The Pros and Cons of Math Tournaments: A Reflection on My Eight-Year Competition Math Career

Updated: Aug 3

I recently officially graduated high school, and I thought this would be the perfect opportunity to reflect and share my perspective on math competitions. As explained in the March edition, GLeaM is now on a monthly article schedule, so this is the May edition of GLeaM!

My first math competition was in fifth grade. It was a small tournament with about a dozen elementary schools—and I was immediately drawn to the fast-paced environment and energized by the prospect of prizes. Since then, I begged my parents to take me to every math-related event we could find, joining my middle school and high school math teams and traveling all over Georgia and Alabama in search of seemingly unsolvable problems that would push me to break through my idea of intellectual frontiers. I have had the privilege to tackle a very wide range of the math competition world, including competing nationally with Georgia's state math team (aka Georgia ARML) and at the prestigious Math Prize for Girls tournament at MIT, while participating in tons of local tournaments and of course, MATHCOUNTS and the AMC/AIME series. I will draw from all of these experiences in this article.

For me, math competitions have generally been intensely positive. They have helped me to find a form of contagious confidence I never would have been able to discover on my own and to seek out so many related opportunities (math summer camps, math-related research projects, math circles, to name a few) that have helped me to grow both academically and personally into the person I am today. They taught me to think deeply and to pioneer my own methods to crack open complex challenges, and these critical-thinking skills will undoubtedly propel me forward in the future as a woman in STEM. Most importantly, by playing cards before award ceremonies, chatting between rounds, and grabbing lunch together in breaks, I've made incredible friends who are also voracious learners who share my desire to transform their corners of the world.

However, there are still a couple drawbacks to my eight-year math competition career that I'm now able to recognize, especially because of the combative mindsets tournaments create by ranking mathletes—coupled with our inherent tendency to value our self-worth on scores.

In this article, I'll give you my list of the pros and cons of math competitions. If you're a current competitor, I hope this gives you the perspective to amplify the positives and reduce the negatives. My goal is to provide you with the awareness that I know would have helped a younger version of me to have a much healthier mentality around success and to give you some advice to navigate the math world. If you're a prospective competitor or a parent, I hope this provides you with another angle to make an informed decision about deciding to compete. As a disclaimer, this represents only my personal experiences, and I do not claim to speak for the perspectives of anyone other than myself. This article is also extremely long, so feel free to skip to the section you most want to read; to me, the last three are the most important.

I came up with this idea in part because of the Art of Problem Solving founder Richard Rusczyk's article with a similar concept. Feel free to read it here!

My first math tournament in fifth grade

Pro: Math competitions teach extensive critical thinking and problem-solving skills, by exposing students to topics outside of the school curriculum.

Con: Some competitions don't accurately portray these values.

From the beginning, math competitions were intended to support middle and high schoolers in learning how to problem-solve. The first international math olympiad (held in 1959) is arguably the model for modern-day math competitions, and its vision heralds “the shared joy of discovery” that comes from the “challenges of mathematics.”

This is indeed still very much the reality of competing; you’ll be presented with problems that encourage you to think about everyday situations (like climbing fights of stairs at school or buying gas) in new and innovative ways, relying on base knowledge about relatively foundational concepts like prime numbers or triangle similarity or even merely the process of counting to devise your own strategies.

This means that math competitions are effective when there is little to no formula memorization required—because it puts all the competitors on the same playing field. You must rely only on your intelligence and your wit to put the picture together, and that is what makes math competitions so engaging, creative, and fun; you’re pushed to develop critical thinking skills and build the solution from the ground up.

For the most part, the AMC/AIME competition series, MATHCOUNTS, Math Prize for Girls, and most of the local tournaments I’ve attended have stayed true to this vision. It may have been the allure of the prizes and the excitement of spending time with my friends that initially brought me to competitions as a fifth-grader, but I stayed for the problems.

