Hooked on Understanding

"Mathletes, take your marks, go!"

The clock projected at the front of the lecture hall begins counting down from 40 minutes. I stare down at the packet of problems with an exciting mix of confidence and nerves. I read, "Let n be a positive integer less than or equal to 1000. If the last two digits of n are reversed, the resulting integer is exactly 85 percent of n. What is the sum of the possible values of n?"

I try to set up a few equations and inequalities: n≤1000, n=100a+10b+c, 0.85n=100a+10c+b. Still, I don't know where to go from there, so I skip ahead. It's frustrating to give up a point, especially after weeks of practice, but that's the reality of competitions: you can't spend forever on one problem. Skipping once feels manageable—but after skipping the next question and the one after that, it begins to feel crushing. Blank pages pile up. The clock ticks down from 35 to 30 minutes, and a quarter of my time has evaporated without a single solution. Finally, I hit the last page. No more problems left to skip, nothing left to push out to later.

I've loved math for as long as I can remember. From competing to be the quickest in my second grade class at reciting my times tables, to the comforting feeling of getting perfect integers after solving a system, looking forward to math class has always been a constant in not only my school day, but my entire life. One of my earliest memories with my family was when my parents would hold up multiplication flashcards at the kitchen table to see how fast I could answer a hundred problems. I raced to shout the answers as soon as I could see the problem, giggling when I beat my best time. The only strategy I knew was to speed-run everything. There's a kind of instant gratification in math that nothing else gives me – one solution, one clear answer, everything neat and logical. And I loved the competition too, not just the winning, but the way it pushed me to climb higher levels, learn new topics, and think in entirely new ways. So when I found myself staring at a problem set full of words I didn't know, questions I didn't even understand how to begin, it was crushing. I wasn't used to feeling completely stuck in a subject I loved so much. The confidence I normally carried into math rooms evaporated. All that was left was doubt.

Almost twenty minutes in, and I'd barely written a thing. I looked around to see rows of other students tapping their pencils and scratching their heads. I could tell they were just as confused. For a moment, I felt a surge of short-lasting relief until I looked more clearly and I saw the occasional student light up with a smile and jot something down. What I noticed about all of them, though, is that no one else was frantically skipping through pages. Even the students who seemed stuck were concentrating on the problem they were on, not rushing to see if another one seemed easier. So I realized my best option was to slow down. No more glancing around to see if others were understanding or skipping questions, or peeking at the clock. From now on, I had to just focus on just the next step of the problem I was on. I flipped back to question one and forced myself to look again, trying to set the pressure aside and just understand. I circled terms, underlined what I did know, and let myself move slower than I ever had during a competition.

My mind, still restless, flickered to something entirely unrelated: the crochet shark I'd been working on that week. The slow, repetitive motion of pulling one loop through another, over, under, over, under. Each stitch building on the last, just like the result of each equation led to a new equation that was one step closer to the solution. I reread the first problem one more time, as if unwinding a fresh ball of yarn for my next crochet project, I set up my first equation, n = 100a + b, the first stitch, then expanded it further, n = 100a + 10x +y, the next few stitches around the first ring of the project, then switching the digits, n' = 100a + 10y + x. The first ring of the project was done, now for the next row, n' = 0.85n. With each new equation and new row, I was one step closer to my final product. I'd never rushed crocheting a piece; the risk of messing up a row was much greater than the reward of being able to get the project done a little quicker, but it always grew into something whole. Maybe math isn't too different. I didn't need to solve everything in one brilliant flash. I needed to go stitch by stitch.

I didn't win that day, but I learned that when something isn't working, the solution isn't just to abandon it; it's to find a new way forward. Even if that means slowing down. I learned how to zoom in and see what was actually in front of me instead of obsessing over the big picture. In practice, I focused more on understanding the reasons why a formula worked or the thought behind finding the solution, rather than memorizing random patterns that lead to an answer, and being able to understand every stitch of the solution, instead of just racing for the final result.

Furthermore, I realized the connection wasn't only between math and crochet; I could see this need to take a step back in many aspects of my life. In debate, during the two minutes of prep time we get between speeches, I wouldn't stress about not being able to find the perfect argument in a split second, but instead I would flip through a few relevant sources to find the perfect statistic to prove a point. In piano, I practiced difficult pieces measure by measure, layering progress slowly instead of expecting perfection in one go. I realized just sticking through things, no matter how slow the process feels, is what gets results. Instead of getting up and shutting the piano when a piece doesn't click the first time, I could at least manage to learn a couple of notes or measures by slowing down and allow myself to take some time to understand. I found this was more fulfilling because I actually understood how I reached the answer, rather than feeling as if I was racing blindly towards completion.

Now, when I meet something unfamiliar, like an equation, a debate, or a new crochet pattern, I don't rush past it. I zoom in and slow down, and most importantly, keep going: one stitch, one step, and one question at a time.