The columnist notes that higher education loses something by leaving the introductory classes in the hands of relatively inexperienced people.
As much as [Williams mathematician Edward Burger] finds math fascinating, he realizes that most people will not use calculus after college. The utilitarian promise "is an empty one," he notes. "You don't need to know how to build a bridge to go over one." He says that the hardest thing professors can ask themselves is "the 10-year question." "What will my students retain from my class 10 years out?" And so his lecture is devoted to showing the audience how to "think mathematically."
Prof. Burger, who acknowledges being one of the tougher graders on campus—"I don't give grades; I just report the news"—says that he is only convinced a student understands a concept when he can "explain it to an 8-year-old." I wouldn't put it past him to bring a fourth-grader to class for that purpose, but he says he just forces students to explain concepts without using jargon.
In an ideal world, senior professors, who have the most experience teaching, would be forced to teach freshman survey courses. Instead, professors at many universities are told by their mentors not to focus on teaching at all. And the joke on many campuses is that the winner of a school's teaching award is guaranteed to be denied tenure.It takes a long time to develop the ability to distinguish a profound, but ill-formed question, from a clueless question, and to be able to answer both tactfully.
Go, read and understand all of it.