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03/31/91

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Osgood helps write a curriculum to pass along the pleasures of math

STANFORD -- For Brad Osgood, mathematics is like playing music: If you love it, you have to do it.

Osgood plays his music as second trombonist and informal leader of "Tuesday Night Live," an eclectic jazz ensemble composed of Stanford faculty members, engineers and business people.

He does his mathematics as an associate professor, known for his research in classical complex analysis and modern differential geometry.

He worries about how students learn to do their math, in undergraduate calculus courses that he describes as "plug and chug - teaching students to perform feats of calculus, without any idea of how they can be applied or what they mean."

Like many academics who teach college-level math, he found it hard to use calculus to teach either the utility or the beauty of the subject. Yet he wanted to follow the advice of one of his own math teachers: "We take so much pleasure out of doing mathematics; it's only right to pass it on."

So he became a leader in the national movement to re-think the way calculus is taught. In the process, he has led a reform of undergraduate math teaching at Stanford, with more changes to come.

He helped develop a new curriculum and wrote major portions of the textbook for the Harvard Calculus Consortium, a project funded by the National Science Foundation. Spearheaded by Osgood, Harvard mathematicians Deb Hughes Hallett and Andrew Gleason, and a handful of their colleagues across the country, the consortium has spread the new curriculum to more than 40 colleges and universities.

At Stanford, it was introduced to freshmen in the Calculus 40 series in 1990-91 and in Calculus 20 this year. Osgood postponed a sabbatical when he decided the teaching program was still too "tender" to leave behind.

Working with a fat spiral-bound textbook and an off-the- shelf calculator that can produce simple graphs, students learn to understand the derivative by plotting the change in temperature of a yam placed in a hot oven. They learn by analyzing graphs of world energy consumption. They learn to interpret and use the area under a curve by estimating the maximum yield of an apple orchard. They test the Fundamental Theorem of Calculus with a graph of the upward - and rapid downward - acceleration of the 18th-century Montgolfier brothers in their hot-air balloon.

The course met some initial resistance. The Stanford Daily quoted such freshman complaints as, "The new way is word problems, and I always hated word problems!"

"Most Stanford students are good at math," Osgood said. "They look at this and say, 'I know calculus. I don't know what you're teaching me, but this isn't calculus.' "

Not only does the book contain word problems, but it explains concepts in the text.

"It's a book meant to be read, and students aren't used to reading math books," Osgood said.

By the end of the course, he hopes students will have discovered "the power of simple ideas" - how they can represent data not only with formulas but with graphs and tables, test problems they don't initially know how to solve, and test the reasonableness of their estimates.

Some standard aspects of the material are still important.

"There are certain things you have to be able to do with your spine, like differentiation formulas," he said. "We want to teach students to answer those kinds of questions, but even more, we hope to teach them to start asking their own questions, and to use their answers to ask new questions."

Osgood seems to have won over most of the initial objectors to the reform. He received a teaching award last year from the Associated Students of Stanford University - "so I can't be all that bad."

The real benefit of the course will come as students tackle the disciplines that calculus is supposed to prepare them for. Osgood said he is beginning to see that result. A sociology graduate student has predicted a rush of fellow sociologists who could use the new calculus to help interpret data. An economics major wrote to say that for a reference in open-book tests, he leaves his econ books behind and takes his calculus text.

The three-year Bing Professorship was an honor for Osgood, but also cause for alarm.

"I called (Humanities and Sciences Dean) Ewart Thomas and said, 'I need to take my sabbatical!' " Osgood said.

Thomas assured him that was no obstacle, and the Osgood family will spend next year near Paris, as he joins the Institut des Hautes Etudes Scientifiques.

Osgood said it is too soon to have an exact plan for the $15,000-a-year award money.

"I've never controlled a slush fund before," he said.

While he is away, Osgood may spend some of the funds to keep the new curriculum percolating at Stanford, sponsoring visits by Hallett or other members of the consortium. Later, he may work to put calculus support materials online, so students can use them via campus computer networks. He also may sponsor projects by groups of students.

What makes a good teacher?

"Treat your students with respect and hope for the same in kind," he said.

"You have to love the subject - that's an essential, but not sufficient, condition. You have to prepare carefully for class. . . . Things will go wrong, but you have to minimize that. (Otherwise), students will think, 'If this guy can't do (a problem), how can I possibly do it?' "

In addition to curriculum reform, Osgood is involved with the reinstituted Math Honors Program, and with a project to recruit students with math talent for Stanford. He works with the School of Engineering on the Science and Engineering Mathematics Achievement Program, targeted at students who show promise but traditionally haven't gone into science and engineering. Nonetheless he said he never imagined he would write a calculus textbook.

"I'm not interested in math education," he said. "I'm interested in mathematics. And I love teaching."

-jb-

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