaning that math is the same but applications are different (like there are different genres in different cultures to accomplish tasks relevant to the culture),–then I would be really interested in learning about a different culture’s mathematics. I have some serious doubts that such things exist, but if they did exist, that would be really interesting.