So if you want to communicate how to do, say, homological algebra, the audience of people who are interested is pretty small, maybe a couple hundred. And you'll meet nearly all of them at conferences. So it's not as useful to find ways to communicate that knowledge at scale.
If someone had said “These are fundamentally different ways of doing math, and some people seem to be naturally better at one or the other, but if you work at it you can manage both, and here’s how to develop your visualization ability” that might have been revelatory.
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There’s stuff that applies only to broader or narrower subdomains of math, but the more general stuff doesn’t seem to get taught either.
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Didn’t know until recently that many Math teachers & faculty are aware of big debates on pedagogical methods in mathematics. Called “The Math Wars” by some, the central contested point is how much Math ed should be simple Darwinianian struggle or something otherwise.
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