Sally says students need more than math ‘appreciation’

The definition of a derivative is a familiar concept in required Chicago mathematics courses for undergraduates.

Paul Sally Jr. says many U.S. college-level mathematics courses for nonmajors are “the equivalent of people taking English and reading classic comics.”

Sally, Professor in Mathematics and the College, delivered this message during an invited address Saturday, Jan. 18, at the Joint Mathematics Meetings of the American Mathematics Society and the Mathematical Association of America.

The trend toward teaching college students about mathematics rather than teaching them to actually do mathematics has led to growing numbers of college graduates who are numerically illiterate, Sally said. “There is almost no situation in life where you’re not going to need some quantitative literacy in order to achieve certain goals,” he said.

“This notion that one has to ‘interest’ students in mathematics in order to make them do it has gone much too far, to the point where real mathematics in many cases has just disappeared entirely from the courses. They’re just a discussion of what mathematics does and beautiful pictures and imprecise ideas.”

The University requires that its students take one mathematics course as part of its Core curriculum. “It’s a serious mathematics course,” he said. But the trend nationwide is toward less rigorous courses. As evidence, he points to a textbook originally published in the 1940s called What is Mathematics? Endorsed by Albert Einstein, it was written to explain mathematics to nonmathematicians.

“It is now regarded as much too hard for that purpose,” said Sally, who has little use for many of today’s mathematics texts. “Many of these books would be excellent for the living room coffee table but they have no place in a mathematics classroom,” he said.

Sally compared reading the books to watching the popular movie A Beautiful Mind, about Nobel Prize-winning mathematician John Nash. “There’s certainly no mathematics in the movie,” Sally said. “They mumbled a few words here and there. Certainly one has no idea what was in the mathematics that he did.”

The problem at the college level stems from a lack of preparation, Sally said. His recommended solution: more mathematicians working with school teachers to im-prove the quality of precollege instruction.

For his part, Sally was the first director of the University of Chicago School Mathematics Project and founder of the Seminars for Elementary Specialists and Mathematics Education program, and the Young Scholars Program for mathematically talented students.

Sally has repeatedly received honors for his educational outreach and classroom instruction. He has received the Haimo Award for Distinguished University Teaching of the Mathematical Association of America (2002), the Distinguished Service Award of the American Mathematical Society (2000), the Amoco Foundation Award for Long-Term Excellence in Undergraduate Teaching (1995), and the University’s Quantrell Award for Excellence in Undergraduate Teaching (1967).

Sally also has co-written a textbook with Diane Herrmann, Senior Lecturer in Mathematics, which will be published later this year. Its working title is Number, Shape and Symmetry. “We made no attempt to water it down,” Sally said.

In his talk, Sally presented examples of problems that lend themselves to quality instruction.

“You could start at very early levels, third or fourth grade, and build on them in such a way that they become serious problems even at the graduate research level. You just have to bring them along,” Sally said.