This short video provides an example of how one teacher in Dallas has used Twitter to enhance her students leaning experience.
While there may be some initial hurdles to overcome, I see Twitter as providing students with a voice in the classroom, where previously they may not have had the confidence to express their confusion or differing perspective.
If a format can be provided that encourages the expression of thoughtful tweets, I can imagine Twitter harnessing the benefits of the Socratic Method, whereby students learn primarily from what they express, rather than what is 'poured in'.
Hopefully I will have a chance to put this into practice with a forthcoming project.