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

Updated: a day ago

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.


If you are a parent reading this, make sure you create the space for your child to discover competition math on their own. If you’re a competitor, it’s so much easier said than done, but doing your best to minimize the effect these pressures have on you will greatly improve how much you benefit from competitions.


However unintuitive, I encourage you to go into a competition expecting failure. That way, you will allow yourself to surprise yourself when you solve a few problems, and you will gain the confidence that the process is intended to bring you rather than psyching yourself out before you even truly begin. Allow your progress to unfold at the rate it naturally does; I promise improvement comes with time. This happens to so many people at some point—including me—and it’s important to be aware that everyone feels overwhelmed at times, and practically everyone ends up overcoming it if they stick with it and continue to work hard.

Posing with Dr. Kuske, the chair of Georgia Tech's math department, at the 2018 Georgia Tech High School Math Competition

Pro: Competitions help build confidence in math and STEM, encouraging mathletes to pursue intellectual careers and showing them that (despite popular belief) math can be fun.

Con: Discouraged participants may equate their scores with their self-worth and convince themselves they are not "good" at math.


People tend to think of math competitions as events for those who already consider themselves good at math, and though that is the demographic they tend to attract, it’s important to remember that competitions are essentially “advertisements” for math in general; one of their goals is to excite people about STEM so they consider pursuing careers in academia. This means that there should never be any sort of prerequisite for joining a math team (which is why I don’t give my math team a tryout or placement test) and it’s important to welcome all people who show any interest in pursuing them. Regardless of who you are, there is a space for you in the math world!


For the most part, I had an extremely positive experience with confidence-building in math competitions. At middle school tournaments, over half of the questions would be solvable for almost anybody, and my fellow mathletes and I would leave the room feeling empowered to solve more. Trophies, certificates, and other awards were major incentives to do the best we could, and enough were given out that so many competitors’ accomplishments were represented on stage. High school tournaments were more stringent, but the same spirit kept us excited to attend as many as we could.


Even back in middle school, I wanted to be a mathematician—and I would tell anybody that would listen that math was beautiful and inspiring, ideas that stood completely against the popular beliefs that math is taxing, boring, and not worth any time. This is one of the most important takeaways from my experience; this shift in perspective was brought about almost entirely by my early exposure to the creative side of math, and it has opened an entire world of possibilities to me. I cannot stress enough how valuable those insights were for me and how much I owe to the math world for shaping my future—and this mindset can come to absolutely any competitor. If you want to see some of these ideas, you’re welcome to read my first GLeaM article: “Math: The Poetry of Ideas.


The success of competitions in motivating students to pursue STEM careers is based on the fact that math competitions are seen as an important example of math as a whole, allowing students to picture themselves in STEM because of their success in math competitions, and that is, of course, extremely positive. The natural counterpart to that, however, is that disillusioned mathletes associate what they perceive as failure in math competitions as inevitable failure in math and STEM, and STEM as a whole ends up losing a lot of brilliant people.


I’ve known many people with so much potential who end up dropping out and convincing themselves that they’re not cut out for STEM in general. If you’re ever in that position, realize that it’s extremely easy to think that everyone around you has it together, especially if you’re surrounded by people who complain when they miss only one question, but that experience is so incredibly common. I want you to remember that you have the intelligence, the strength, and the drive to succeed in math competitions if that’s what you choose to do.


However, if it turns out you don’t thrive in such a high-pressure environment, that is absolutely okay. Math competitions are actually not the poster child for math in general. They imply that problems must be solved quickly, when the pace in the real world is the opposite: mathematicians take months to successfully formulate theorems. I highly recommend math summer camps and math circles that emphasize investigation rather than speed and accuracy, as they more accurately interpret what math itself is actually like—whether you attend them instead of math competitions or in addition to. So many negatives can come with associating competition scores too heavily with your worth in STEM, and it is incredibly important to realize that other opportunities exist where you can (and will!) thrive.

My hall at AwesomeMath 2018. Photo courtesy of AwesomeMath.

Pro: Preparing for competitions teaches time management and dedication.

Con: It is easy to expect linear progress, which can create negative cycles and burnout.


Just like any “sport,” competition math does require practice and preparation. Though the questions do not necessarily require background knowledge, studying does help, and it can be very important to teach yourself tricks and tips to solve questions more quickly and to make connections you might have missed if you had not previously been exposed to a particular idea. Especially because there is an intersection between mathletes and those who tend to do well in school, there is a major culture of studying and practicing before each competition.


