From The Boston Globe, page H5, 09/19/99Teaching math in wider context
By Paul Bush, Globe Correspondent, 09/19/99
Sarah Billmeier had always done well in math, but shortly after enrolling in her second calculus course at Dartmouth College, she quit.
"I just didn't understand the point anymore," Billmeier said.
Her classmate Elizabeth Cullen's distaste for math was even stronger. "I hated it, and wanted to get out of it," she said. "I had had just horrible math experiences before."
However, both found themselves drawn to an unusual math course called "Pattern" that showed, among other things, how fractals and chaos theory could help with painting and textile patterns. By the time it was over, both students had changed their minds about math.
"It made you think about math in a different way," Cullen said. "It was actually useful. I can't say now I'd be comfortable doing equations, but I definitely feel more comfortable with my ability to do math."
Billmeier said, "I had never learned what calculus was applied to when I was learning it before. ["Pattern"] showed us where math was basically everywhere."
"Pattern" is part of Dartmouth's Math Across the Curriculum Project, now in its fifth year. Backed by a $4 million grant from the National Science Foundation, the project has changed how math is taught at this college of 4,300 undergraduates. Thirty new courses have been created that take math out of its usual confines and spread it around campus, frequently in areas where it has never been before.
Some classes, such as "Math for Medicine and Biology," are giving science and pre-med students a more intensive exposure to math than usual. In the past, despite the apparent connections between the subjects, students in these fields had only limited math requirements.
Other classes in the new curriculum attract students with their unusual combinations of disciplines, such as "Math and the Philosophy of the Infinite."
Jane Korey, who has been responsible for evaluating the outcome of Math Across the Curriculum courses, regards the project as a success. She has interviewed at least 10 students in each course offered, out of the approximately 2,100 students who have taken the classes since 1994.
"We've been able to learn a lot more about how students learn math and respond to it," Korey said. "When I was a student way back when, we always thought that smart people learned math best. But what I see is that motivation is far more important than anything else.
"Tapping into their interest is key," she said. "It's a step that has to precede the teaching of skills."
The project already has produced results among math and science students. Calculus students who had taken a course that showed its real-world uses were tested seven weeks later. They scored twice as high as students who had taken a traditional "pure math" calculus course.
The impact has also shown up in a rigorous, yearlong course that taught how math is used in science, yet another topic that mathematicians do not traditionally teach. At the start of the course, 68 percent of the students, all of whom were freshmen, said they planned to major in hard sciences, such as math, chemistry, engineering, and physics. By the end of the course, the figure had risen to 88 percent.
The most unusual new courses are those blending math and the humanities. One such course, "A Fire in the Equations," combined science-fiction stories and math. Professors Laurence Davies and Jody Trout spent a year preparing the course. Davies covered the literary aspects of the stories each week, while Trout taught the math. The third class period, on Fridays, was reserved for discussions.
One week the focus was "The Infinite Assassin" by Greg Eagan. "It's a parallel world story," Trout said. "A lot of things are going on across dimensions, but if you don't understand [dimensional] construction, it's hard to understand the story on a deeper level."
Trout introduced students to the Cantor set, a mathematical concept. "It has some very bizarre properties which have dire consequences for the main character," he said. "By appreciating the math you can see the character is doomed."
Teaching the course was not easy, the two said. For someone who had not taken math in years, said Davies, "it was a stretch." Davies noted that he also had to adjust his free-flowing lecture style to Trout's highly structured math lectures.
The course did not work for all students. One, who asked not to be identified, said, "The range of students in the class was so broad, the professors had to approach both subjects at a high school level."
Nonetheless, Korey said that most students are positive about the approach to math taken in "The Fire in the Equations" and other courses.
At Dartmouth, students are often exposed to connections and applications they have never seen before, Korey said.
"What I heard over and over was, `At last I understand why they wanted me to take calculus,'" Korey said.
Mathematics professor Dwight Lahr concedes that math is almost always taught in isolation from other fields. "The connections with other disciplines and other parts of life are of very small importance in math," Lahr said. Yet when Lahr taught "A Matter of Time" with professor Beatriz Pastor more than 160 students signed up, making it the first math course to require an enrollment cap, he said.
The course looked at time from both mathematical and literary perspectives, beginning with Aristotle and Plato and concluding with Gabriel Garcia Marquez's "One Hundred Years of Solitude."
"For the science students, we said you could study all of Newton's theory [of time] and you had not covered one-tenth of the complexity and depth in the monologue of the clock in [Shakespeare's] `Richard II'" Pastor said.
The course also tried to show how math could enrich the humanities. Pastor used the example of a paradox presented by the Greek philosopher Xeno in 500 BC that was not resolved until the development of a mathematical solution in the 19th century. "In between you have 24 centuries of debate," Pastor said, "but humanists couldn't close the debate. It took a mathematician to do so."
The two professors faced the usual difficulties adjusting their teaching styles and dealing with unfamiliar disciplines, but Pastor and Lahr had the additional challenge of being married to each other.
"We'd be brushing out teeth and one of us would say, `Hey, what about this?'" said Lahr. "Then you'd be thinking about it all night. We had to come up with rules" to limit discussion.
Pastor and Lahr said that their focus on one of the central issues of human existence, time, tapped into students' interest in the major questions of life. However, the mixing of humanities and math did not satisfy everyone.
Responding to questions e-mailed to her, sophomore Rochelle Bourgault said, "I am now very skeptical of courses that radiate `Take me!' from the course guide. `A Matter of Time' sounded wonderful. To me, it was sheer drudgery."
She added, "I think I've had my fill of these experimental interdisciplinary courses. I think it's very difficult to draw together two disparate disciplines in a purely lecture-oriented class."
On the other hand, philosophy major Tam Boyar ranked "A Matter of Time" as "one of the top three courses I've taken at Dartmouth."
Other colleges and universities are already at work making math courses more "applications based." However, Dartmouth's embrace of courses combining math and the humanities appears to be the most advanced and wholehearted, and education experts said its approach is likely to spread.
Workshops at Dartmouth have attracted faculty from colleges and universities from the Midwest and East Coast. Although Trout reported that the idea got a skeptical reception from some of the audience, at least nine professors at other schools have begun using the approach in their classes. As books, classroom videos, and other materials are produced as part of the Math Across the Curriculum project, the approach is expected to spread.
Introducing students to the world of math through an existing interest in the humanities worked for the six students who took "Pattern." Five have graduated, and all say they have gained a new appreciation for math.
"I don't understand why these connections aren't made earlier on," said graduate Mamie Lawrence. "I think it's a disservice when people graduate and think of math as this subject and not as everyday life."
This story ran on page H5 of the Boston Globe on 09/19/99. (c) Copyright 1999 Globe Newspaper Company.
