Wednesday, March 08, 2006

Teaching Notes

  1. The misunderstandings between me and one of my calculus students grew today. We were locating where some (polar) curve has horizontal tangent lines, and it came down to solving sin x = - cos x. I finished off the problem by noting that we were looking for angles whose cosine was the negative of their sine, sketching a bit of unit circle, and then stating that the angles would be 3π/4, 7π/4, and either of those plus an integral multiple of 2π. My student used a calculator (possibly to solve tan x = -1) and came up with -π/4. Student was unable to comprehend that our seemingly different answers were compatible with each other. Student was disappointed that there may be more than one way to get the answer to the problem. Student's problems are compounded for not really knowing what radians are.

  2. Current math department meme: success rates. This topic has the potential for heated discussions.

  3. I really need to do more of the politic-y stuff to make students happy. Encouraging the discouraged, that sort of thing. Raising my success rate without artificially inflating the grades.

  4. My honors students hate it when they don't get things immediately. They do not deal well with struggling with a problem -- even if I dare to allow their confusion to persist for two minutes. Today we were using the extended Euclidean algorithm, and they did not immediately get the hang of what to substitute back in and when to simplify and when to not simplify. Doesn't help that our textbook makes it more confusing than it needs to be.