Although MIT students are good at math, there are ways they can be better, Professor of Mathematics Hartley Rogers Jr. told a gathering of science and math teachers at MIT last month.
He would like to see students who are better able to visualize in three dimensions. This skill is needed for multivariable calculus, he said.
Professor Rogers also wants to see students well-versed in logical arguments. "Teach them to reason," he said he hears from other departments that rely on those skills.
And finally, he said students should understand before they get to college that geometry is a model for how physical phenomena work, but it doesn't precisely reflect the real world. "If you're looking for counterparts of lines, circles and planes in the real world," you won't find them, he said. "Euclidean geometry is a different world, created by the human mind to understand what's true and not true."
He would like to see geometry taught in a way that emphasizes its three-dimensional nature, such as thinking about the relationships of planes, lines and points and picturing configurations of lines and planes in space.
On the other hand, he said today's math students are better prepared in fields such as probability than they were in the past.
A version of this article appeared in MIT Tech Talk on July 15, 1998.