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Math Switches Calculus Focus

Courses Stress More Visual Approaches to Learning

By Toyia R. Battle

A picture is worth a thousand words, or, if you're in Harvard's Math Department, a thousand integrals.

In an effort to make calculus more applicable to other fields, the Math Department is revamping its approach to calculus, stressing more graphics and fewer formulas when it comes to problem-solving.

Deborah J. Hughes Hallett, senior preceptor of the Math Department, said the switch is a reaction to growing concern among mathematicians that those who learn calculus no longer recognize its applications in other disclipines.

"One of the many complaints is that people from other fields have felt the kind of material in calculus courses are not recognizable in their fields," Hughes Hallett said. She said that fields such as biology, ecology and economics often require calculus, but present students with data sets and graphs--not formulas.

This summer, when Hughes Hallett and experts from other universities rewrote the standard calculus textbook, they gave it a new look with more graphing and problems drawn from various fields.

"The calculus courses of the past almost never had graphs or data. They started with a function," Hughes Hallet said. "The other fields frequently find it hard to recognize what was calculus."

In so doing, the scholars hoped to better demonstrate how math is used in other fields, Hughes Hallet said.

Graphic Calculators

After studying student learning patterns, professors at Harvard this year designed courses around the use of graphic calculators and computer programs. And while graphing has traditionally come secondary in most calculus courses, the focus in many classes has now shifted to ideas and pictures, instead of formulas.

For instance, Math 21 a now has a graphing program to help students visualize the three dimensional figures the course deals with, she said.

"I remember trying to make surfaces out of my sweater or coat," Hughes Hallet said. "The computer is a lot easier and makes better shapes."

Applauding the Changes

Other departments applauded the new changes, but some students said they are finding it difficult to adjust to the more visual teaching of calculus.

"I don't know if it's worth $82.50--that's what the calculator cost," said David G. Hill '94, a Math la student. "I prefer a more straight-forward math approach."

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