Calculating a new approach to college math

Math seems like a bedrock when it comes to academic disciplines. Change may swirl in other parts of the university, with "dead white males" being consigned to the dustbin, for instance, or a new core curriculum being launched. But pi still equals 3.1415926....

Yet even in the stolid realm of undergraduate mathematics, dramatic change is afoot.

After nearly two decades, college and university mathematicians are overhauling the undergraduate mathematics curriculum recommended by the Mathematical Association of America (MAA).

It's a needed change, many professors argue. Few students, they say, really understand the principles behind the numbers they are crunching. A key goal of this reform is to ensure that students will know not only how to generate the right answer, but understand the concepts underlying the problem. And to get it right, math professors are seeking comment from physicists and engineers, computer scientists, chemists, and economists - as well as members of other math-dependent disciplines.

"If we're successful, these workshops with other disciplines will force [mathematicians] out of conventional thinking," says William Barker, a professor of mathematics at Bowdoin College in Brunswick, Maine, and a member of the curriculum committee of the MAA, which is driving the reform effort. "We want to enrich mathematics in a way that makes our students better able to apply math concepts - and better because they have seen its utility."

The end result, expected within two years, could fundamentally alter how undergraduate math is taught to millions of college students in the coming decade.

Mathematicians say they need fresh views on what the new curriculum stew should taste like - what skills, concepts, and topics should predominate in the college math of a new millennium. At the first of a series of math curriculum workshops held recently at Bowdoin, a bevy of physics and computer-science professors from around the country gave math professors an earful.

"I want students who can think - and that's not what we get out of our math programs today," thundered Ernst Breitenberger, an Ohio University physicist, to a roomful of physicists and a few mathematicians furiously scribbling notes. "My greatest problem is the student who thinks math is just a bag of tools."

Dr. Barker, too, sees many students "who can compute, but who don't understand."

The impact of the reform will be widely felt. While the MAA simply makes recommendations, its suggestions are taken very seriously and widely adopted on campuses.

But its reach extends beyond the university. The quality of college math graduates will affect high schools and American business in particular. Math majors who go on to teach at the high school level, for instance, may provide a deeper level of understanding - if that was conveyed to them.

"The first rule of teaching is that a teacher will teach how they were taught," says Stanley Haan, a professor of physics at Calvin College in Grand Rapids, Mich., who shared his views at the meeting. "If there are changes in how math is taught, I would expect that to filter into the high schools fairly quickly."

Technology and business are both key drivers of math curriculum reform and potential beneficiaries. The IBM personal computer appeared in 1981, the same year of the last math curriculum review. Businesses are desperate to manipulate a mass of data gathered with expanded computer horsepower - but can't find enough people with strong math skills. The number of math majors is declining - another reason for curriculum review. If there's a way to make math more appealing, it will be found this time around, some say.

"Everybody is seeing that the technical preparation of the work force is totally inadequate," says Thomas Berger, chair of the MAA committee overseeing the curriculum review. "The mathematics-education community is confronted with the challenge of better preparing people in all the math-intensive disciplines and that may mean making math programs more engaging."

But reconciling the mathematical desires of the different disciplines may be the committee's largest challenge.

At the Bowdoin conference, the computer scientists and physicists were cordial despite grumbling by one surly physicist who, over dessert, challenged a computer scientist to prove that his relatively new field of study was actually an academic discipline.

Such flaps hint at larger differences. Physicists said they want more "continuous" math - involving calculus concepts - earlier in the college career. Computer scientists want more "discrete" math - basic logic, proof by induction, and elementary set theory - which physicists care little about.

As a result, the reform effort is putting everything on the table - from differential equations to vector analysis. Even calculus - Sir Isaac Newton's creation and a central math tool of the 20th century - is not exempt.

Calculus makes it possible to plot an astronaut's orbit or design a microchip. Yet it could be downgraded from its current perch as the premier umbrella math course.

Donald Small, a professor of mathematics at the US Military Academy at West Point, N.Y., hopes that will happen. He shocked a room of physicists at the Bowdoin conference by predicting that the fat calculus text that math majors lug around will "be dead in 10 years."

Several moments of stunned silence followed as his audience struggled to grasp whether he hopes to dump calculus - which is to physics as gasoline is to the internal-combustion engine.

He doesn't. Calculus will continue to be important, but Dr. Small expects that mathematical modeling will supercede it in rank in the next decade.

Meanwhile, computer scientists brainstorm about their ideal math curriculum in another room on the leafy campus. It may have been wise to separate the two groups, given the disparate views. Still, the ultimate goal of both seemed identical.

"This whole thing is about the overriding feeling most students are left with from high school - that subconscious sense that math is not something that has meaning - that it's just moving symbols around," says Douglas Baldwin, a computer scientist at State University of New York at Geneseo.

"We have to get students' attention loose from the mechanisms of the mathematics and focused on the deeper issues," he says. "That's when they begin to understand that there is some real meaning."

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