Skeptic's Guide to the Universe had an interview with Professor Richard Wiseman of the University of Hertfordshire who had just used Twitter for an investigaiton of "remote viewing," a psychic theory that claims people can see something at a distance from the subject that would ordinarily be obscured by intervening distance or obstacle.
Since this is about Twitter in the classroom and not about the eighteen million Google returns you get if you use it as a search term, I will dismiss remote viewing and urge my reader to do the same.
Wiseman is using Twitter as a quiz engine for remote voting using handheld devices.
If this reminds you of the now ubiquitous "clicker" for embedded evaluation in the classroom, it should! What we need to do is take the twitter stream consisting of a question or series of teacher tweets and a series of student response tweets, parse it, evaluate it, and display it.