Everyone probably knows Jordan Ellenberg's fabulous bestseller from a few years back, "How Not To Be Wrong." A few days ago at "Mathematical Enchantments" Jim Propp put up one of the odder math posts I've seen in quite awhile (and a bit longish, but nonetheless entertaining) entitled (taking off from Jordan), "How To Be Wrong." It has to do with the benefit of teachers, for the sake of teaching, making mistakes and facing them square-on... and, not being too dogmatic or pompous along the way; what he calls "the art of being wrong":
At one cogent point Propp writes:
"I stress to my students that the earlier you make your mistakes, the better. Every mistake you make in the classroom, or on your homework, is a mistake you probably won’t make on the exam, where mistakes can really hurt you. And, carrying this idea further: a mistake you make in college or graduate school is a mistake you’re less likely to make after you graduate, when you’re building bridges or designing cancer treatment protocols. So my answer to the question 'How to be wrong?' is: 'Early and often!'”By name or initials he brings a number of interesting folks into the post, as well as many interesting ideas/examples. I'm actually surprised there haven't been more responses in the comments section to the post, though maybe it is so odd that folks aren't sure just how to respond to it.
Anyway, check it out, especially if you're a math teacher.
Also, all of this emphasis on "mistakes" reminds me of an older Keith Devlin post on the importance of "failure":
It too, should NOT be missed, nor should the two commencement addresses Dr. Devlin links to at the end (Steve Jobs and J.K. Rowling). Great stuff!