Math Camp, and the value of learning discipline

So let's say you've got a "natural" in math. What then? You know your school isn't challenging your child, and unless you're already a math prof, you don't know where to find that challenge (and if you were a math prof, you wouldn't need KTM, would you?) So where do you go from here?

There are some incredible opportunities out there for kids with natural math talent. These are the kinds of things that the guidance counselors at Thomas Jefferson in VA or Bronx Science know, but the guidance counselors in your normal, well funded college prep school do not.

They are known informally as "math camp". There are quite a few now, and not all are created equal, but the top math camps have created material to take bright kids who have nothing past 9th grade algebra and teach them math that is typically reserved for undergraduate math majors. Usually, the material is number theory or discrete math (meaning subjects like combinatorics, graph theory, etc.)

But the most important feature of math camp is that it introduces your child to the notion that they are other bright, smart, talented kids out there--and some of them ARE A HECK OF A LOT BRIGHTER AND OTHERS WORK A HECK OF A LOT HARDER THAN HE DOES.

This, not to mention the happiness that a nerd might find at actually being surrounded by peers, is the real value of the place: weeks of people who think it's FUN to work hard on a math problem, and an environment where you are SUPPOSED TO WORK for HOURS A DAY on math problems--maybe even JUST ONE math problem in all that time!

This is one of the few places where your kid will actually be able to see that hard work matters, and to learn it before college. Because if they do want to go to Harvard math, they will meet all of these kids there, and they will already know all of this background. Their mastery and readiness for new intellectual ideas will be zooming past your child, who will probably not find that a pleasant challenge to live up to, but a demoralizing one.

Googling will get you a list such as this one from the American Mathematical Society, but that's not enough to see which ones are really rigorous. Some of these are more "let's have seminars for a week", and that's nice, but that doesn't really hit the mark. That's the kind of thing that was invented to "introduce" math topics to women or minorities, but if you want to challenge your kids, you want them to go to camp for 6-8 weeks and learn a subject, surrounded by kids who have come from the top magnet schools, or internationally, etc. This is an introduction to what Mathematicians Actually Do not by sitting in a seminar hearing about it, but by doing it themselves. And this is why you should be careful of sending your child to summer "opportunities" that are of the "let's have seminars" type, because you want to unlock doors in a way that builds up their skills, not just flits by from topic to topic, yet again denying them any chance at mastery.

These programs have entrance exams, and I guess parents might game them now, but largely, if your kid doesn't like the test, they aren't going to like math camp.

The most famous camps are Ross at Ohio State, Hampshire College Summer Studies in Math, and PROMYS at Boston University.

They are NOT cheap. We're talking a couple thousand dollars or more for a month or two, but perhaps that's on par with any other summer camp these days, I don't know.

Update: the most famous camps listed above are also the most rigorous and well respected in academia. Others may definitely be on the rise, but those are the oldest and have maintained their excellence. Also, all of these camps have financial aid applications, though I know nothing about how generous or available it is.

The best way to evaluate the rigor is to evaluate their web sites for a "typical" day, and look at how much of the day is spent in lecture and "doing homework", literally. There should be plenty of time for working with other kids. This is different than attending a talk or playing ultimate--there's ample time for that, too, but you'd much rather you could see a syllabus than just see a list of available talks.