It’s difficult to explain what makes competition problems so exciting until you try a few, but the essence of it is that they guide you through a path of insights that individually follow each other in a relatively straightforward manner but together form a journey from problem to solution that is intrinsically creative and unintuitive. The process of discovery that comes with realizing each individual insight is quite satisfying and elegant, and it teaches mathletes to absorb the entirety of the problem-solving journey.

For an example of an elegant problem (though this one is quite challenging), click here!

This is what made math competitions so enjoyable for me, and it helped me gain the courage to feel confident enough to try whatever was put in front of me. I started to understand that the answer was tucked away somewhere in front of me, and by picking up my pencil and being resilient enough to persevere, I would find it.

Remarkably, this also teaches students subject material from math outside of the curriculum—areas like number theory and combinatorics—practically by osmosis. Competitions expose students to problems in these areas that they are able to solve without too much prior knowledge, and in doing so, they encourage the students to continue to learn more, allowing them to leave high school equipped with way more mathematical knowledge than even a calculus track will bring. (Of course, this setup is not perfect, and there are many concepts incorporated into math competitions for which those with prior knowledge do have a significant advantage, but this spirit does keep tournaments engaging for people of all skill levels.)

However, you do have to be wary because many competitions do not fully fulfill these ideals. There are many tournament committees who, for whatever reason, do not maintain the spirit of math competitions, either by writing problems directly from the math curriculum (essentially merely replicating a middle school or high school math test) or by writing “uncreative” problems.

The latter group tend to mainly give questions that encourage a ton of calculation, like adding a bunch of numbers together, or that require students to literally count objects by writing them out in lists because there is no more efficient method. In math competition lingo, solving these problems is called “bashing” or “blitzing,” and it mostly reduces competing to speed and luck—rather than ingenuity.

To an extent, since these are problems anyone can solve, a few of them are fine, but more than that essentially reserves the advantage of math competitions, reinforcing the idea that a deeper level of thinking is not necessary or important and that math is only what is directly taught through the Common Core.

Another pitfall of some competitions are those that rely too heavily on memorization, assuming that the competitors know formulas they do not necessarily know. This ends up discouraging a lot of students and giving a disproportionate advantage to others, and it also reverses a lot of the advantages of competing.

In short, I maintain that math competitions are very beneficial in developing important critical thinking skills you can use for most of your life in “the real world,” but I urge you to be extremely careful with competitions that are heavily based on speed, memorization, or the “common curriculum.” With practice, you’ll be able to spot them, and you can avoid their dangers by simply taking your results from them with a grain of salt.

My first middle school math tournament (with my middle school math team coach)

Pro: Competition problems stretch you and continually push you to think in new ways—even under pressure.

Con: Many mathletes become discouraged when problems seem to be out of their reach, especially with stringent time limits

As I alluded to earlier, the goal of math competitions is not only to inspire creativity but to also challenge mathletes.

Math competitions have stretched me past what I thought were my limits of understanding, inspiring me to take on more than I ever thought possible. The process of discovery that comes from one problem carries to the next one and the next and so on—until doors open that you didn’t even think were there in the first place. They have taught me as much creativity as any artform, and the adrenaline that comes with breaking through entirely on your merit leaves you feeling completely invincible. (In fact, I would argue that math is an artform, but that’s a topic for another day.)

For me, I wouldn’t trade that feeling for anything, but I will warn you that you can hit up to a hundred walls before you finally solve a problem. Though, as I described above, competitions are set up so anyone can try them, it is extremely challenging to balance the difficulty levels and abilities of an entire room when writing a tournament. No matter how well-written a competition is, a significant portion of the room usually leaves only having solved a few problems, and that can be extremely discouraging. If this happens to you, remember that it as much a reflection on the competition itself as it is on you.

Competitions also come with many additional pressures. The time limits force you to solve problems super quickly—or not at all—and often, you may have parents or friends or siblings with expectations of their own. That can all add to the discouragement if you’re not careful, and so many mathletes end up harboring resentment towards competitions—and even math as a whole.