In general, this is very positive, and it teaches students to manage their time and to stay dedicated to learning as much as they possibly can. Because I was so excited by it, I spent the summer between seventh and eighth grade teaching myself as much competition math as I could, and that period of time taught me more dedication than school did, setting me up for success in so many aspects of my life. By buying a couple competition math books (tip: I recommend my favorites in the “Resources” section of GLeaM), I had just enough structure to stay motivated while having the freedom to work on it on my own time and in my own way. There is no set “curriculum” for competition math, so it’s very easy to improve and stay diligent without feeling obligated to tackle every single concept known to man, giving mathletes room to develop their own repertoire at their own pace, which helped me with independent work—ultimately giving me the skillset to start GLeaM itself.


After my sophomore year, however, I did manage to create a rather toxic relationship with preparing for math competitions, and I began working more out of obligation than out of passion—which led to substantial burnout. Once I started achieving at a particular level, I felt pressure to continue to achieve at that level, and that ended up stressing me out to the point where I lost sight of the joy the rounds once brought me. I obsessed over the clock and how many problems I was solving rather than the exciting connections within those problems. I also found myself strategizing excessively to make sure I could reach as many problems as possible within the time limits, which quickly became overwhelming. Because each competition brought another ranking and another set of scores that I could compare to my friends’ scores (or even more often, my past scores), I psyched myself out and ended up fueling my own negative thoughts.


This is true for so many activities—not just competition math—but burnout is such a substantial risk for tournaments, especially as they tend to mirror school more closely than we would like. For me, it took some time off (unintentionally due to the pandemic) to cultivate a healthy mindset and to find all the joy in what I once found joy in. I spent a lot of that time teaching math to others, and it gave me such an important perspective on what aspects of competing make it so valuable and what aspects are merely superficial.


My advice would be to always stay in tune with your relationship with competitions and to not find any shame in taking time to figure out your priorities; if competing ever becomes a negative experience, it can be a lot more damaging to push through rather than to step back and make an informed decision about continuing.


Progress is never entirely linear. You end up taking a lot of steps backward as you continue to improve, and that is completely okay. When you expect yourself to improve at each and every competition, you will inevitably run yourself into the ground. There are always a lot of aspects outside of your control, and your worth is not based on one score (or even a pattern of scores). It is much more important to prioritize your mental health than others’ expectations—especially because others don’t perceive you quite as much as you think they do. Never let yourself interpret anything as superficial as a score as a judgment on your character.


This is one of the issues I tend to advise my mentees on, so I would like to remind you that you’re always welcome to reach out if you need help coping with burnout while working to reach your goals.

Playing cards at Math Prize for Girls at MIT 2018. Photo courtesy of Math Prize for Girls.

Pro: Scoring is completely objective, minimizing bias and discrimination.

Con: Discrimination still exists among competitors.


It would be wrong to speak about my experiences as a mathlete without addressing the gender-based discrimination I experienced. There is, after all, a reason I started GLeaM, and I think it’s important to address this briefly here.


I’ll start with the positives. Unlike other environments with more subjective scoring systems, there is zero room for the administration of a tournament to show bias towards any individual or group. Scores are calculated based only on multipliers of the number of questions the competitors get correct, and if you get a certain ranking, you know it is correct.


As a girl in STEM, I’ve been accused of getting into certain summer programs, top-tier universities, and other scenarios because I was a girl—as if my gender was somehow more important than my merit—but nobody could ever dispute that I earned my spot on any competition stage. On the other side of that coin, there is also no way for anybody to discriminate against women and knock them down to lower places—in the highly unlikely scenario where somebody was to harbor that malicious intent. On the surface, this meant that math tournaments were always fair, and I was very reassured by that dynamic.


However, it cannot be overlooked that (especially upper-echelon) competitions are often less than 10% female, and this can intimidate the few girls in the room to leave, which of course perpetuates the cycle. It took a lot of inner strength to continue to compete where I was initially underestimated, and though that helped me grow tremendously as a person, it was not always an easy journey.


At my first state math team practices, I was overlooked by my peers more than other rookies, and it took quite some time for me to feel accepted as an equal member of the team. I ended up overcompensating in team rounds to show my teammates I knew what I was doing, and for the most part, the vast majority of people were welcoming in the end, but it was difficult for me at first to see past their initial impressions.


(Granted, it is possible that a lot of this was due to the fact I was in eighth grade at the time and I didn’t really know anybody yet, but the fact that a few other rookies were middle schoolers as well and based on some comments I heard through the grapevine later, it was most likely also gender-based. It's also important to add that despite a few challenges, I came to really love this group of people, I made so many friends, and I had so much fun competing with them.)


I had similar experiences at local tournaments, and though it ended up being extremely exhilarating and empowering to stand on stages with people who, for the most part, did not look like me, it was somewhat isolating.


