Despite my enchantment with unschooling, I haven't made much progress in rethinking mathematics.
Sure, on the surface, it may seem like my opinion about learning mathematics is radical. After all, I stopped teaching all math for three years, except for what came up naturally in conversation.
However, when it came time to teach math because my daughter asked me to, because she wants to go to high school, I find myself trapped in the same mindset. The order of learning things. The way of teaching kids how to solve math problems.
I've read a comparison that stuck with me. It's like not allowing children to sing, make up songs, play with rhythm, play around on musical instruments, until they have been taught to read music, know the differences between all the types of instruments, and have mastered the technicalities of scales, etc.
We have lost the character of play in math. And math is essentially playing with abstract concepts and playing with numbers. The whole idea of, for example, reciprocals, would be so enjoyable if it were discovered by playing around with numbers and how they work. Most of the concepts of math would be so much fun if we were playing with them. But we are so busy mastering them that we have no time to play with them.
This is not to get into a debate about should math be taught, should there be basic mastery of math. I'm a homeschooler and that gives me the luxury of not being concerned with policy. What I want is for my children to approach the area of mathematics as something they are curious about and something they can play with.
The book Family Math has been suggested to me and I even went so far as to buy it. Why I did that when I ought to know from science that I don't homeschool like that, I don't know. A girl can dream. My friend is using it for a homeschool class and says it's great.
I had a moment this week when Chana asked me how fast a human can run. We were in the car in traffic, and she was wondering if a human could run faster than we were traveling. All I knew about was the 4 minute mile. Then she asked how many miles per hour that is.
Basic math, which I hope an education would afford a person the skills to solve. So I asked her if, instead of algebra, tonight she wanted to play around and figure out how to do that problem. She was pretty interested in doing that. So we did. We chatted about it, and talked it through, and saw how if you aren't sure about multiplying or dividing, you can see if the answer makes sense in the larger context of what you are trying to solve.
Tomorrow's algebra work has a problem that I can't remember exactly how to do. I'm thinking that instead of teaching it to her, I'll let her play around with it and see where it goes.