Online Math Center

Competition Math: the Good, the Bad, and the Complicated

Math competitions are a perennial topic of discussion among students, teachers, and parents, and for good reason. Competitive math is challenging, illuminating, and a fantastic way for mathematically-inclined students to develop skills in more advanced subjects while indulging in their competitive streak.

But for students whose relationship with the subject is more complicated, investing time and energy into preparing and performing well in competitions can be a difficult calculation. Today, we’ll discuss some of the major points to consider when deciding if competition math is right for your student.

Competition Math: The Good

Let’s start with an uncontestable point: math competitions, especially top-tier contests like the AMC 10 and 12, are incredible challenges that look great on college applications (though with some caveats—more on that later). They’re highly comprehensive in scope, covering virtually all aspects of secondary math curriculum, and are fantastic ways to sharpen skills for admissions tests like the SAT and ACT. Other competitions, like those of state math leagues and the International Mathematical Olympiad, often push students beyond the scope of high school subjects and can generate interest in advanced topics like number theory and combinatorics. In short, they’re difficult and doing even remotely well on them is a huge boost to both learning and future prospects.

Additionally, students who are otherwise only vaguely motivated to study math but enjoy competition can achieve a helpful balance in math competitions. This is especially true of team-based competitions, in which individual students are not only accountable to themselves to perform well but must also support the efforts of their comrades. For kids who need just a bit more motivation to help explore mathematics, competitions offer a singularly engaged and focused environment that may help them reach greater heights of understanding.

Related to both of these points is the ability for math competitions to build both personal and academic confidence. Especially for quieter or more introverted students, competitions can offer experiences that encourage more engaged cooperation with teammates and a sense of belonging based on shared interests and talents. And even in the individual competition, performing well can mean a huge boost to self-esteem that will help them head into post-secondary coursework with greater trust in their abilities.

Competition Math: The Bad

Like most extracurriculars, math competitions are very much subject to the rules of “your mileage may vary” (YMMV). Not every student thrives under pressure, and the added stress of competitive academics in hand with the unavoidable stress of simply making one’s way through high school can sometimes be simply too much to weather in a healthy manner.

Let’s take our hypothetical introverted student from the point above. Sure, a math olympiad may help them wriggle out of their shell more, but it may also backfire and create a negative feedback loop that weds group social stress with an already challenging field of study.

Related to this, students for whom competitiveness either doesn’t come easily or at all may find it alienating to push themselves outside of school in a field of study they’re already highly engaged with during the school week. Adding a layer of fierce competition to something already challenging may, for some students, make math even less enjoyable. The worst potential outcome for students engaged in competitive math is lingering frustration and distaste for the work itself, even outside of the pressure-cooker of contests.

Competition Math: The Complicated

With the above points in mind, it’s important to address some of the more complicated aspects of math competition that require some additional support or perspective.

The first is the very nature of competitive math problems. As a commenter in the r/math subreddit points out:

One of the big differences between contest mathematics and real-life mathematics, is problems in the latter don’t always have a solution, and even if they do, it is not guaranteed to be “clean/nice/elegant” (also “attackable with the right theorem” as you’ve suggested) like contest solutions invariably are. I’ve heard that many successful IMO students have had real trouble coming to this realization…  

Emphasis on speed and concise solutions is a big obstacle for many students heading into higher maths in college. And as this commenter rightly points out, this difficulty can be made worse by spending lots of time developing skills to solve problems on those terms, rather than engaging with and internalizing the process and open-endedness of mathematical thinking. This doesn’t mean competitive math is bad, but for students to have a healthy perspective on it they must also grapple with the limited nature of its modes of thought.

Second, and related to the discussion of confidence above, students who are by nature extremely committed to either competition, mathematics, or both, may have a hard time if things don’t go well. Frustration and burnout are real dangers with any competitive activity, but especially in the speedy, intellectually demanding realm of competitive math. This isn’t a mark in the “bad” column though, it just means that parents and teachers alike should seek to support students’ mental health as part of the training process. Making sure students don’t get too monomaniacal in focus, and that they’re able to adequately put their feelings into perspective when things get tough, are crucial dimensions of psychological health important not only for math competitions but life in general.

Last, and connected to the concern about burnout and a somewhat skewed sense of mathematics, it can be difficult for students engaged in competitive math to maintain other extracurriculars that may ultimately be even more important for admissions consideration. Having performed only somewhat well in a series of math competitions may not help a student’s application stand out as much as more time dedicated to volunteering, admissions exam prep, or other “surefire” extracurriculars. Again though, this doesn’t mean competitions are less important categorically, just that your mileage may vary. As with most things, students should seek to maintain a balanced approach when working toward their long-term goals.

Fortunately, OMC’s contest math tutoring programs are helpful in navigating many of the challenges and complexities we’ve outlined above, in addition to providing stellar coaching and tutoring on problems, proofs, and concepts. Contact us any time to discuss these or any of our other programs.

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