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Innovative approach wins math teaching award for Paul Blanchard

By Brian Fitzgerald

Many professors today do their best to incorporate technology into their classrooms. But why does Paul Blanchard, a CAS associate professor of mathematics, show a movie of the Tacoma Narrows Bridge collapse in his Differential Equations course?

"Galloping Gertie," the bridge that oscillated dramatically in the wind before collapsing in 1940, makes for fascinating footage, but what does it have to do with math? In the past, the undulating bridge had been used as an example of a linear harmonic oscillator equation -- until recent research indicated that it doesn't make an accurate model of the movement of a suspension bridge. So Blanchard and his students look into alternative types of differential equations to explain the disaster.

	Paul Blanchard. Photo by Kalman Zabarsky

It is this kind of approach to teaching math that caught the attention of the Mathematical Association of America (MMA), which named Blanchard Distinguished Teacher of the Year in the group's northeast section. His recent efforts at reforming traditional differential equations courses -- including workshops for high school teachers and college professors on his innovative approach to teaching the subject -- have caught on at high schools and colleges across the country.

"When we revised the course, we added a dynamical systems flair to it," says Blanchard. "It's now very technology-oriented. The course hadn't been revised in about 50 years. The students find it unusual to do projects with an open-ended nature, but it helps a lot."

Blanchard's students agree. "His explanations are clear, and he makes good use of technology to illustrate formation, solution, and application of differential equations," writes one in a teaching evaluation. Another has this to say: "Professor Blanchard is the best teacher I've ever had. The ease with which I learn the material from this relatively difficult class is incredible."

Blanchard puts many of his classroom demonstrations on his Web site, and students can use QuickTime animation -- which they can download for free -- to see pictures of slope fields, vector fields, and phase portraits from any angle. "The availability of technology is undoubtedly the biggest change that has occurred since I started here," says Blanchard, who has taught at BU for 20 years. "The material is easier to disseminate. Using the Web, students can now see these equations in their dorm rooms." He is also wary of technology's pitfalls, however, and knows that it must be used rationally. "It's important to be well-grounded in traditional teaching techniques," he says. "Students still have to understand the math. We can't just have them enter commands and expect them to learn."

But if they do have difficulty learning, Blanchard is always available to help during office hours. "That's what teaching is all about," he says.

Steven Rosenberg, chairman of the CAS department of mathematics and statistics, nominated Blanchard for the MAA award. Blanchard, he says, has not been seduced by technology's glitter. "In all of Paul's teaching activities, both at BU and in national forums, he has kept sight of the true goal of developing mathematical intuition, while teaching fundamental concepts and techniques," he says. "His work with graduate student teaching assistants has allowed his example to directly affect teaching at many campuses."

Blanchard has lectured at more than 80 workshops and seminars, many of them on the BU Ordinary Differential Equations Project, a National Science Foundation-funded effort to teach differential equations from a dynamical systems point of view. Blanchard and math department colleagues Professor Robert Devaney and Associate Professor Glenn Hall have written a textbook on the subject, published by Brooks-Cole in 1998.

Blanchard's workshops on his innovative approach have been widely praised. "Paul Blanchard's impact on my development as a teacher has been profound," says Maeve McCarthy, a math professor at Murray State University in Kentucky. "I attended a workshop that he organized at Mathfest in Providence in 1999 on the use of technology in the teaching of differential equations. He provided me with a wealth of ideas to take back to my own classroom, and a great deal of insight into the practical use of technology in the classroom. It was obvious to all of us that Paul is an extraordinary teacher."

What drew Blanchard to BU? "It's the closest university to Fenway Park," says the Sutton, Mass., native and lifelong Red Sox fan with a smile. "Actually, in 1980 I was a math professor at the University of Southern California." Dennis Berkey, now Provost and Dean of Arts and Sciences, at that time was chairman of the CAS math department. "Dennis Berkey had a plan to expand the department, which grew like crazy in the 1980s, and now we're in the top group I ranking of graduate programs by the American Mathematical Society," he continues. "My wife is also an academic, and we wanted jobs in the same location." Blanchard's wife, Dorothy Kelly, now chairs the CAS modern foreign languages and literatures department.

As a result of the award, Blanchard will give a presentation in November at the fall 2001 Mathematical Association of America's northeast section meeting at Bridgewater State College. "I'm kind of nervous about that," he says. "A lot of good teachers will be in the audience."

If past presentations are any indication of future success, Blanchard has nothing to worry about. "He is a leader, by example, in what constitutes dedicated teaching," says Rosenberg.

23 February 2001
Boston University
Office of University Relations