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stoutfellowWhat job wouldn't be dull, without those little unexpected ups and downs?
1) Last night, in my geometry class, a student asked me to go over one of the problems in the book. There was a diagram, displaying a circle and a number of line segments; the lengths of some of the segments were given, and the problem was to deduce the length of another. I copied the diagram onto the board and set to work. "Let's see, that's a right angle, so that over there is a diameter of the circle. We can compute its length, and then..." I covered half the board with calculations, and was closing in on the answer when another student asked, "Is there some reason we aren't using [Theorem So-and-So]?" I looked at the diagram, thought about [Theorem So-and-So], and said, "Uhhh..." Then I moved to the other end of the board and started over; it took about three lines to determine the required length. Just to be ornery, I then returned to my first calculation and completed it, to make sure I'd get the same answer. (And I did, so there.)
2) This morning, as I arrived at my calculus class, I noticed two students in back calmly discussing the class. I think one of them was the student who set me off Wednesday. The other student, as far as I could tell, was doggedly explaining to him why it was a good idea to be able to compute derivatives from the definition. Sometimes they listen...
1) Last night, in my geometry class, a student asked me to go over one of the problems in the book. There was a diagram, displaying a circle and a number of line segments; the lengths of some of the segments were given, and the problem was to deduce the length of another. I copied the diagram onto the board and set to work. "Let's see, that's a right angle, so that over there is a diameter of the circle. We can compute its length, and then..." I covered half the board with calculations, and was closing in on the answer when another student asked, "Is there some reason we aren't using [Theorem So-and-So]?" I looked at the diagram, thought about [Theorem So-and-So], and said, "Uhhh..." Then I moved to the other end of the board and started over; it took about three lines to determine the required length. Just to be ornery, I then returned to my first calculation and completed it, to make sure I'd get the same answer. (And I did, so there.)
2) This morning, as I arrived at my calculus class, I noticed two students in back calmly discussing the class. I think one of them was the student who set me off Wednesday. The other student, as far as I could tell, was doggedly explaining to him why it was a good idea to be able to compute derivatives from the definition. Sometimes they listen...
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no subject
Date: 2004-09-19 12:06 pm (UTC)HLC
January 4
Date: 2004-09-19 04:40 pm (UTC)