I’m going to push back on the advice to learn higher grade math rather than competition math, as I feel the author is ignoring an important skill that competition math helps develop. They allude it in passing:
> A student can wrestle with a competition problem for long periods of time, and all the teacher needs to do is give a hint once in a while and check the student’s work once they claim to have solved the problem.
Wrestling with a problem for long periods of time is not just a convenience for the teacher, it is a skill that will serve students well for decades to come. Sitting with a problem that you don’t know how to solve for hours, trying various approaches, failing and failing and trying again, is a life skill that learning calculus two years early won’t teach you.
Many of the tactics used in competition problems are also useful in general quantitative situations: identifying symmetries, invariant quantities, properties that can only increase under perturbations.
> A student can wrestle with a competition problem for long periods of time, and all the teacher needs to do is give a hint once in a while and check the student’s work once they claim to have solved the problem.
Wrestling with a problem for long periods of time is not just a convenience for the teacher, it is a skill that will serve students well for decades to come. Sitting with a problem that you don’t know how to solve for hours, trying various approaches, failing and failing and trying again, is a life skill that learning calculus two years early won’t teach you.
Many of the tactics used in competition problems are also useful in general quantitative situations: identifying symmetries, invariant quantities, properties that can only increase under perturbations.