by Paul Karafiol, teacher at Walter Payton College Prep and Chicago ARML coach.

With all the contests and activities my students are already involved in, I often find myself in the odd position of convincing them to try something whose value, to me, speaks for itself. What follows is a condensed version of the reasons I give students for doing ARML and a short description of what ARML is.

What is ARML?

ARML is a nationwide math contest that takes place at three sites (Penn State, University of Iowa, and San Jose State) over the first weekend after Memorial Day. Most teams, including Chicago’s, are regional teams: like sports “traveling teams,” they are composed of strong students from schools across an entire region.

Chicago’s teams, the Chicago Area All-Star Math Teams (CAASMT), are selected at an evening tryout contest Thursday, January 31, 2008 at Evanston Township High School. Students do 24 problems given in pairs; each pair has a separate time limit, and a student’s score is the total number of problems correct. A “good” score for the team is anything 9 or 10; typically the cutoff for the top 30 students is around 10-12. An additional 30 students, primarily underclassmen, are selected based on tryout participation, score, and a coach’s recommendation. The teams practice four times (weekday evenings) through the spring before traveling to Iowa in June.

How is ARML different from other math contests?

As a contest, ARML’s problems are harder, unusual, and, on the whole, a little more interesting: rather than testing students’ recall of obscure theorems and ideas, they generally require that students put together two or more ideas. ARML includes a “Power Problem” consisting of a series of related problems that students must solve, with justification; the quality of their proofs, not just the correctness of numerical answers, is an important part of the team score on this section. Recent “Power” contests have discussed subsequences of the Fibonacci sequence, combinatorics and scoring of Olympic events, grouping of students into cliques according to axioms, and unusual numerical relationships in triangles.

A short answer would be: “Because the math is cool.”

Lots of math is cool. Why do CAASMT?

Although practicing with CAASMT is a significant commitment—not just the four evenings, but time spent working on problem sets in between practices—it is also rewarding in a way that “ordinary” math team practices may not be. Top students from each school are challenged by top students from other schools, and material that may be an “objective” of a typical school-based practice is often just a starting point for a CAASMT practice. Although knowing obscure theorems and tricks won’t guarantee a good ARML score, we do try to expose students to new ideas and methods that may prove useful, and so CAASMT participants often find they do substantially better in later math contests.

So the second answer is “Because you’ll get better at doing math.”

From a coach’s perspective, having a student in CAASMT means that the student can bring back ideas, theorems, and problems to the rest of the team. Most teams with regular CAASMT participants find that their younger students learn a great deal from these “experts.”

So the third answer is “Because the other students will learn from you.”

Finally, and not insignificantly, the practices and trip are a lot of fun. Students get a fair amount of time just to meet and socialize with other math students from across the Chicago area and across the country. While at practices and the contest, students often find out about (and are spurred to pursue) opportunities to study math over the summer and through the year, some of which are genuinely life-changing. For many CAASMT participants, ARML was just the beginning of an adventure they hadn’t really anticipated when they came to tryouts.

How do you know all this stuff? You’re just a coach.

I’m a coach but, in 1987 and 1988, I was also a participant. And I’ve watched my students grow from the experience. If you encourage your students to do ARML, their growth will impress you.

Okay. So where do I sign them up?

The most important thing is for them to come to the tryout Thursday, January 31, 2008, from 4 to about 10 pm (there is a dinner break!). The second most important thing is for them to practice some ARML-style problems. To that end, two complete tryouts are available on my webpage, http://www.wpcp.org/karafiolp/ARMLD. That page also contains more information about the D (“Developmental”) team, a PDF version of the coaches’ recommendation form, and links to information about summer programs.