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Symbiotic Relationships

An interview with Paul Davis, Worcester Polytechnic Institute

One of NSF's current goals is to integrate the learning of mathematics with technical education through joint efforts by mathematics and technical faculty. What do you see as the main challenges in implementing interdisciplinary projects of this type? What would be the benefits?

I feel strongly that most students are better off being taught mathematics from a perspective that encompasses many disciplines. After all very few of them will go through life viewing the world in the same way as a Ph.D. mathematician. But many will pursue careers in other fields that would be enriched if they included a mastery of mathematical ideas in these other contexts.

Mathematics faculty may not know as much as they need to about applications, and they may not be comfortable working at this interface. As mathematicians, our training is to hide in the library doing mathematics, not rub shoulders with people doing completely different things.

As you suggest, some mathematics faculty may not know as much as they need to about applications. How has WPI addressed this problem?

Our campus tends to have an interdisciplinary atmosphere, and our department is very applications-oriented. Almost everyone in the department knows something about another field and is usually willing to learn new things (within reason) to support various kinds of project activity.

We're not talking rocket science here. If faculty are willing to admit what they don't know, willing to learn some vocabulary, and willing to acquire some sense of a different discipline's perspective, they can learn as much as a typical undergraduate knows about some small area of engineering or science without making a career out of it. However, if someone has been through many years of undergraduate and graduate education without learning a bit about fields where mathematics can be applied, then there may not be much that can be done. But someone with a range of interests can usually expand that range fairly easily.

So the short answer is: hire people with broad scientific interests.

Many mathematicians and mathematics educators worry that in most interdisciplinary programs mathematics exists to serve science and that the mathematics itself gets lost. How important is it that students see mathematics as a separate subject rather than just as a powerful tool in the service of other subjects?

Is language a powerful tool in the service of history? Is history a powerful tool in the service of politics? Is physics a powerful tool in the service of engineering? Is engineering a powerful tool in the service of industry? Where does this litany end?

Mathematicians need to be more secure about the integrity of our discipline. Student should see mathematics from many perspectives, our discipline's and those of other disciplines. Mathematics is strengthened by its ties to other disciplines. The relationship is symbiotic, not parasitic.

Mathematics faculty also worry that the context-rich environment of an interdisciplinary course will impede rather than enhance learning since it will be harder for students to sort out the mathematics principles from the surrounding context. And they worry that students will not have the opportunity to take the mathematics they are learning to the next level. What has been your experience in this regard?

My experience with modeling-oriented courses has been a stream of student comments saying, "This is the first time I understood what mathematics could do." Who would want to take something to the next level when they have no idea what it's good for? Except for the small number of nuts like us who fell for mathematics at first glance, it is an acquired taste. Let's help students by giving them context and significance. Don't hide the power of mathematics. Display it in contexts that mean something to students.

What might be other strategies, besides interdisciplinary courses, to help students learn to use mathematics in a variety of real-world contexts?

Several of the recommendations in the SIAM report Mathematics in Industry address this issue. As I said earlier, other disciplines should appear regularly in mathematics courses and mathematics faculty should set an example for dealing with ideas from a variety of disciplines, even if their own mastery is (inevitably) incomplete. Students should regularly have to attack projects (open-ended problems) that originate in other disciplines. (WPI is trying to formalize this with bridge projects that connect mathematics, science and engineering.)

Paul Davis is Professor of Mathematics at Worcester Polytechnic Institute in Worcester, Massachusetts. He can be reached at pwdavis@wpi.edu.

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Last Update: June 17, 1997