I didn't realize till I had kids how early plug-and-chug started. No wonder it felt so natural in college. I'd been doing it since 8.
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In school, 8 yo is learning mechanical methods for multiplication. As an antidote we do the same problems in our heads on the way to school.
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I did a while ago, just not the name. (You can't do much mental multiplication without it.)
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I don't think it's so much to avoid learning principles as to make kids into reliable calculators (rather than e.g. good mathematicians).
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I personally think that's a terrible tradeoff, but I can understand historically how it happened.
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