Natural Math (vs. school math)

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:
We weren’t always unschoolers, but we always chose alternative ed environments for our kids. When my son was in 1st grade (age 6), his class used to have an activity called “number of the day” or something along those lines. The kids would all be gathered with the teacher on the carpet and there would be a number written on the board. Kids would raise their hands to call out “number sentences” that equaled the number of the day. early in the year, the number was 10. kids called out 5x2, and 4+6, and even 10 divided by 1. Then my son raised his hand (I was there, volunteering), and said “5 divided by a half."

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.

Lyla W.
(on the Unschooling Basics list, October 2011)

Unschooling and Math Some kids are born mathematical: Gardner's Intelligences