Presumably some of you have already read this, but my mother and little brother forwarded me an interesting essay by Paul Lockhart, a math teacher, which was written in 2002. You can read a PDF of the essay here. (It's 25 pages long - so I'll forgive you for skimming it instead...). Called "A Mathematician's Lament," the essay makes the case that the way math is taught is usually boring and irrelevant, turning children off to the beauty of mathematics. Or to use his words:
"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."
He writes that instead of learning formulas, students should play games, play around with shapes, pose their own word problems based on questions that are actually interesting in real life, etc.
It's an interesting read, though I'm of mixed mind about it. I took a geometry class during the summer after 7th grade that used this conjecture method, and while it was fine, I can't say that it made me enjoy math more than the traditional geometry class I took the next year. I also think that creativity and discipline have to be closely linked. One of the most frustrating things, looking back on my own writing education, is how often teachers just encouraged me to be creative. It turns out that there are actually rules of grammar and best practices of argument and story plotting and other such things which can be enormously helpful in getting your point across!
But anyway, I'm quite curious what Gifted Exchange readers think -- does the usual method of math instruction kill all the joy of the subject?