I agree with Colinsmum. That article is by Richard Rusczyk. He is founder of AoPS and a guy writing some of the best math textbooks for smart kids. He argues that most kids never encounter hard problems in typical school environments. In my experience as a child and a parent, that has been true, even with enrichment, multi-year subject acceleration, and GT math classes. Math Olympiad at elementary level hasn't offered my children the kind of challenge offered by AoPS. The level of problems with AoPS courses or higher level math tests require great problem solving skills. If there is never a problem that isn't obvious (which was definitely my experience in school math before college), then a student has no chance to learn those skills. Like most skills, problem solving increases with practice. Like much of GT research, AoPS takes the approach that a kid ought to encounter difficult things and learn from working through mistakes and struggling with unsuccessful attempts rather than do repetitive easy problems in typical textbooks.
The problem sets in their classes are really hard. They often require trial and error, thinking through many different steps, considering deeply whether one possible solution meets every criteria demanded by the problem, etc. They don't expect all or even most students to be able to get them all right, which means a talented kid has more room to grow. Since I see most of the beauty in math as coming from the hard stuff rather than the plug-and-chug, I think this approach is most likely to hold the interest of a talented math kid.
I have no connection to AoPS, but I admire their program and their approach to math. In all the GT-friendly things my children have done, I see AoPS as coming closest to offering exactly what they needed for the reasons Rusczyk expresses in the calculus trap.
