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A Good Day
Nov. 8th, 2018 04:57 amTeaching-wise, yesterday was a good day. I had two appointments and one lecture scheduled.
The first appointment was with a young woman who, for her Senior Assignment, is writing an expository paper on Miquel's Theorem, which is a very nice piece of triangle geometry. She'd read the material and understood the theorem and its proof, but was anxious about writing the paper. I gave her a bit of a pep talk and some advice on how to structure her paper, and also pointed out a special case of the theorem that the usual proof wouldn't quite cover. I used Sketchpad (love that program) to show her what the theorem said in that special case, and I think she'll have no trouble proving it. She left in better spirits.
My second appointment was with my Master's student. She's working on organizing some of her results, and showed me what she'd gotten so far. It looked good overall, but there was one section where she had made a wrong turn. (The classes of hexagons she's investigating are "X-positive" or "X-negative", and the techniques needed for the one are significantly different from those for the other. She'd been applying X-negative methods to a couple of X-positive classes. She was chagrined when I pointed that out.) One of her lines of investigation had produced results which she was puzzled by. I explained how those could happen, and then used Sketchpad (love love love that program) again to show her an example hexagon, which was rather bizarre-looking but revealing. She had one more set of results that she was dissatisfied with - they were kind of ugly. After a few minutes of discussion, I hit on a way she could link it to her earlier work, in a fairly pretty way. She, too, was much happier when she left. (Unfortunately, she has a hefty midterm in one of her other classes next week, and the week after that is Thanksgiving Break, so we won't meet again until the 26th.)
In the lecture, in my geometry class, we ran into one of the thorny patches I mentioned before - a section where intricate and non-intuitive arguments are necessary - but managed to work through it without major difficulty. I was trying a new line of attack, one which is visually easier to follow, and I think it worked well.
A good day, teaching-wise.
The first appointment was with a young woman who, for her Senior Assignment, is writing an expository paper on Miquel's Theorem, which is a very nice piece of triangle geometry. She'd read the material and understood the theorem and its proof, but was anxious about writing the paper. I gave her a bit of a pep talk and some advice on how to structure her paper, and also pointed out a special case of the theorem that the usual proof wouldn't quite cover. I used Sketchpad (love that program) to show her what the theorem said in that special case, and I think she'll have no trouble proving it. She left in better spirits.
My second appointment was with my Master's student. She's working on organizing some of her results, and showed me what she'd gotten so far. It looked good overall, but there was one section where she had made a wrong turn. (The classes of hexagons she's investigating are "X-positive" or "X-negative", and the techniques needed for the one are significantly different from those for the other. She'd been applying X-negative methods to a couple of X-positive classes. She was chagrined when I pointed that out.) One of her lines of investigation had produced results which she was puzzled by. I explained how those could happen, and then used Sketchpad (love love love that program) again to show her an example hexagon, which was rather bizarre-looking but revealing. She had one more set of results that she was dissatisfied with - they were kind of ugly. After a few minutes of discussion, I hit on a way she could link it to her earlier work, in a fairly pretty way. She, too, was much happier when she left. (Unfortunately, she has a hefty midterm in one of her other classes next week, and the week after that is Thanksgiving Break, so we won't meet again until the 26th.)
In the lecture, in my geometry class, we ran into one of the thorny patches I mentioned before - a section where intricate and non-intuitive arguments are necessary - but managed to work through it without major difficulty. I was trying a new line of attack, one which is visually easier to follow, and I think it worked well.
A good day, teaching-wise.
