I think this article - "A Mathematician's Lament" by Paul Lockhart - is something everyone should read Not exactly an answer to your questions and not exactly aimed at math beginners, unfortunately, but it's a really engaging rant about this topic https://www.maa.org/sites/default/files/pdf/devlin/LockhartsLament.pdf …https://twitter.com/graciegcunning/status/1298804338727489536 …
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The actual answers to your questions take a long time to learn, in the same way that a musician explaining in words "What makes this chord the right one to play at this point in the song?" would take a while But it's a very worthy question, it's the whole point
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And I think Lockhart does a really good job of at least getting across to non-math people - like me - how the way he thinks about math is all about those questions and it's night and day from the stuff bad math classes make you think math is about
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(Kind of like how you'll find a lot of professional authors, including really famous ones whose books are taught in school, who don't have much nice to say about their 7th grade English lit classes)
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Like, rote memorization kinda is the right move for early stuff like addition and times tables. But they just keep using that for more esoteric stuff
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Even there, rote memorization is not necessarily best. (The 9 times table, for example, has a lovely pattern with a simple mathematical explanation behind it, and discovering that makes it much easier to remember.)
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Soft like charmin...
#Triggered#Snowflake.
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