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Paul Lockhart, a Columbia math PhD, former Brown professor, and K-12 math teacher, writes in the influential essay A Mathematician’s Lament of a nightmare world where children are not allowed to listen to or play music until they have spent over a decade mastering music notation and theory, spending classes transposing sheet music into a different key. In art class, students study colors and applicators, but aren’t allowed to actually paint until college. Sound absurd? This is how math is taught...