Home > math education, rant > Follow up on: math contests kind of suck

Follow up on: math contests kind of suck

July 20, 2011

I have been really impressed with the comments and thoughts of my first post about how I think math contests kind of suck. Thinking about it some more, I’d like to make two corrections to my original thoughts as well as a clarification.

The first correction is that it’s the MAA, not the NSF, that mysteriously only seems to support contests, or at least for the most part supports contests and not enrichment. The NSF, as has been pointed out in the comments, mysteriously supports primarily college-level math enrichment (through REUs) instead of high-school level stuff, but that’s a different mystery.

The second correction is that, instead of saying about contests “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,” I should have said, “most people don’t get close to winning, and for the subset of people who care about winning, in gives them the impression that because they lost a contest they don’t “have it” when it comes to math.” In other words, I’m not discussing the subpopulation who don’t care if they win. (To those people I’d say: you are rare and you are lucky.)

Except I am discussing them, and this is where the clarification comes in. My point about girls is this: girls are more likely to be in the subpopulation of kids who care, and therefore more likely to be disappointed in themselves. In fact I would add that girls are more likely to underestimate their performance, even if it was great, and moreover they are more likely to do badly in the presence of the negative stereotype that tells them girls aren’t good at math.

These are all statistical statements. In particular, an argument that won’t convince me I’m wrong is something like: I’m a guy and I didn’t care if I won or lost and I loved (or hated) contests. That just means you are not in the population of kids I am talking about. Another argument that won’t convince me I’m wrong goes like this: I’m a guy and I cared and I did awesome. In fact won’t even really change my mind if a woman writes and said she cared and did badly (or well) but loved (or hated) them anyway. Because what I’m talking about is essentially a statistical statement, and idiosyncratic examples probably won’t change my mind.

In fact I’d argue that it’s very very difficult to prove or disprove my claim, at least with comments, because there’s a strong survivorship bias in place, namely that people who got scared away from math won’t be reading my blog at all. In order to give evidence to support or discredit my claim we would have to look at examples of populations which were or weren’t exposed to enrichment, versus contests, versus perhaps something else (like no math outside their classroom) and see who became mathematicians. Oh wait here’s something.

By the way, it’s important to make clear that I’m not suggesting stripping contest math out of the picture altogether. I think there’s a case to be made that they’re better than nothing. But we don’t need to settle for nothing! However, I think we should be creating alternatives that are not competitive or timed. I was very happy to hear about the month-long test and I also heard about a team 24-hour test (does anyone know the name of that and if it still exists?)

Two last tangentially related issues:

  1. I would argue that any time a bunch of nerd kids get together they have a blast. So we definitely should be getting math nerd kids together. We just shouldn’t be having them compete against each other. I claim they’d have an even better time that way.
  2. Also, has anyone else noticed the prevalence of girls who are good at competitions and very involved fathers? It’s really interesting. My dad is a mathematician too, and many (but not all) of the women mathematicians I know have heavily involved and/or mathematical dads.
Categories: math education, rant
  1. Matt
    July 20, 2011 at 8:09 pm

    Why do the majority of kids in a math contest think they have failed? (Assuming that’s even true, but I will assume for the sake of argument that it is.) It can only be because of how we present the contests to them.

    Compare the MAA brochure for the AMC 10/12 with the Wikipedia article on the same topic. The MAA brochure focuses up front on the kinds of problems that appear on the tests — if you like those, you’ll like the test. The tests are described as “interesting”, “enjoyable”, “generate great discussions”, etc. Details about advancing up the competition ladder are definitely not the focus of this brochure. I think the brochure is nicely done. Now look at the Wikipedia article. It is paragraph after paragraph all about the competition ladder! It idealizes IMO team members and names their coaches, pretty much completely forgetting what the article is supposed to be about. The first example under “benefits of participating” is what you get for a perfect score. Good grief! It goes on to put on pressure by saying a good score is needed to get into a good college. It just makes me want to yell at the authors. By the end of the article, you have no idea what kinds of questions are on the test, but you already have a nagging fear that you probably suck at math.

    We can edit this (to my mind offensive) Wikipedia article, and others can edit it back. This would be a miniature version of what should be a larger discussion of what math contests are all about (including how students talk about them). I like the MAA version. I believe most of us reading this strongly prefer the MAA view to the Wikipedia view.

    What can we do?

    1. When talking with students about any of these tests, do not start talking about the ladder. Do not imply that the point of the test is to get a high score. The point of the test is the math within that test, regardless of whether you get it right or wrong. I (and you too, I bet, dear reader) learned many interesting things from those tests, often from problems we got wrong.

