Mathematics Across the Curriculum at Dartmouth

By Dorothy L Wallace

At the front of the room the art professor is demonstrating techniques of block printing to a dozen students. On the board is a diagram of a graph of subgroups drawn by the students, indicating which of the seventeen wallpaper groups are contained in each other. The students are getting ready for their fourth assignment: printing a series of three block prints, each of which displays a symmetry group containing that of the previous one. The finished prints will take hours of work, require mathematical precision, and dazzle the eye.

A room of thirty premedical students watches as the professor connects some flexible plastic tubes to an apparatus. This class has been developing a model for changes in blood pressure due to constricting arteries. In addition to actual medical data, they are using this apparatus to test their model. Later, students will say this class "opened their eyes" to the fact that math is "more than just taking a derivative" and has many applications in real life.

Forty first year students are gathered in groups of three or four to work out a problem in vector calculus as both their math professor and their physics professor look on. They know that the physics they learned yesterday ought to inform the problem they are working on right now, and that the math they are studying today is likely to be used in tomorrow's physics class. They help each other master the material they know they will need. More of these students will be inclined to major in engineering by the end of their two quarters of intensive interdisciplinary study than when the class began, making the course a recruiting force for engineering.

A mathematics professor is explaining the basis of relativity theory to a lecture hall of a hundred and sixty liberal arts students, who sit quietly taking notes. The silence is broken by the professor of comparative literature, who demands to know why the students do not question the information they are receiving. "Do you believe him? This would never stand in one of my classes! If I said something incomprehensible, students would be all over me until I explained myself thoroughly. Why do you accept this from a scientist?" Discussion breaks out about the information we take at face value, the authority of the "expert" and the role of critical thinking as it pertains to science and mathematics.

"Pattern, Applications of Calculus in Medicine and Biology," "Integrated Mathematics and Physical Science," and "A Matter of Time" are just a few of the 26 courses developed or enhanced at Dartmouth College as part of the Mathematics Across the Curriculum project funded by the National Science Foundation in 1995. In addition to courses, this project sponsored the development of many materials, including an interdisciplinary text in math and physics, parts of a text on the math and biology of Lake Victoria, (intended to address the diversity of students taking math), several new modules in statistics and data analysis, and a collection of course readers in mathematics and humanities. All of these materials make interdisciplinary teaching of math more accessible to a national audience.

By 1998, the MATC project had benefited over 2,000 students at Dartmouth, directly involved 178 faculty at Dartmouth and collaborating institutions, created 78 modules, books and videos, and sponsored or cosponsored five workshops serving faculty in mathematics, literature, history, philosophy, art, art history, biology, geology, and engineering. Other institutions interested in such interdisciplinary activities might find the course syllabi and materials at (http:// www.dartmouth.edu/-matc/) a useful feature.

While the cries for increased numeracy of the undergraduate population have fed the development of mandatory general education courses in "quantitative literacy" throughout the country, Dartmouth has taken a different and more difficult road, with the creation of a broad swath of courses designed to attract rather than conscript students into mathematics. This alternate path stems from a lengthy discussion of the goals of a liberal arts education. One of the best descriptions of these goals is due to Gerald Holton, historian of science, who twenty-five years ago made his case in an essay on the teaching of physics:

"Here I must explain in more detail just why I believe it to be wrong to force a nonscience student to take, as is often done to "fulfill a science requirement," simply the regular introductory specialty course given by a science department. I start from a general belief that the total orienting process of a young student in college, it seems to me, has at least five goals.

"If he or she is to emerge as an educated and sane person from our educational institutions, the student should be well on the road to recognizing which are his own talents, whatever they may be; second, he should know enough about his physical home, this universe, not to feel either overwhelmed by it or a total stranger in it; third, he should know how to be in fruitful relationship with his fellow men; fourth he should know what the past means and what the probable future may be; and fifth, he should know the difference between, and the relative functions of, his mind and his soul." ("Physics and Culture, Criteria for Curriculum Design", Thematic Origins of Scientific Thought, Harvard University Press, 1973).

Holton's vision of what an interdisciplinary physics course could be offers a model which Dartmouth independently pursued with respect to mathematics. The process of delineating their goals and designing their courses created consensus and camaraderie among faculty. The courses themselves fostered a new attitude toward mathematics among the students taking them. Clearly a large variety of courses would have different kinds of impact on students, some resulting in measurable differences in mastery of the mathematics, some improving retention in science majors, some affecting the attitudes of the students toward mathematics. Independent evaluators studied the impact of the Dartmouth courses on Students through subject tests, surveys and interviews with individual students. Three results stand out across all the curriculum interventions as potential guideposts to future development in any mathematics curriculum:

Students' interest in mathematics is more important than their perceived math ability in determining whether they study more mathematics. Many students who view themselves as able mathematicians forego college mathematics because they see no career utility or intellectual reward.

Real-life applications make mathematics more approachable and more interesting. Whether students' interests are pre-med, pre-engineering or pre-history, connecting mathematics to their existing interests transforms math from a "cut and dried" requirement to a relevant tool for advancing their learning.

Expanding the range of mathematics topics accessible to average college students increases their interest in mathematics. To most entering college students, calculus is upper level math. As a result, many who do not need calculus in their careers turn away from college math altogether. Students were excited by courses that offered non-calculus topics (combinatorics, number theory, group theory, probability, etc.), revealing unsuspected new worlds of mathematics to discover and enjoy.

For many students, these courses have been a source of great insight into the doing of science and math. As one of the future engineers in the Integrated Mathematics and Physical Science sequence put it: "Math and science are scary and messy and wonderful and exciting. It's no longer about right and wrong answers; there are so many more things to think about. IMPS math and science isn't cameo, homogenized topics; it's the real thing at times-headaches and all."