American Regions Mathematics League (ARML): 7 Tips to Help You Win

If you are a high schooler with a passion for solving complex mathematical problems, the American Regions Mathematics League (ARML) might be the perfect opportunity for you to both hone and highlight your skills. This prestigious competition brings together the brightest young minds from across the United States and Canada to test their mathematical skills in a fun and competitive environment.

What is ARML?

The American Regions Mathematics League, or ARML, is an annual high school mathematics team competition. The competition brings together teams from various regions of the U.S. and Canada to compete in a variety of mathematical challenges at 4 different locations - the University of Iowa, Pennsylvania State University, University of Nevada at Las Vegas, and the University of Alabama in Huntsville. It's a unique opportunity to test your mathematical skills against some of the best young minds in the country.

Due to the structure and scoring of the ARML competition, it is not just about individual brilliance but also about the power of teamwork. Teams are typically organized by region and are often sponsored by local schools, universities, or math circles. Each team consists of 15 students, guided and mentored by two coaches, who work together to solve a variety of mathematical problems. This structure encourages collaboration and communication, essential skills in the world of mathematics and beyond.

The Prestige of the Competition

Aside from being a nationally recognized competition, the rigor and talent required to compete at the ARML make it a highly respected event in the academic community. This year, 115 teams i.e. over 1600 students participated. The significance of the ARML is underscored by the fact that it is sponsored by renowned institutions and organizations, such as the Mathematical Association of America (MAA), the National Council of Teachers of Mathematics (NCTM), and the Society for Industrial and Applied Mathematics (SIAM).

Another barometer for the respect and admiration the ARML is held in is the success of its alumni. Many former competitors have gone on to attend top universities and pursue successful careers in fields such as mathematics, engineering, and computer science. Participating in the ARML competition can open doors to a world of opportunities.

Eligibility and Participation

According to the Competition Rules, “a student can not have turned 19 before the December 31 immediately preceding the ARML Competition. If the student turns 19 between January 1 and the competition dates he/she would be eligible as long as he/she did not graduate high school (K-12) prior to March 1 of the year of the competition”. If you're interested in participating, the first step is to find out if your area has a team already. Each ARML team comprises 15 students and is drawn from a specific geographic region, like a single school, city, county or state.

Note that team composition and qualification criteria are left to the individual teams and their coaches to manage. ARML advises coaches to use scores of students from other exams such as AMC or AIME as well as practice qualifiers to shortlist students and divide them into teams.

Timeline and Structure of the Competition

The competition takes place annually on the weekend after Memorial Day, typically in late May or early June. The competition consists of 6 rounds:

1. Team Round - a 20 minute round in which 10 questions are given to teams to solve together

2. Power Round - a difficult, 1 hour round which may require justifications or mathematical proofs and a combination of individual and team efforts. This is also the only round with partial credits awarded

3. Individual Round - each student is given 5 sets of 2 problems with 10 minutes per set

4. Relay Round - teams are divided into 5 groups of 3, and given problems in sets of 3 (one per student). The solution of the first student is plugged into the problem given to the 2nd student and so on. Submission is at 6 minutes, or at 3 minutes for bonus points. There are 2 such relay rounds.

5. Tie-Breaker - a series of questions given one at a time, with the student answering the quickest declared winner

6. Super Relay - a relay round where each team submits one answer

The variety of rounds ensures that all aspects of mathematical ability are tested, including accuracy, speed, individual acumen and teamwork. This makes the competition a comprehensive assessment of a team's mathematical prowess.

7 Essential Tips for Success

1. Understand the competition format

Familiarize yourself with the structure of the competition and the types of problems you will be asked to solve. This will help you prepare effectively and know what to expect on competition day. You can find more information about the ARML Competition Format here.

2. Work effectively with your team

Make no mistake, success in multiple rounds of the ARML is largely dependent on teamwork. Practice working together with your teammates to solve complex problems, and identify your respective strengths and weaknesses. Here are some team building tips that will help you form an initial bond and set the foundations for the many practice sessions to follow.

3. Master the Fundamentals

The problems in ARML often require a deep understanding of high school level mathematics, including algebra, geometry, trigonometry, and calculus. Make the effort of finding lectures and lesson plans that go in-depth into these topics. Khan Academy is a great resource for this, and a broader list may be found here.

4. Learn from Past Competitions

ARML organizers have helpfully made past ARML problems and solutions available online. It cannot be overstated how important these are in understanding the types of problems you will face and the strategies that can be used to solve them.

5. Practice, practice, practice!

Work with your coach in developing a regular practice regimen, both in person and at home. Don’t restrict yourself just to ARML either, other competitions like MATHCOUNTS, USAMTS, HMMT or PUMaC are all similar enough to ARML that working on their practice problems is also helpful. The more you practice, the more it will help you build the mental discipline and focus you’ll need on the day of the competition itself.

6. Prepare for the Power Round

The Power Round is arguably the trickiest part of the ARML, involving a set of problems based on a common theme and requiring both individual problem-solving and team collaboration. Make sure your team is prepared to work together effectively under pressure. You will need to be familiar with reading and writing mathematical proofs. There are a few resources to help you and your team ace this round, like the Prove It! Math Academy program or articles on solution writing at the Art of Problem Solving website.

7. Stay Calm and Focused

Remember, the goal is not just to solve problems, but to enjoy the process of mathematical discovery. Alumni of the ARML often talk about the sheer joy of cracking tough problems with their peers and the sense of victorious teamwork. Work hard on your math, but also work on maintaining a healthy mental state so that you’re able to both give your best as well as enjoy your experience. Here are some stress management techniques by Harvard that might help.

To wrap up, the path to winning the American Regions Mathematics League Competition is a comprehensive endeavor. You must understand the competition's unique structure, work towards fostering a collaborative spirit within your team, and hone your mathematical skills. You will have to be dedicated in your practice, especially for the Power Round, all while nurturing a mental state that allows you to remain clear headed amidst the intensity of the competition. Use the resources at your disposal, put in your best effort, and above all, enjoy the process! The ARML competition is a golden opportunity to challenge your limits, learn new things, meet like minded peers and fuel your personal growth.

Lumiere Research Scholar Program

If you are passionate about research, you could also consider applying to the Lumiere Research Scholar Program, a selective online high school program for students I founded with researchers at Harvard and Oxford. Last year, we had over 2100 students apply for 500 spots in the program! You can find the application form here.

Stephen is one of the founders of Lumiere and a Harvard College graduate. He founded Lumiere as a PhD student at Harvard Business School. Lumiere is a selective research program where students work 1-1 with a research mentor to develop an independent research paper.

Image Source: ARML logo