At the SLAC I have often ended up with a young woman frustrated and sometimes near tears who is asking questions about, say, optimization. They are not usually asking about a typographical error or the meaning of the question. Often the student is stuck and "knows what to do" but can't figure out how to do it. I've had so many of these conversations by now that I have a set of stock phrases. Conversations go like this:

Student: "I'm really stuck on this question about optimization."

me: "Talk me through your work so far."

Student: "Well, I have, like, an equation... for... volume..."

me: "Yes?"

Student: "Oh, I forgot (blank) in the formula..." (writing)

me: "Ok? What's next?" (regardless of correctness)

Student: "And then I was trying to put in my constraint... but then I got stuck differentiating..."

me: "Where did you get stuck?"

Student: "Right here.... oh, I see, I need to simplify..." (writes down correct derivative)

me: "Ok? What's next?"

Student: "And then I have to (set derivative function to zero, solve for critical points, use one of various tests to show it's max or min, find dimensions of whatever)."

And then the student writes down the entire correct solution. I didn't say anything but "Yes?", "Ok?", "What's your next step?", "Write things down!", or "Keep talking!"

I hardly ever have this conversation with male students, but with female students it happens at least once per final (sometimes more). I asked one student this year about what was happening in her head as she talked through it, and she said, "It just makes more sense if I can talk out loud about it!"

I am by no means an essentialist: I think most notions of what is "essentially female" or "essentially male" are bullshit. (There are some clear physical differences like the ability to bear children, but even notions of men being stronger than women are obscured by a culture that prizes slender women with little muscle tone. Look at the survey results.) Our cultural baggage obscures any subtle underlying genetic whatever, and epigenetics is changing our whole notion of how genetics impacts life anyway. Given all that, by college we've got to work with what our culture has wrought. My female students seem to really need that processing of mathematics through conversation. I enjoy it myself and am really benefiting from my conversations. I did not have so many of these conversations in graduate school because of a need to not look stupid in front of R1 professors so they would not think poorly of me. Now I figure I've succeeded (gotten a PhD) and failed (gone to a teaching school) and so it doesn't matter anymore!

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