At EconLog, Bryan Caplan has a great post on "unschooling," and specifically the fact that he thinks "unschooled" children ought to be required by the parent/instructor to do one or two hours of math a day, even though such a requirement violates the principle of "unschooling."
He thinks so because, in his experience, unschooled children are seldom strong in math. Here he is elaborating on the problem:
Won’t kids who would greatly benefit from math choose to learn math given the freedom to do so? The answer, I fear, is: Rarely. For two reasons:
First, math is extremely unfun for almost everyone. Only a handful of nerds sincerely finds the subject engaging. I’m a big nerd, and I’ve done piles of math, yet I’ve never really liked it.
Second, math is highly cumulative. Each major stage of math builds on the foundation of the previous stages. If you reach adulthood and then decide to learn math to pursue a newly-discovered ambition, I wish you good luck, because you’ll need it.
I think I'm less experienced than Caplan is, but for whatever it's worth, my experience has been this: The main difference between kids who become successful later in life and kids who don't is that the successful ones learn how to engage in "pain today" for "gain tomorrow." It's the ability to relate a current very unpleasant task to a handsome reward in a far-distant future.
The kids I know and knew learned this skill from practicing either sports or music. Once they learned it, though, they were able to apply that skill to things like math, computer languages, foreign languages, and anything else that ended up giving them an advantage later in life.
So, I like Caplan's keyhole solution here a lot; but I also wonder what the best way to teach this kind of perseverance is. As I said, the only way I really know how to teach this skill to somebody is by introducing them to a sport or musical instrument and helping him or her excel. The process of tirelessly practicing a thankless task like free-throws or etudes, followed by eventual success, imparts upon the child an indelible sense that hard practice over the course of weeks and months produces excellence. Once you've learned that, nothing in life can stop you.
But, what's your opinion? How do you think we can best teach this skill to children?