### Empathy with Students

- You have to remember that I teach four sections when I post gripes about my students. They're not all like that. Most of them are fairly decent people most of the time.
- I first took multivariable calculus in the fall of 1990, and I've only taught it once since then. This made me a perfect candidate to emulate a student and to take my colleague's test to make sure that it wasn't too long or too difficult. It took me 20 minutes, and I got an 80%. The fastest student took 30 minutes; two students scored 100%. I completely screwed up the limit question, and I didn't remember how to use the second derivative test.
- Now I understand where some of that test-nonsense that we see comes from!!! One of the questions was about calculating the directional derivative of
*f*at*P*in the direction of*Q*. My thinking: "I remember that directional dervatives have something to do with unit vectors, so I need a unit vector. I guess I'll find a unit vector in the direction from*P*to*Q*. OK, now I have a vector, and I need something with derivatives. I guess I'll take the gradient. Since the question says 'at*P*', I guess I'll plug*P*into the gradient. Now I have two vectors with two components each. The only possible thing to do with them is to dot them together." Looking at my work, you would think that I remembered what the directional derivative was. - Sure, my students don't always know the definitions, but if you walked up to me and asked me what a fully bounded noetherian ring was, I'd sputter a bit. OK, quite a bit. I might try to fake something by mentioning the second layer condition, even though I'm not entirely certain if it's related -- or what it is. Of course, I fully recognize that the problem is that I forget definitions when I don't really understand them.
- It's not like I always paid attention in class.

**Or: It's the Friday before spring break, and I don't want to go to class, either**