[rayiner]

I find this angle particularly interesting in context of mathematics education, because it presupposes a certain mathematical intuition that many (most?) people lack. If you don't have reasonably strong spatial skills, chances are you're not going to find in pleasure in "exploring" K-12 mathematics. I went to engineering school and made it through on a "okay this is the equation I have to use" basis because for the life of me I couldn't visualize even simple things like order of rotations not being commutative. Even if I did it with a ruler to show myself, it didn't mean anything to me.

So when I see people say that the solution to mathematics education is to just get kids to explore, my reaction is "meh." At 28, I can do all the math I learned just fine, even though I learned it in an answer-seeking way. Had I been left on my own to just try and see the underlying nature of how it worked, I probably wouldn't be able to do even that much.