Gifted Issues Discussion homepage Forums General Discussion Value of high level math competition prep?

If you were advising your mathematically talented child, rising high school sophomore, would you urge a focus on the hours necessary to prep for top level math competitions, or on advanced math classes--or both?

He has finished AP calculus AB, his math teacher says that BC would not be worth the effort, and he is ready to move on to more more advanced course material.

He is working with a math PhD tutor, who was himself an International Olympiad Silver Medalalist. His tutor says now would be the time to begin serious preparation for competiton--at least an hour one two each day, minimum. Whether or not he does that his high school will probably allow him to move ahead in math in conjunction with an independent study course--overseen by his tutor. When he is a junior, he will be able--as part of a local program--take math courses at the local Ivy.

His tutor says there is a great deal of luck involved in making it onto the US team--only 6 each year, but the preparation may have value to his development as a mathematician. But it's not absolutely necessry. Many top mathematicians have had no great record or interest in compettions, and some top competitors have has so so meh careers.

So is the time worth it? Not everyone who practices a musical instrument for hours a day wins a competition, or even makes it into Juilliard, but I wouldn't say that the time wasn't worth it. On the other hand, he might use the time alternatively in math research.

Locally, he's been the top competitor, without much effort.

Anyone have any experience with this type of decision?

Anyone have tips to motivate a child for whom effort has not been necessary so far?

As a parent, I'm more interested in his intellectual development than medals and trophies.

It really depends a lot on how much the child enjoys the competitions. If it's a straight choice between following a more advanced course and competition prep, and if he doesn't actively dislike the latter, then I'd say the competition prep is more valuable hands down. But there might be a third option that might be even better, and especially might be so if your DS doesn't like the competition per so: starting with some material (book, paper, whatever) about some aspect of maths that interests him, even if it isn't course-shaped, and having the freedom to explore, define and attempt to solve his own problems, go off in whatever direction is interesting, etc.

More is true than that many top mathematicians have no great record or interest in competitions: in fact the vast majority don't have such a record/interest. Competition maths is great but it's weird in several ways. It presents you with problems to which you know a solution exists, in fact even a solution that can reasonably be found in X minutes and using techniques within set Y; and it does not give you any input into what the right question is (other than the freedom to e.g. ask a more general question in order to solve the set one). In this way it's profoundly different from "real" maths, though undoubtedly the skills it develops can be useful. OTOH maths as presented in maths courses is also profoundly different from real maths, so you take your choice!

I am going to guess that the preparation the tutor is talking about consists of spending time thinking about and creatively solving high-level problems. I can't see that this would really have a down side in terms of intellectual development, honestly. I would see this kind of practice as having great value to his development as a mathmatician. It's not about whether he wins medals or if he even enters: it's about spending lots of time practicing thinking flexibly and creatively about dificult issues in math.

Thanks for your replies.

Looks like he's going the solving high-level problem approach, at least for the summer. His tutor assigned him a number of problems/proofs ranging in difficulty, expecting him to need one to two hours per day. If he gets the competition bug, this is not a bad start but it is also a way to think about and experience what mathematicians outside of a curriculum based approach. When school starts in the fall, we'll rebalance and shift some of the focus to moving ahead on a college level curriculum--mutivariate calculus and linear algebra.

Incidentally, he is using the book, "What is Mathematics?" by Robbins and Courant--a classic, which surveys the full-range of math fields with challenging problems.