Six Is a Perfect Number

By Lisa Stein

The number 6 is not only the School of Education and Social Policy's new spot on U.S. News & World Report's annual rankings of graduate programs in education. It also enjoys a long history of being regarded as beautiful, even magical, and one SESP professor thinks it can shed light on ways to improve math literacy in the United States.

Ancient Greek mathematicians proclaimed it a "perfect" number, one of the lucky few that equal the sum of their positive proper divisors (3+2+1=6). The Christian scholar Augustine postulated that God could have created the world in an instant but chose to do it in a perfect number of days - 6 - as is stated in the Bible. Early Jewish philosophers thought that the perfection of the universe was illustrated by the moon's cycle of 28 days, and 28 is the next perfect number after 6 (14+2+7+4+1=28).

Uri Wilensky, associate professor of learning sciences and computer science and director of the Center for Connected Learning and Computer-Based Modeling, says that 6 and its perfect brethren hint at the possibilities open to U.S. mathematics educators and students. Wilensky views the wide range of kinds of numbers, including perfect ones, as underrepresented and understudied in math curricula.

"Math educators in this country present such a restricted set of categories of numbers," Wilensky says. "For instance, we talk a lot about squares, which are numbers that can be arranged into squares, such as 4, 9 and 16. But we don't say anything about triangular numbers, numbers such as 3, 6 and 10 that can be arranged into triangles, even though they're almost as important as squares. There are a lot of different kinds of numbers out there that are just as accessible as the few we are teaching, but people don't know about them."

Wilensky notes that math instructors in other countries, such as China, foster a culture of exploration and inventiveness among their students. "Teachers at the high school level in China consider themselves mathematicians. They encourage kids to create and improvise, which in turn makes for a much richer literacy. Math instructors here are competent in terms of knowing what is in textbooks, but they don't have the ability to improvise with numbers, to play with them."

True literacy, Wilensky argues, includes the ability to explore a subject and develop original thoughts about it. "You wouldn't teach kids only to read and not to write. We expect them to write about what they've read and to communicate effectively. It's the same with math."

Wilensky believes that many of today's students are capable of exploring more deeply in the math universe. "The more categories of numbers that students know - there are thousands of them - the more they can imagine inventing their own. Suddenly they're doing research mathematics, and that's exciting."
By Lisa Stein