Reinvigorating The Mathematics Culture: The Problems Are Not Only Quantitative

Curriculum quality must change in order for the depleted math profession to attract young scholars, workshop attendees agree The teaching of mathematics requires drastic change, according to a group of academic mathematicians who met in Oakland last month. The approach and the content of university mathematics are dangerously out of synch with the needs of both students and industry, and the result, the mathematicians contend, is causing the number and quality of mathematics students to dwindle. "We're just not getting students into the pipeline," says Naomi Fisher, codirector of Mathematicians and Education Reform (MER), a four-year-old center at the University of Illinois at Chicago, which sponsored the March gathering, entitled "Joint Mathematics Workshop on Changing the Culture: Education and the Research Community." The Oakland meeting was the center's eighth, with more planned. "The number of students who say they're interested in mathematics is declining, and the half-life of mathematics students is one year," she says, referring to a mathematics community truism that as a group of students progresses in college, half the mathematics students leave the field each year. D.J. Lewis, a workshop attendee, said that the meeting enabled interested academics to share methods to improve math teaching. "You've got to think of a math teacher more as a coach, or an art or music teacher," says Lewis, a professor and chairman of the department of mathematics at the University of Michigan. "Students learn by doing. They do something, you critique it, and they go back and do it again. It's becoming very evident that they need instant feedback." This approach would be a radical change from the usual 200- person freshman calculus lecture in which the professor sets up 20 problems and methodically moves down the board and solves them. According to George Rublein, an associate professor of mathematics at the College of William and Mary, mathematics has another problem: Students are taught material "that is nothing like what mathematicians really do." The problem, then, seems to be that mathematics students are taught the wrong way, and that they're taught the wrong things, according to Lewis and Rublein. The pair's views are representative of those of a burgeoning movement in the mathematics community, as evidenced by the 58 workshop attendees. With a goal of getting mathematical researchers back into the educational process, the workshops are an attempt to change the culture of mathematical education. Noting that less than half of the 1991 mathematics Ph.D.'s granted by United States institutions were given to U.S. citizens, Fisher says, "Something crucial is happening here. Why is it that other countries are producing an interest in mathematics, but American universities are not engendering it, as well?" The answer comes, Fisher says, from a basic change in university priorities that occurred in the 1950s. "Universities took a strong turn towards supporting research, and teaching really got attenuated," he says. And with researchers thus treated as an elite group, little of their excitement or innovation filtered into the classrooms because they either weren't teaching or weren't concentrating on their teaching duties and conveying the real content of their profession in their teaching. "Universities are still laboring under guidelines that say that the only thing of real value is mathematical research, rather than education," Fisher says. "We hear stories of people interested in teaching being told, `Be careful, teaching is not going to play any part whatever in hiring or promotion.'" William Jaco, executive director of the American Mathematical Society, a cosponsor of the workshop, agrees. "Many universities have a typical mission that includes statements of goals like `teaching, research, service,'~ " he says. As research has grown out of proportion, service and teaching have been left behind, creating an imbalance in the community, he says. Moreover, Jaco says, economic changes requiring a more technical and mathematically proficient work force "have intensified the need to determine how we can get back in balance." The methods teachers discussed in the workshop are twofold: changes in teaching methods and changes in the content of math curriculum. Teaching methods are being changed to favor smaller classes and more cooperative work. Says Lewis, "We're going through a training process" with mathematics instructors. "Instead of the student asking, `How do you solve problem A?' and the instructor sitting down and showing him, we're teaching them to, in response to each question, ask a question." In this way the students learn mathematical thinking rather than rote problem solving. "It's a slower process, but in the end they usually understand," he says. It was his own version of the Socratic teaching method that got Rublein interested in the MER workshop. "There are days I spend the whole class time asking questions of students" in his lecture courses, Rublein says. "And [the students] don't like it [because it's more difficult]. I found this meeting so refreshing because I found that there were other people floating around who were worried about the same things I was." Rublein also wishes to focus on the change in mathematical content of course work, teaching "the kind of aspects of mathematics that are absolutely central to the way mathematicians work, but are absolutely hidden to math students," he says, because of the separation of research because of the separation of research and teaching in universities. The workshops do address ways to change the content of mathematical teaching, Lewis says. At Michigan, instead of giving students problems, he is focusing on "real mathematical modeling--where they cooperatively work on really open-ended problems. Since a lot of what you're doing is maximization-minimization, you'll take a problem from manufacturing or biology." Rublein feels that this approach gives students a better, "more intuitive" grasp of what they learn. "Their intent," he says of the workshops, "is to put a very heavy emphasis on people's ability to describe what they're doing--there's a very heavy emphasis on qualitative features," which he says is essential in real mathematical work. And because of the current emphasis on research, all parties agree on the importance of researcher participation in the modification of curriculum content. As Fisher says, "Because of our perceptions of what it means to be an academic, the researchers are considered the elite, and they have a certain amount of leadership whether they want it or not." Fisher doesn't labor under any beliefs that the changes will be easy. "We get into these issues of culture," she says. "It's a slow process, but it seems to be a process that works." It had better, says Rublein. If not, "we know who is going to pay the price: it's the students."

Reinvigorating The Mathematics Culture: The Problems Are Not Only Quantitative

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