An Evaluation of Mathematics Competitions Using Item Response Theory

D uring the past century, mathematics competitions have become part of the landscape in mathematics education. The first major mathematics competition in the United States began with an idea of William Lowell Putnam in 1921 [6], and the mathematics competition named in his honor has become the premier mathematics competition in the United States for undergraduates, with 508 schools and 3,640 individuals participating in 2006 [3]. For high school students, the largest current competition is the American Mathematics Competitions, which are a part of the qualification process for the International Mathematical Olympiad [5]. The American Mathematics Competition began as the “New York High School Contest” in 1950 with over 6,000 students from 238 high schools and was sponsored by the Metropolitan New York Section of the Mathematical Association of America [16, 17]. Since then, the competition has expanded to a nationwide contest with over 413,000 students from over 5,100 schools participating in at least one part of these competitions [5]. In addition to the American Mathematics Competition, there are also hundreds of other local and regional competitions [10]. While these competitions have been in existence for over fifty years and involve over half a million students every year, very little has been done to evaluate these programs [10]. What little has been done has generally involved qualitative studies involving participant surveys [10, 8] or a long term study involving winners of these competitions [12, 13].