But moreover, as you observe elsewhere, this knowledge does get communicated in person, through advising and conferences and conversations over drinks. And it's easier to communicate this stuff in person, which is one reason the communication happens there.
“My cognitive tools work well in algebra, and much less well in analysis”— Just saying THIS might be hugely helpful at about the sophomore level. I figured out then, on my own, that my roommate could integrate by seeing/feeling the surface and the shape under it, and bam.
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I couldn’t do that; I had to integrate syntactically. So I’m also much better with algebra. However, I did eventually develop visualization abilities (for abstract algebra and such). In retrospect, I’m pretty sure I could have learned to visualize surfaces much more.
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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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