’ve always had a sort of love/hate relationship with math competitions. While I participated in the AMC and a few others, my perception of math competitions was really shaped by my experience in the American Regions Mathematics League (ARML).
ARML is a national high school mathematics team competition that is held simultaneously at four locations across the US. The Lehigh Valley, the region of Pennsylvania I grew up in, had a strong presence at the Penn State location.
By the time I joined in 10th grade, we had four 15-person teams: Fire, Ice, Lightning, and Thunder. In sports terms, Fire was our varsity team, competing in the A Division of the competition, and Ice was our JV team, competing in the B Division. Lighting and Thunder were our training teams that also competed in the B Division but consisted of newer or younger students.
From the beginning, I was already behind. One of the coaches handed out copies of his 23-page “High School Playbook” and the 8-page “MATHCOUNTS Playbook” which served as a prerequisite. Each contained a multitude of things to memorize, and even the MATHCOUNTS Playbook, which was aimed at middle schoolers, seemed overwhelming.
What I Wanted vs What My Parents Wanted
Kids with a strong love of math have a number of options to meet up and compete to show off their skills. But while I was interested in math in 10th grade, I’d still never participated in these competitions. A few years before, my public middle school had disbanded its MATHCOUNTS team. The teacher who had been leading it for years was disillusioned with the state of math education in our school district and had decided that we simply couldn’t be competitive.
My parents weren’t too happy about that. They saw my burgeoning interest in math and wanted to find ways to support and challenge me. For context, I started middle school in 2002, back when AoPS was just getting started and there weren’t as many math enrichment options available.
That being said, once I’d heard there was no MATHCOUNTS team, I had secretly been relieved. I didn’t really know anything about MATHCOUNTS at the time, but I pictured it as the math equivalent of a spelling bee. The idea of having to quickly solve a math problem while other kids watched from the audience seemed terrifying and not at all something I’d be good at.
Personal Goals Over Competition
At ARML practice, most of the students on the Fire team were MATHCOUNTS alumni, and many had even joined ARML while still in middle school, giving them years of competition experience by the time they reached 10th grade.
And, while there were a few girls on the other teams, Fire was all boys.
If I had been a more competitive person, I might have buckled down, spending hours every day studying those playbooks as well as the solutions packets that were handed out after each practice. I might have made it my goal to get onto the Fire team by my senior year.
But that just wasn’t me.
My main reasons for participating in ARML were that I enjoyed working on the challenging problems and liked being around other people who were into math. And of course, the trip to Penn State was a big plus. We got to play Mafia on the bus, spend the night in a college dorm room, eat as much ice cream as we wanted from Penn State’s creamery in the dining hall (Penn State has their own creamery, so it was especially good ice cream), stay up late trying to play Mao, and laugh over each other’s ridiculously nerdy entries in the song contest. I even got to meet up again with friends I’d made at HCSSiM (the Hampshire College Summer Studies in Mathematics).
I knew that I didn’t really care how well I did—my goal was to be part of the community of math enthusiasts. So I ignored the playbooks and the solutions packets. I attended the weekly practices but didn’t do any of the extra preparation that was expected of us.
What Happens When You’re Not Competitive?
I became friends with some of the other girls, and spent two years on Team Thunder. Being on Thunder was great. No one expected us to do well, so there was no pressure, but at the same time we could still share in the excitement when Fire came out on top.
During that time, I had a lot of other things going on in my life besides math. I was a black belt in karate and spent many evenings taking and teaching classes at my local dojo. I was a member of my school’s Outreach Education club, which went on hiking, camping, and white water paddling trips. I was also a budding photographer, holing up for hours at a time in my school’s dark room.
In my senior year, I finally made it to the Ice team, where I was the only girl that year. On top of that, I was appointed captain, which meant that I got to tell everyone else what to do during the two team rounds.
While Fire was the National Champion that year, the Ice team and I had our own little moment of fame when we came in third in the B Division. This meant that for at least the next three years, Ice would be in the big leagues, required by the competition rules to compete in the A Division. Our performance had been strong enough to change how other students from our school would compete in the future!
It was the perfect end to my math competition career. Or at least my time as a competitor: during my college years, I devoted a lot of my time to helping run PUMaC, the Princeton University Mathematics Competition for high school students.
Despite That, I Don’t Love Math Competitions
What are my concerns about math competitions?
Mostly, I worry that many competitions emphasize the wrong things about math. If your sole experience of math is through math competitions, you’ll think that math is about solving problems quickly, without using any resources or consulting any colleagues, all in a high-pressure setting.
In fact, math competitions are almost the exact opposite of the research math I’ve worked on as an adult. Professional mathematicians can often spend months or years working on a single problem! They use that time to read up on all the literature, talk about it with others, try out ideas that don’t end up working (but can teach them something important), and get stuck for long periods of time.
After all, mathematics is more than just solving the problems you’re given. It’s just as important to learn how to ask good questions. I worry that math competitions make it too easy for kids to think that being good at math competitions is the same as being good at math, because that’s just not the case.
But at the Same Time, I Love Math Competitions
And why do I love math competitions?
Because, as a student, they were my first exposure to interesting, challenging problems. As a coach, too, I’ve seen plenty of students get excited about problems while taking part in math competitions.
Some of the most valuable competitions ask students to write proofs, work together with their teammates, or think deeply about just a handful of problems. Competitions like these provide an environment where students are surrounded by peers who also like math.
Think of it this way: kids who love basketball can join a basketball team to deepen their mastery of the sport and spend a lot of time connecting with like-minded players. Math competitions can play the same kind of role for kids who love solving math problems.
Of course, other math enrichment activities, like summer camps and math circles, can have the same benefits without the competitive aspect. But hey, some kids thrive on competition!
Which path is the right one?
Any math competition that students enjoy is a good one. Does it allow for building friendships, learning new things, and having fun experiences surrounded by math? Then it’s a good thing! And if you’re a student who really wants to win, check out AoPS’s Alcumus, For the Win! and MATHCOUNTS Trainer, and other resources. Just try to avoid putting too much pressure on winning. Like in sports, the desire to win is a strong motivator, up to a point, but can become overwhelming past that point.
Even if you’re a less competitive person by nature, like I was, math competitions are still a great place to make friends and learn new skills. I’m glad that my experience with ARML back in high school made room for both kinds of students.