Thing-a-day #4: First-and-a-half draft of my problem statement

Here’s the outline of my doctoral program requirements:

  1. Three years of coursework, with qualifying reviews at the end of years two and three.
  2. In the semester after that, submit a problem statement and take an oral exam based on it.
  3. After passing orals, get a dissertation proposal approved.
  4. Write and defend a dissertation.

So, no comprehensive exams or anything like that (just distributional coursework requirements). Since I started part-time, I’m a semester out of sync — I have another semester of classes to go and my second qualifying review isn’t until November — but I try not to let these big requirements sneak up on me. For example, I always want to have an idea of what I would propose for my dissertation, if I had to do it today. So this semester I started working on my problem statement.

This is not a genre that was familiar to me. I asked around a little, and the general format in my concentration seems to be state a research question, explain your approach to it, identify four broader areas of existing research that will be important for you, and cite lots of sources. Here’s my outline:

The problem: What are the discursive practices (i.e., ways of speaking) of the secondary-school mathematics classroom? How do students position themselves relative to these practices, and to mathematics itself, as they participate in this community?

Important areas in the literature:

Epistemicity: What does it mean to “know” math, according to the people who do math? How is this reflected in the language they use?

Enregisterment: How do certain uses of language, as well as other meaning-making systems like equations and visuals, constitute a particularly mathematical way of communicating? How do people use that sort of language to position themselves as “math people” or not?

Language socialization: What’s the role of language in the process of learning math? This has two components: language is used as a tool for explaining math, but there are also math-specific ways of using language that have to be learned somehow.

Identity construction: How does students’ sense of their own identity change and develop as they go through math education? Which students are the ones who think of themselves as “math people”? How is this reflected in their use of language?

So far this amounts to a two-page document that cites all of my favorite sources. Yesterday I got a first round of feedback on my first draft, which was exciting, encouraging, and helpful, and I spent some time this morning making edits. (I should have been doing other things at that time, but that’s the danger: I’m more interested in this, which is why I picked it in the first place.)

I’m calling it a first-and-a-half draft because there’s still more to do before I show it to someone else.

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