### When it’s bad it’s bad, and even when it’s good it’s bad

All hundred-odd of my students wrote tests last week, and so I spent the entire weekend grading them.

My precalculus classes, as expected, did poorly - though I was surprised by just how poorly they did. I knew that my students didn’t know how to factor, but I was surprised by the number (6) of students who thought that the graph of -2^x was a jagged line. There’s also the fact that despite my having spent three (3) weeks on the graphing arts, the preferred method seems to involve graphing functions pointwise and connecting the dots, asymptotes be damned. (One angry student told me that if I wanted a better graph, I should let him use his graphing calculator.) If I were to test my students instead on, for instance, Fermat’s Last Theorem, I think the results would be similar: pages of gibberish, followed by a dozen students whining that I never showed them how to do *that* question. In any case, I feel like I’ve utterly botched precalculus. Half of me wants to try it again so that I can get it right, but the other ninety percent of me never wants to teach a precalculus class again.

My discrete classes, though, surprised me: class average in the mid-seventies on what I thought was a moderately challenging test. I was happy about this, until I got into the class today, and found that a good half of them were shocked by their good marks: they’d thought they’d failed. (This didn’t stop many of them from complaining regardless that I shouldn’t have asked this question or that one.) This is making me wonder if I know anything whatsoever about setting tests. At the very least, perhaps I should rethink my generous part-marks policy.

incidentally, have you ever read the proof for fermat’s last theorem? i wonder if it would be understandable to someone with no math beyond a few upper-level undergraduate math courses (i.e., number theory, etc.).

I can answer that: no.

I have been to explanations of the overall research arc that got to the proof of FLT, and that was understandable as an undergrad. But it’s like have the proof of the 4-color theorem explained. You may understand the overall structure or strategy, but you need some heavy-duty experience and at least an entirely free month or two to get through the proof.