Math Circle - Competition Decisions

Competition Decisions

Math competitions involve comparing speed, depth, or accuracy of math work among several people or groups. Traditionally, European competitions are more depth-oriented, and Asian and North American competitions are more speed-oriented, especially for younger children. The vast majority of math competitions involve solving closed-ended (known answers) problems, however, there are also essay, project and software competitions. As with all tests requiring limited time, the problems focus more on the empirical accuracy and foundations of mathematics work rather than an extension of basic knowledge. More often than not, competition differs entirely from curricular mathematics in requiring creativity in elementary applications—so that although there may be closed answers, it takes significant extension of mathematical creativity in order to successfully achieve the ends.

For some people, competition carries with it a negative connotation and corollary of greed for victory rather than an appreciation of mathematics. However, those who run math circles centering mostly on competition rather than seminars and lessons attest that this is a large assumption. Rather, participants grow in their appreciation of math via math competitions such as the AMC, AIME, USAMO, and ARML.

Some math circles are completely devoted to preparing teams or individuals for particular competitions. The biggest plus of the competition framework for a circle organizer is the ready-made set of well-defined goals. The competition provides a time and task management structure, and easily defined progress tracking. This is also the biggest minus of competition-based mathematics, because defining goals and dealing with complexity and chaos are important in all real-world endeavors. Competitive math circles attract students who are already strong and confident in mathematics, but also welcome those who wish to engage in the mathematics competitive world. Beyond the age of ten or so, they also attract significantly more males than females, and in some countries, their racial composition is disproportionate to the country's demographic.

Collaborative math clubs are more suitable for kids who are anxious about mathematics, need "math therapy" because of painful past experiences, or want to have more casual and artistic relationships with mathematics. A playgroup or a coop that does several activities together, including a math club, usually chooses collaborative or hybrid models that are more likely to accommodate all members already in the group.

Most math circles and clubs combine some competitive and some collaborative activities. For example, student-founded and student-run Orange County Math Circle, while largely centering on competitions, hosts seasonal tournaments as well as infuses their competition seminars with fun mathematical lessons.