Jane, I read Professor Blumenthal’s Pope Center article, and while I found the hostile tone rather off-putting, I’ll concede the possibility that his course may do what he says — discuss current mathematical research in a rigorous way that is intelligible and illuminating to non-specialists. He doesn’t make clear whether it’s a required course or an elective, but either way, if Blumenthal’s description of his own accomplishments is true, it’s quite impressive.
But there’s danger in generalizing from the success of one highly talented and motivated teacher with a novel method of instruction. Reading Blumenthal’s piece, I couldn’t help being reminded of Max Beberman and the New Math. As this article explains, in the late 1950s Beberman came up with an unconventional theory that elementary-school students should be taught about math, rather than being taught to do it (this was at least a decade before calculators became commonplace). By all accounts, Beberman himself was a wonderful and enthusiastic teacher, and the schoolchildren he taught learned to love the subject.
The problem was — as I learned as a student in the 1970s, though it was clear to others years before — that what worked for Beberman the evangelist was ineffective in the hands of less talented and motivated public-school time-servers. I and my grade-school classmates suffered through years of “open statements” and “solution sets” before finally reaching the promised land of middle-school algebra, where you could actually solve real-life problems instead of floating around in the ethereal plane all day long.
New Math crashed and burned pretty quickly, though it keeps coming back in new guises, such as the “fuzzy math” that my nephew recently suffered through (and don’t get me started on that). But I suppose that if we ever reach that orgastic future that my Phi Beta Cons colleagues look forward to, one good teacher will be all you need, and students around the world will be able to take Professor Blumenthal’s class. Still, I hope everyone will forgive me if I’m skeptical. Getting a general notion of how mathematicians think may be interesting or useful to a small fraction of students, but I think most of them would be better served by actually doing some math themselves.