Writing for the Chronicle of Higher Education blog "Casting Out Nines," Robert Talbert discusses mathematical proof in light of how Guershon Harel and Larry Sowder frame it in a 1998 paper: "as a back-and-forth tension between certainty and uncertainty."
Talbert quotes Harel and Sowder, offers his own thoughts on teaching proof, and gives a "short list of what a professor teaching a transition-to-proof class has to accomplish."
This is no joke:
In such a course, students not only have to learn new mathematical content and proper professional writing standards but also come to grips with notions of doubt and certainty that are at the center of humanity itself.
Read the post.