On the topic of teaching kids math: I have a vivid memory from kindergarten when the teacher was showing us shapes, and asked us to name them (we already knew basic names, and we knew that we were supposed to say the most specific ones, e.g. square instead of rectangle etc). Now she showed us a square, so all the kids yelled "square". But then she rotated that square 45 degrees, and the kids yelled "rhombus", because we knew that "rhombus" was "a skew square". And the teacher said "no, it's a square, it's the same square, don't you see?", and just rotated it back and forth. I remember we were baffled and lowkey amazed.
In retrospect, this lesson taught me not only about group actions (Klein's Erlangen program vibes), but also about semantics - that the words are just tools to carry ideas, that one is not smart by knowing definitions ("a skew square is called a rhombus") but by identifying patterns and their flexibility.
I guess this was one particular lesson that just clicked for me, but sometimes I wish more lessons were like that instead of memorizing another definition and feeling smart for sounding latin.
