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Mathematician challenges idea of average class size

Aug. 9, 2007

KALAMAZOO--Calculating average class sizes to better reflect students' actual experience is the topic of an article by a Western Michigan University professor who was recognized in August by a national mathematics organization.

The piece by Dr. Allen Schwenk, "Distortion of Average Class Size: The Lake Wobegon Effect," received the George Polya Award Aug. 4 at the Summer MathFest in San Jose, Calif. The award is presented by the Mathematical Association of America for articles of excellence published in the College Mathematics Journal.

The journal published the article, named for the fictional town made famous in by National Public Radio personality Garrison Keillor, in its September 2006 issue.

Schwenk writes that the current method school administrators use to determine average class size--dividing the total number of students by the total number of classes--is not an accurate portrayal of the classroom experience.

Instead, a class that is attended by 100 students should be counted 100 times, and a class with only 10 students should be counted 10 times.

"Large classes are experienced and reported many times, and small classes are reported and experiences only a few times. This causes the average to shift to a larger number," says Schwenk.

The concept for this calculation has been around at least 20 years, but it has not been widely recognized. Schwenk not only provides the mathematical formula--proved three different ways--for computing class size from this perspective but also a series of well-developed examples.

"We won't get schools to change the way they report class size, but we might get consumers to alter their expectations. A prospective student will get better guidance by asking current students about their experiences," he says.

Schwenk, a professor of mathematics specializing in graph theory, joined the WMU faculty in 1985. He received an undergraduate degree from the California Institute of Technology and master's and doctoral degrees from the University of Michigan.

Media contact: Deanne Molinari, (269) 387-8400, deanne.molinari@wmich.edu

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