Gilbert Strang: Teaching Math by Example
00:00:00.000 | - Do you think for teaching and in general,
00:00:04.320 | thinking about new concepts,
00:00:05.680 | do you think it's better to plug in the numbers
00:00:08.480 | or to think more abstractly?
00:00:12.020 | So looking at theorems and proving the theorems
00:00:16.580 | or actually building up a basic intuition of the theorem
00:00:21.180 | or the method, the approach,
00:00:22.860 | and then just plugging in numbers and seeing it work?
00:00:25.880 | - Yeah, well, certainly many of us like to see examples.
00:00:30.880 | First, we understand,
00:00:34.020 | it might be a pretty abstract sounding example
00:00:36.920 | like a three-dimensional rotation.
00:00:39.760 | How are you gonna understand a rotation in 3D?
00:00:44.640 | Or in 10D?
00:00:46.600 | And then some of us like to keep going with it
00:00:53.800 | to the point where you got numbers,
00:00:55.680 | where you got 10 angles, 10 axes, 10 angles.
00:01:00.080 | But the best, the great mathematicians probably,
00:01:06.080 | I don't know if they do that 'cause they,
00:01:08.560 | for them, an example would be a highly abstract thing
00:01:14.480 | to the rest of us.
00:01:17.800 | - Right, but nevertheless,
00:01:18.720 | working in the space of examples.
00:01:20.520 | - Yeah, examples.
00:01:21.360 | - It seems to--
00:01:22.200 | - Examples of structure.
00:01:24.800 | - Our brains seem to connect with that.
00:01:26.640 | - Yeah, yeah.
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