This matters because if you pun scalars and 1x1 matrixes then a lot of expressions no longer become associative because the reassociated version wouldn't match up. e.g. (x^t y) z is valid if you pun x^t y as a scalar, but x^t (y z) is an invalid multiplication.
I can’t learn that way; I have to get the concepts first, then the algorithms, then work examples. My assumption that everyone would learn math better if only the explanations came first is apparently an instance of “typical mind fallacy.”
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My ideal approach to teaching maths is a kind of concept sandwich: * examples of problems * hand wavy idea about what a solution might look like * work through what the precise version of that must look like * examples of solutions with a bunch of cross linking and checking.
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I don't think people can understand concepts without examples, and I don't think people can remember examples without concepts - everyone will do better if you can properly shore each up with the other, but different people will do differently well depending on which you fail at.
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