I just came across this article from the New York Times and thought it was rather good. I’m including the Diigo annotated link rather than the original link, because I thought that some of the other user comments from teachers were quite good, too: http://diigo.com/09xux. Click the speech bubble icons near the highlighted text scattered throughout the article to view these comments.
I like the story (p. 6-7) about the elementary student who started a debate over odd and even numbers, suggesting that a number can be both. Rather than immediately correcting the misunderstanding, the teacher allowed the students to discuss this basic of math for themselves, devise their own definition of “even and odd” through experimenting with adding different types of numbers, and reach their own conclusions. The end result was an improvised spontaneous lesson the students directed themselves.
References
Green, E. (2010, March 7). Building a better teacher. The New York Times. Retrieved from http://www.nytimes.com/2010/03/07/magazine/07Teachers-t.html