Math contests kind of suck
I’m going to annoy quite a few people with this post, but I’ve been thinking about this for a while and it comes down to this: I think math contests for kids kind of suck.
Here’s the short version of my argument.
Math contests discourage most people who take them, because most people don’t get close to winning, and in particular give those people the impression that because they lost a contest they don’t “have it” when it comes to math. At the same time, although they are encouraging for a few people, it’s not clear to me that the kind of encouragement they give those kids is healthy. Finally, they are bad for women.
Now I will argue this more thoroughly.
The way math contests are set up nowadays, they start in middle school, at the school level, and if a student does well at a given test they move on to a larger stage, perhaps at the state level, and they typically culminate in a national test, or sometimes even an international test (in the case of the IMO).
This system sets up nearly all the participating students for a feeling afterwards of having not been good enough. It encourages competition over collaboration, which is a huge problem in my opinion, but even worse, it tends to make young people feel like they aren’t smart enough to be mathematicians. It is in fact well-documented that people seem to think that one is either born good at math or not, in spite of the fact that there’s ample evidence that practicing math competition-type problems makes you good at them (why else would Stuyvesant kids consistently beat other kids? Is it really possible that smart people somehow know to be born in New York?). The bottomline is that these extremely young, impressionable kids get early impressions that the contests are measuring their genetic abilities, and that they aren’t cutting it.
When I was in middle school, there were no math contests. I was lucky enough to have a great teacher in 7th grade, who let us nerds debate amongst ourselves for an entire class whether 0.999999… is equal to 1 or not. He put himself in the position of a mediator. It was a great moment for me, and made me realize how much creativity and originality could be involved in the process of making and understanding math.
When I got to high school, I was on the math team, and although I wasn’t bad, I also wasn’t good – and I felt bad about that, consistently. In fact there were definitely moments when I doubted my chances at becoming a mathematician. It is really a testament to my internal love for mathematics, combined with finding this math camp that I’m teaching at now, that motivated me to become a mathematician. If I had not had that 7th grade teacher, and if I had had earlier experiences being so-so at math contests, it’s possible I would have been turned off of math altogether.
Perhaps you are thinking, well of course there’s a selection process for math contests, because they select for people who are good at math! I discussed this with another mathematician today and he refined that argument as follows: some people are good at understanding concepts but can’t work out the details, and some people are good at working out details by rote but don’t understand the concepts- you can’t really be a good mathematician without both, and perhaps the contests select for the details people, but after all you need that aspect.
But I would go further: although I agree you can’t be a good mathematician without both, I don’t think the contests select for the details people. They actually select for people who do or don’t understand the concepts (probably do for the higher level tests) but who in any case are extremely fast at the details. I have never been particularly fast at working out the details of something from the conceptual understanding (for example, it takes me a long time to solve a 7x7x7 Rubik’s cube) but it turns out the Rubik’s cube doesn’t mind. And in fact mathematics in real life isn’t a timed tests- the idea that you need to be original and creative really quickly is just a silly, arbitrary way to select for talent.
I guess if you could have math competitions that aren’t timed then I might start being okay with them. Especially if they were collaborative.
The reason I claim math contests are bad for math is that women are particularly susceptible to feelings that they aren’t good enough or talented enough to do things, and of course they are susceptible to negative girls-in-math stereotypes to begin with. It’s not really a mystery to me, considering this, that fewer girls than boys win these contests – they don’t practice them as much, partly because they aren’t expected by others, nor do they expect themselves, to be good at them. It’s even possible that boys brains develop differently which makes them faster at certain things earlier- I don’t know and I don’t care, because I don’t think that the speed issue is correlated to later deep thought or mathematical creativity.
Finally, I don’t necessarily think that winning math contests is even all that good for the winners either. In spite of the fact that many of my favorite people are mathematicians who were excellent at contests, I also know quite a few people who were absolutely dominant in math contests in their youth who really seemed to suffer later on from that, especially in grad school. From my armchair psychologist’s perspective, I think it’s because they got addicted to the rush of doing math really fast and really well, and winning all these prizes, and when they get to grad school and realize how hard math really is, they can’t stand it.
One related complaint to this rant: it seems like there is way money out there for math contests for young people than there is for math enrichment programs like the program I’m working at now (I’m looking at you, NSF). Why is this? Probably a combination of the fact that’s it’s easier to organize, it seems quantitatively measurably “successful” because there’s a winner at the end, and maybe even because it makes the United States look good compared to other countries to have a winning IMO team- in other words, spin. Booo! How about throwing a little bit of money towards programs that sponsor a sense of collaborative, exploratory mathematics and which encourages women?
Before I get people too riled up, I will say this in favor of math contests: they do tend to expose kids to different kinds of math than is normally offered in their classrooms, which can be really great, and expansive, for kids that have drab math curriculums with drab teachers. Lots of kids first find out there’s math beyond quadratic equations by going to a math contest. That’s cool, but can’t we do it in a better way?