For three hours on March 11, four exceptional Rowland Hall mathematicians—juniors Zach Benton and Yuchen Yang, freshman Zach Klein, and eighth grader Sophie Zheng—were in the Eccles Library, focused on the 15 problems that made up this year’s American Invitational Mathematics Examination.

The AMC 10 and AMC 12 are optional mathematical exams designed to promote the development and enhancement of students’ problem-solving skills. Each test is 75 minutes long and consists of 25 multiple-choice questions. The AMC 10 is offered to students in 10th grade and below, while the AMC 12 is offered to students in 12th grade and below. AMC 10/12 qualifiers are invited to take the AIME, a three-hour exam that consists of 15 questions, with each answer an integer number between 0 to 999.

Known to test takers as simply the AIME, this exam is offered to students who excel at the American Mathematics Competition (AMC) 10 or AMC 12 exams (see sidebar). According to the Mathematical Association of America (MAA), which creates the AMC exams, approximately the top 2.5 percent of scorers on the AMC 10 and the top 5 percent of scorers on the AMC 12 qualify to take the AIME.

“The fact that we had four students from Rowland Hall take the AIME is extraordinary,” said Upper School math teacher Adella Croft. In fact, this is the largest number of AIME qualifiers in Rowland Hall history. (It’s also worth noting that Nathan Zhou, who took the AIME at Rowland Hall on March 11, attended the school last year and was coached with the other qualifiers.)

“The AIME is about mathematics beyond the classroom, about kids’ ability to be creative,” Adella explained. “And it’s typically non-traditional problem-solving—it’s very clever, sometimes even humorous. It’s cool.”

The MAA points out a variety of exam benefits, from helping students develop positive attitudes toward analytical thinking and mathematics that can assist in future careers, to challenging them with interesting questions that align with what they’re learning in school. But to be prepared for this level of competition, students must be willing to devote hours outside of class to studying topics like number theory, set theory, geometry, and probability. Rowland Hall students also meet weekly for Math Club and with coach Hiram Golze, one of Adella’s former students and a one-time USA Mathematical Olympiad qualifier (the Mathematical Olympiad is the next level of competition for top AIME scorers). Adella likened these preparatory measures to violin soloists who devote hours each day to mastering their instrument. “This is like taking math to the level of an artist,” she said.

And it’s that devotion to mathematical proficiency that truly motivates these students. While earning as high a score as they can on the AIME is always a goal, it’s clear there’s much more to the experience than that. These exams, taken by some of the brightest young mathematicians in the world, are extremely difficult—in 2006, for example, 22,764 students sat for the AIME and earned an average score of 2.741 out of 15 points (and only four students had a perfect score that year). In 2019, the average score was 5.87. But rather than discouraging them, the difficulty drives the Rowland Hall students toward their individual bests, helping them sharpen problem-solving skills, embrace hard work, and enjoy pursuing knowledge for its own sake—skills that will serve them for life.

It is a persistence exercise. They do it in absolute silence and isolation, pitting their mental faculties against each problem.—Upper School math teacher Adella Croft

“It is a persistence exercise,” said Adella. “It’s too bad it’s not a spectator sport because these are as competitive performers as any. They do it without an audience. They do it in absolute silence and isolation, pitting their mental faculties against each problem. They’re resilient, they’re passionate, they’re driven, they’re fearless.”

And they’re also not letting social distancing stop them. Each week, the students are meeting virtually for tutoring and for Math Club—amazingly, as a bigger group.

“It’s growing!” Adella said, noting that after she sent an email to students about ways to participate in Math Club during distance learning, she received several replies from kids who were interested in joining for the first time.

“Beyond finding a way, it’s spreading. It’s infectious in a good way,” she laughed.

STEM

Due to COVID-19, the MAA has put an indefinite hold on all aspects of the AMC program, including postponing until further notice competitions and the scheduled grading session. We will update this story with news as it becomes available.

In the meantime, if you’re curious about what the AIME looks like, visit Art of Problem Solving. They create test prep resources for math exams and offer a collection of past AIME questions and answers.

Top photo, from left, standing: Yuchen Yang, Nathan Zhou, Sophie Zheng, Zach Klein, and Hiram Golze. From left, seated: Adella Croft and Zach Benton.