So, I've been helping a family friend with her geometry homework every now and then. Note that this is a bit complicated since she lives in the Chicago area, and I'm in Ohio. She faxes her stuff to me, and then we usually IM and talk about things, and I try to do guided questions so I'm not doing it for her, but instead helping her. (Though in one time crunch I did fax her the problem worked, so all she had to do was copy. I was optimistic and hoped she'd take the time to understand it.)

Anyway, so tonight we've got a problem that's simplified to r^2 + Rr - R^2 =0. At which point we're supposed to apply the quadratic formula (the directions tell us to do this). So I ask "what's a?" I give her a few examples with x, like 2x^2 + 3x + 5 = 0, and things like that. Anyway, we're really stumbling through this and she's struggling with the idea that the quadratic formula starts from an equation of the form ax^2 + bx + c = 0. I eventually tell her what a, b, and c are (1, R, and -R^2), to which she responds "i never knew how to find a, b, and c for the quad. formula until now . . . i think i partially get it" While I'm thinking "holy shit, how'd she get through algebra," I respond "oh wow, how'd you get through algebra w/o being able to do the quad. formula?" and her response is "well, i knew how to do the quad. formula, not just...not the* equation that helps you find a, b, and c"

*sighs* One has to wonder just what kind of teaching is going on sometimes . . . .