    2. If a student starts focusing on the ladder or their score, dismiss it as irrelevant. The only point of the ladder is to bring each individual to some level where they get challenged and stuck, because that is when you have the best chance to learn something.

    We can’t force students to not be interested in their score, but as parents and teachers we can minimize the importance of the score and maximize the importance of the math.


    • Dan L
      July 22, 2011 at 10:10 am

      Matt, if you really think that the point of the AMC competitions is the wonderful math problems and not the competition or the recognition, this begs the question of why you would bother to *compete* at all. After all, if you’re wholly uninterested in competition/recognition, there is no difference between doing the AMC officially and sitting in your room doing old AMCs (unless you are in the very small group of people with a realistic shot at MOP).

      I always thought that AMC had the best problems but the least fun format–once a year you get to sit around and take a test. On other hand, where I went to high school, there was a series of local tournaments that were much more fun (because of the social/collaborative aspects) but the quality of the competition itself was abysmal.


  2. July 20, 2011 at 8:25 pm

    I am not sure about the 24-hour math contest you mentioned, but there are several team competitions in applied math under SIAM auspices in which the team has an entire weekend to work on the problem.

    Here is a link to the high school version of that contest:

    On a related note, you might find the following article of interest:
    Collective Intelligence: Number of Women in Group Linked to Effectiveness in Solving Difficult Problems


  3. harrison
    July 20, 2011 at 11:37 pm

    “Also, has anyone else noticed the prevalence of girls who are good at competitions and very involved fathers? It’s really interesting. My dad is a mathematician too, and many (but not all) of the women mathematicians I know have heavily involved and/or mathematical dads.”

    I’m not that sure there’s a really significant correlation; maybe in your experience there is, but of the girls I knew who excelled in competitions or were otherwise heavily math-involved, I think more of them had involved mothers (or in one or two cases, maternal grandfathers).

    I also knew plenty of young men with heavily involved fathers; and I had a heavily involved and mathematically inclined (although not professional) mother. I suspect there’s a stronger correlation between math-parents and math-children, and if there’s a father/daughter correlation, it has more to do with the fact that math was viewed as a “guy thing” even more in the past.


  4. Angela
    July 22, 2011 at 4:48 am

    Interestingly, the 2011 IMO has just ended and the highest-scoring student was Lisa Sauermann from Germany (the only perfect scorer this year). This will be her 4th Gold medal in a row, and this makes her the best performer in the history of IMO (4 golds and 1 silver).


  5. FogOfWar
    July 25, 2011 at 11:49 pm

    I’m kinda in the “any excuse to get math nerds together so they know they aren’t the only math nerds out there is a positive thing” camp. Never let the perfect be the enemy of the good.

    That being said, I do remember that there isn’t much collaborative problem solving in math competitions & that’s too bad, because so much of good math is collaborative.


  6. July 29, 2011 at 4:16 pm

    Hi Cathy,
    I agree with much of what you say. Through Girls’ Angle, I’ve been developing an event which I hope will become a significant event in the math educational landscape alongside competitions, but will not at all be a competition. Instead, it will be a math-intensive, massively collaborative event where nobody has any incentive to withhold any ideas or observations or compete against anybody. I’ve been creating such events each semester at Girls’ Angle and am wanting to take this outside of Girls’ Angle to a wider group. If you’re interested in learning more details and maybe even helping out to realize it, please drop me an email!!!
    Also, this fall, we’re offering a new Math Contest Prep class…my hope and plan for this class is to extract what is good about contests and focus on that side of it. The beauty of Math Contest Prep (I am hoping…) is that we can explore the neat math that does appear on contests…without actually having a contest!


    • July 29, 2011 at 4:17 pm

      I guess I should have signed that…
      -Ken Fan


    • December 2, 2011 at 7:33 pm

      Just a follow-up…Girls’ Angle has teamed up with MIT’s Undergraduate Society of Women in Mathematics to take the math treasure hunt out of the club and to the general public. The first “SUMiT” happens January 21, 2012!


  7. August 25, 2011 at 2:29 pm

    The 24-hour math test (hmmm… now 36 hours) is called the High School Mathematical Contest in Modeling (HiMCM), run by COMAP:
    It’s very cool and deserves more press. Unlike the other competitions mentioned, it is about applied math and you just study one real-world problem in great depth as part of a team. That problem has no one right answer. Teams are not ranked, although they do get put into groups (Successful Participant, Honorable Mention, Meritorious, or Outstanding). I think it’s brilliant.

    There are also competitions (like the ARML Power Round) where teams work together as a group, and I even judged a competition in Illinois where teams gave oral presentations! That said, both of those competitions still come out with strict rankings, etc.


  1. August 8, 2011 at 4:10 pm
  2. August 25, 2011 at 1:43 pm
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