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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Lockhart's Lament is partly him just getting mad and asking what the point of math class is at all Like the traditionalists say the really important thing isn't all this highfalutin philosophical bullshit, it's whether you can work out the square root of 7 with a pencil if asked
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And Lockhart is just like "Well they can't Most people don't remember how to do any of that shit after they're out of school for like two years It's a total fucking waste of time and money already so why yell at me that my version of math education is 'impractical'"
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