Originally Posted by Kai
My point is that I am continually astounded at just how much needs to go right in a kid's math education for them to be truly successful in, say, multivariable calculus. You need proper instruction and regular practice year after year after year with no significant gaps. You need someone forcing you to pay attention to the concepts rather than just default to pattern matching. You need to see how it all fits together. You need to learn how to learn difficult material and how to deal with the fact that you will be wrong again and again and again.
One reason I had my children attend Russian School of Math through middle school was to increase the chance they would be in the top track in math. So far it has worked, although it probably was unnecessary for the eldest.