Memorization is such a strange thing to try to teach. I was never good at that in school but could sing any song on the radio after hearing it once. In school I was good enough at math up to a point because I was so bad at memorization got good at thinking my way through it. Was much better at word problems than equations in elementary school.

I do agree with the premise of the shower thought - part of being educated is learning through mistakes. Making mistakes is one of the fastest ways to learn something, and is the main reason I’m good at my job. I am happy to work in accounting where mistakes don’t kill anyone.