Most significantly, I was cyberbullied by older members of my math team frequently during my sophomore year, and I gave their opinions a lot more weight than I should have at the time. This translated into an extremely hostile environment for practices, competitions, and even occasionally my classes at school, and it undermined a lot of the progress we made as a team over that year. As much as I learned from growing past that, it should never have happened in the first place—and it affected me for much longer than I would like to admit.


I would not trade these experiences for the world because they helped me gain such a valuable and confident perspective, but the math competition world still does have much further to go towards inclusivity. Working to change that is why I founded GLeaM and why I joined the staff of the international organization inteGIRLS (check them out!), and it’s been such a transformative experience.


I want to stress that I share this with you not to discourage you at all—but to spread awareness. It was, in fact, this dynamic that brought me some of my best friends; because there were so few girls at math competitions, we became extremely close and we made so many memories that I continue to treasure. The stronger the community we form, the more progress we can make in turning the math competition world entirely inclusive. The current movement of girls in STEM is so incredibly powerful, and it’s absolutely amazing to be a part of the turning tide. There is so much support in this community to combat any negativity, and those relationships will end up meaning so much more to you than anybody that attempts to tear you down.


I would also like to stress that the majority of the boys in the math world are also very supportive and amazing people; they are a major part of why our community is strong, and the movement for inclusivity includes them as well.


If you’re currently going through anything like this, feel free to reach out! My main takeaway from these experiences was that the positives of growing from them far exceeded the negatives at the moment—and I encourage you to stay strong, to stand up for what you believe in, and to encourage and support your friends as well. (I could write so much more about my thoughts about improving these dynamics, so let me know if you’d like to see an article about that!)


Note: I can only personally speak to gender-based discrimination, but that definitely does not mean that other underrepresented communities are not affected. My mission for inclusivity in STEM is for our spaces to be inclusive of all people, and if anyone reading this can grant me insight into other perspectives, I would greatly appreciate it.

With friends at the 2019 Georgia Tech High School Math Competition.

Pro: The math competition world comes with an incredibly interwoven community, lifelong friends, and tons of memories.


This is by far my greatest takeaway from math competitions, and this one comes with no cons.


Though they are, of course, competitive, math tournaments encourage mathletes to collaborate through team competitions, relay rounds, and even friendly informal rounds while waiting for awards, and the intensity of this environment is such a bonding experience.


I’m incredibly blessed to have been a part of the math community (and specifically, Georgia’s math community), and I cannot overstate how much good it has done for me. Though I mentioned above that not everyone was kind, those moments were completely minuscule within the overwhelming support I received. My coaches, my mentors, my peers, and my mentees have all shaped the course of my life, and I am a thousand times more confident, more determined, and more empathetic because of them.


I could honestly write an entire novel full of memories from math tournaments, math summer camps, math circles, and more, but for the sake of wrapping up this article, I will cut it short. Just know that there is a niche for absolutely everybody in the math world, and once you find it, you’ll benefit enormously from the tight-knit support network all around you. Mathy people tend to have such unique views on the world, and you’ll grow (and laugh!) so much by being surrounded by them.

Georgia ARML 2019. Photo courtesy of Debbie Poss.

SUMMARY:

I hope you enjoyed today’s article! In short, there are so many amazing upsides to deciding to compete in math tournaments, but there are a couple downsides to look out for. For the most part, the cons represent the dangers that can come from approaching math competitions in ways that could ultimately discourage and disillusion you from STEM and keep you from experiencing all of the positives. I did my best to include a lot of advice about avoiding these pitfalls, and I hope this insight helps you in building an inherently positive competition math career.


I should also take this opportunity to mention that math competitions are, of course, also a major benefit for your resumes and your college applications. (For example, AMC scores are a component of MIT applications) To me, this is an entirely different conversation because it focuses on the end results rather than the benefits of the time you spend competing, but it should not be excluded from this discussion. I also know a lot about the college application process, and you’re welcome to ask questions about it if you would like.


If you have any questions, comments, or feedback, feel free to leave them in the comment section, post them to the forum, or email me at catherine@gleammath.com! If you would like a more extended conversation with me, I also offer Zoom sessions through GLeaM when we can talk about your goals, any subject in math, or anything in this article. Thank you for reading to the end!

My math major friends at Georgia's Governors Honors Program 56 in 2019

Note: All of the photos above were taken in or before 2019 due to the pandemic because they all represent in-person events. They are all directly from my personal camera roll unless indicated otherwise, and they are included in chronological order, so they do not necessarily directly reflect the text around them.

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