Relatedly: linear algebra would be *much* easier if, at the beginning of the course, the professor explained that it has only a couple of ideas, explained over and over in different terms.https://twitter.com/Meaningness/status/947639049413468160 …
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Advice of this kind is meta-rational: about how to efficiently learn rational methods, how to apply them effectively, how they relate to each other, and about how and when and why they work in the real world.
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That last one comes up in proof by induction. A teacher once told me that one and two are "too magical" and so make poor base cases.
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Exactly right!
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Point one is why in the future, when good teachers exist again, they will open the class with a problem you can't solve, and subsequently progressively introduce the tools to solve it. The purpose of the class becomes immediately obvious, among other benefits.
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Also show why they wsnt to solve that problem.
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