As we recently discussed, competition math is a challenging extracurricular option for students who either love math, competition, or both. Doing well in math competitions like the AMC 10 or 12 can boost confidence, strengthen college applications, and greatly increase students’ abilities to solve difficult problems quickly.
Like most big challenges though, doing well in competitive math takes time, discipline, and careful strategy. Let’s discuss some general and specific ways to improve student performance in the demanding world of math competitions.
Consistency vs Cramming
Although the structure of most weeks can make this difficult, it’s far better to do a few practice problems daily or semi-daily than to block off huge chunks of time to cram on the weekends. Memories aren’t formed the instant we first process new information, but rather as the result of repetition and effective storage of that information.
Studying is sort of like planting a tree in this way, we need time for things to take root before they’re firmly anchored. For that to happen, information has to comfortably and coherently settle long term memory, and to be refreshed over a period of days and weeks. For learning and mastering new approaches to mathematics, this means doing a smaller amount of work consistently, strengthening this knowledge, and not overloading or overly stressing ourselves in exhausting bursts.
Maintain Mental Wellness
On the heels of the prior point, it’s important to remember that memory processing, storage, and organization happens largely while we sleep or rest. A tired and frayed mind will not digest its contents well, nor retrieve them effectively. This means ensuring a math competitor gets at least 7 hours of sleep each night, and regularly employs some form of de-stressing activity like meditation or exercise to help maintain the ability to remain calm under pressure.
While there are hundreds of different meditation apps and “mindfulness” guides out there, the best technique is the simplest: simply sit still in a comfortable posture, focusing on breathing, and let thoughts pass through without fixating on any one thing. This is of course a tall order at first, and may feel downright impossible, but the key is simply patience and dedication—qualities that are vital to doing well in academic work as well.
Practice Like it Counts
It’s vital to not let practice sessions be unfocused, distracted endeavors. Rather, simulating the conditions of an actual competition will yield far greater results and build confidence for the big day. Remove distracting electronic devices, turn off any music or videos, and only allow in those items or texts permitted during the actual competition.
This point also works in harmony with our first tip—it’s a lot easier for a student to commit to spartan practice conditions for 20-30 minutes than for an entire Sunday afternoon. Make your practice sessions count, and to do this it should simulate the actual competition environment as closely as possible.
Study Past Competitions
This may be obvious to some students and teachers, but it bears repeating: the best study questions, just like the best study environments, are those that mirror the real thing. Past AMC problems, for instance, can be found in a variety of websites, and there are of course quite a few books full of problems nearly identical to those used on the test as well.
Practicing with problems that are in fact harder than those used on the test is another popular strategy, and often yields great results, but it’s important for students to get a sense of what the actual competition will test before strengthening their mental muscles with more difficult material.
Study With a Buddy
Keeping in mind that the bulk of studying should take place in exam-like conditions, students should nonetheless occasionally work with a peer to discuss and collaborate on material. One of the best strategies is to teach each other material after working through practice problems or reviewing methodology. Being able to explain mathematical operations or strategies in their own words ensures that students more deeply understand the information, and similarly helps increase their confidence.
On the listener’s end, some students may be better able to seize an insight in conversation with a peer that would’ve otherwise eluded them had they simply turned the material over and over mentally by themselves.
Focus on the Target
A more specific point, it’s vital for students to utilize all the patience and mental focus they’ve developed when they first read a question. Especially during a competition, students often have trouble fighting the urge to move quickly, glossing over phrases or chunks of sentences in order to pluck out what they think is relevant at first glance. It’s crucial, and maybe the most important part of expert problem-solving, to carefully and receptively read the problem before moving into solution mode.
We can’t effectively judge information in the blink of an eye despite many math competitors trying to do so—instead, think of each new problem as a moment to breathe, reset our mental compass, and carefully read what’s being presented. You can’t build a strong solution on a shaky foundation!
Know When to Hit the Gas, and Know When to Slow Down
Everyone gets stuck on a problem eventually. The crucial distinction to be able to make is between a problem for which you completely lack a convincing solution or strategy and one which you’re simply trying to solve in a hurry or in a confused state.
We can break this down further into knowing when to guess and move on, and when to dig in and try to clarify things. While that’s not something that can be taught in a single trick or tactic, it is an ability that will come to students over time through copious practice and careful coaching. Sure, if there’s 1 minute left and you’ve got 4 problems left to solve you’re going to have to hit the pedal and make as educated a guess as possible, but in most cases, there will come a point with a difficult problem where a student feels like they’ve hit a wall and are just spinning out. In these cases, it’s important to remember that they can always come back and change an answer if they have time in the end, but also that missing a single problem or even two likely won’t sway their results too wildly. Be patient when at all possible, but staying stuck on something for too long can not only eat away too much time but further deteriorate a student’s sense of inertia and confidence.
For this last point especially, expert coaches can find the right strategy for a student to know when to dig in or move on. Our competition math coaching team is composed of experienced former competitors and talented teachers who can help illuminate and motivate students interested in the high-intensity world of competitive math. Contact us any time to discuss our available programs and classes.