Making Mathematics Meaningful

BY NANCY SERRILL

The lines wax and wane, ribbons of cobalt, turquoise, robin's-egg blue: It's a textile design, a work of art. But Dartmouth professor Dorothy Wallace sees other dimensions of the tempera painting that sits on her desk - symmetries and relationships she describes in the language of mathematics.

"This is mathematics in its context," she says.

This fall, through a five-year, $4-million grant from the National Science Foundation, students at Dartmouth should also begin seeing the mathematical principles in the world around them. The grant, one of four awarded as part of a $12-million national effort, is designed to "promote broad and significant improvements in undergraduate education that can lead to increased student appreciation of and ability to use mathematics," according to the agency. The funded projects are expected to serve as national educational models.

Dartmouth's Math Across the Curriculum grant will involve a collaboration of more than 50 faculty members, who will integrate mathematics into everything from music and architecture to earth science and engineering. The interdisciplinary approach is expected to enhance retention and make math more useful to students.

Wallace, associate professor of mathematics, approached her Dartmouth colleagues two years ago with an idea for a new class called "Pattern" - she wanted to teach with an artist - a class that would combine textile design with a branch of abstract algebra called group theory. In the class, students would create something beautiful, then analyze their creations, "learning by doing rather than listening," says Wallace.

The response from colleagues was enthusiastic. Suggestions for other interdisciplinary classes flooded her mailbox. "The idea obviously hit a nerve," she says.

Having students develop a working knowledge of math - rather than a passive acquaintance - is good news for science professors, says Delo Mook, professor of physics and astronomy. "For some time we've been aware that students who did well on math tests were not learning to translate those applications to other fields." Learning applications along with theory will bring math into the active vocabulary of students, he says. "We won't have to be reteaching them calculus when they encounter it in physics."

Last month a group of faculty members gathered at the Dartmouth Institute for Science Teaching, a Women in Science Project-sponsored retreat at the college's Minary Center on Squam Lake, to plan implementing changes in the curriculum. "It was an opportunity to see what cross-fertilization of ideas could take place," says Mook.

Drawing on the non-mathematical interests of students to motivate their exploration of mathematical structures is an extension of using physical examples, or problems, in teaching, says Wallace. It marks a further return to the roots of mathematics - the natural world and science.

"People didn't just walk into the Woods and invent science or mathematics," she says. "Isaac Newton created his laws of motion and the principles of calculus to explain things he saw in nature."

Returning math to its context answers a fundamental question posed by many students: Why are we learning this?

Scott Listfield '98 found himself asking that question when he first learned calculus. "I never found a whole lot of relevance to it in everyday society," he says.

The Pattern class was different. "I am an art student, and for me learning the math involved in artistic works was far more interesting than learning math that was fairly disassociated with anything but math," says Listfield.

The approach may make math more engaging to students in more ways than one.

Says Jason Bunyan '98: "I'd liken learning math this way to the philosophy courses here. There has to be a lot of thought invested; it's not just ingestion and regurgitation. There's more thought and personal research."

And the reward is more than a passing grade on a transcript. "You actually use the knowledge and make something tangible from it," he says.