There’s a good article (albeit not about unschooling) by Alfie Kohn about how learning the ”steps” to solve math problems actually poisons the well of understanding, when compared to just fiddling around with ideas and coming to one’s own approach. It’s an article that is an answer to “why not allow both approaches” (instruction and fiddling). here it is:
The teacher was absolutely convinced that he was wrong. She didn’t say that but asked if he could explain how he got that.
It took more than 24 hours, and her asking her chemist husband about it (because I guess she knew she wasn’t so great at fractions), for her to come around and apologize and tell him that she realized he was correct.
I presume she learned the steps for solving fraction problems, and didn’t really *understand* fractions, which my son clearly did without ever having had a single lesson or conversation about it. He just saw the world that way, and it made sense to him.