Some quotes from "A Mathematician's Lament", an essay by Paul Lockhart from 2002
The first thing to understand is that mathematics is an art. The difference between math and the other arts, such as music and painting, is that our culture does not recognize it as such. Everyone understands that poets, painters, and musicians create works of art, and are expressing themselves in word, image, and sound. In fact, our society is rather generous when it comes to creative expression; architects, chefs, and even television directors are considered to be working artists. So why not mathematicians?
If I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done — I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.
A complete prescription for permanently disabling young minds — a proven cure for curiosity. What have they done to mathematics! There is such breathtaking depth and heartbreaking beauty in this ancient art form. How ironic that people dismiss mathematics as the antithesis of creativity. They are missing out on an art form older than any book, more profound than any poem, and more abstract than any abstract. And it is school that has done this! What a sad endless cycle of innocent teachers inflicting damage upon innocent students. We could all be having so much more fun.Two thoughts strike me instantly. First (and easiest to understand) is that this is another beautiful explanation of why my children will never set foot inside the doors of a school, as far as it concerns me.
Second, I'm troubled that it's difficult for me to think of the practice of math as an entirely creative act. Not because I have any objections to the idea, but because I have been so thoroughly schooled to think of math as the manipulation of rules to achieve a goal set for me by someone else. Why are the results of a child's (or an adult's) mathematical explorations not celebrated as creative endeavors? I wouldn't suggest we let a person tell us 2+2 is 5 and clap our hands in response, "Yay, art!". I would suggest, though, that the fact that correctness trumps the act ("if you're wrong you should stop, maybe you're just not a 'math person'") illustrates how deeply messed up our understanding of the place of math in society is. I'm not even troubled as much as I am frustrated at all the wasted years of brain-dead, worthless problem solving this broken system told me was "math". Never too late to start, though.
All thoughts of homeschooling aside, I strongly suggest you read the article.