Many high schools have math teams, so their young math enthusiasts can experience the competition and teamwork of sports, while engaging in the subject they love. My own school had one, and I have friends that still attend and even proctor the national events. I'm sure the kids are having a lot of fun, and I don't mean to denigrate that in any way. But I was just reading about a 17 year old girl who has been awarded $1000,000 to build her own spectroscope, and well, that's pretty darn impressive. I have been reading about math and science my whole life, and I wouldn't have the first clue as to how to go about building one. This in turn, reminded me of an idea my friend Matt (aka Jebus to Appalachian Trail thru-hikers) told me about.
He was pointing out all the time and effort that goes into these math teams. What if all those hours went into doing actual math? I'm not talking about more book learning, I'm talking about research. If teenagers can build machines for sniffing out the chemical composition of molecules, then they can publish in peer reviewed math journals. I would think that would be more fun than winning trophies, and it would give them a head start on a career in math, while impressing the hell out of colleges.