December 7, 1998
Volume 51, No. 14
Rogers 'proofs' that mathematics need not be scary
As much as education has changed since Michael Rogers first arrived on a college campus, words like "statistics" and "calculus" can still be counted on to strike fear in the hearts of the non-mathematically minded, especially since at least one such course is required for all students.
In fact, that's why Rogers, an assistant professor of mathematics at Oxford, decided to design a math course for more right-brained students, one they wouldn't have to dread. Enter Math 120, being taught for the first time this semester to an intimate group of five students. Rogers approaches geometry from the perspective of "pure mathematics" in the course, trying to understand the analytical, logical process behind mathematical proofs, as opposed to memorizing formulas and applying them to situations. Though he'd been thinking of such a course for years, Rogers said a trip to the St. John's Summer Institute in Santa Fe, N.M., in 1996 helped solidify the idea.
"All sorts of people go to this institute," Rogers said. "There are faculty members, people who are trying to get a master's in liberal studies. So I saw a wide range of students and a lot of them were math-phobic. We read some of Euclid and some non-Euclidean geometry, and I could see that they could do that. I could see it was possible."
In fact, it used to be more or less the norm, Rogers added, before world events dictated that college mathematics be nudged into a different, more practical direction. "I suspect that since Sputnik, for instance, the general push toward producing engineers and technically proficient members of society has changed the emphasis on mathematics away from reasoning and proving, more toward technique and problem solving," he said. "Calculus, for instance, could be done without the emphasis on algebraic technique, but it wouldn't necessarily prepare students in the same way that calculus does the way it's taught now."
That's not to say it wouldn't be useful, however, to math students to take Rogers' course. Since it doesn't count toward their major requirements and is plainly directed toward non-majors, Math 120 may strike math majors as a crib course, Rogers said, but the theories and skills he teaches in it are those which budding mathematicians will need as they advance into higher-level coursework.
"Proofs are very hard to learn, and you cannot learn how to do them in a semester," Rogers said. "I think there ought to be more proofs in calculus for the few math majors who are coming through. When they actually get to the higher-level math, where all they do is prove things, they'll be better prepared."
Oxford's administration has been very supportive of the class, Rogers said, since it seems a natural fit for the idea of what a liberal arts education is all about. The analytical skills students learn in math are just one of the many tools they collect across a broad range of subjects from a liberal education. Indeed, Rogers has distinguished himself as a renaissance man of sorts, since he personally translated two books of Euclid's Elements from the original ancient Greek to use as texts in Math 120. Rogers taught himself to read ancient Greek; he also speaks French and Russian, taught himself some German for his mathematical work, and even dabbles in Latin. "The Latin and the Russian helped with the ancient Greek," he said.
"There have been lots of translations of Euclid," Rogers said, "but right now there's only one in print in English, and that was done in 1908. The fellow who did it, T.L. Heath, his primary area of research was ancient mathematics, and he collected all the commentary on Euclid into this three-volume set. So there's a theorem, and then there could be two or three pages of commentary. I think there are things that can be improved. Part of it is that in the time lag, vocabulary has changed, and some of the ways Heath describes things are not mathematically current.
"But primarily I started out translating Euclid because I wanted to see what he wrote. There are things in Euclid that are hard just because they are so elliptical; the translation I did was very close to the original, so even when things were sort of ambiguous, I kind of left them like that, where Heath would sometimes try to explain what he thinks is going on."
As for how the students have responded to his new course, Rogers said they've surprised him and that it's gone better than he expected it to go. Although the class does read Euclid and two other books, there is no "textbook" for the course, in terms of a book that explains theorems and then presents a set of exercises for students to complete. "I know that in other courses that's how they do it all the time-in English they don't have exercises at the end of the books they read-but that's outside my training."
Even so, Rogers said the students have taken to the unorthodox approach and responded to the subject in a way they might not have in a traditional math course. "I've got great students, students who've struggled in other math courses, who are really catching onto this stuff and are interested, who like it, and who are able to achieve."