I found that the was a lot of "news" worthy stuff on Twitter related to topics that I teach and decided that incorporating Twitter into my classes might be a nice way to introduce students to wider classics networks, public reception of classics stuff, and promote continued dialogue on course related material outside of class. I've also found that using Twitter has made me more conscious of my writing. Cramming what you want to say into 140 characters and maintaining coherency and some semblance of nuance requires some real thought sometimes!
So I signed up for another Twitter account as @ProfChristensen, generated some hash tags for my spring 2012 courses, and away I went! Except my students didn't really follow. I had a small number of students who actively used Twitter already and they came along, I had a few more who had Twitter accounts, but hadn't used them in months, and they signed on too. But by and large my first experiment with Twitter was a not a resounding success. I have no doubt that it failed because I did not require all of my students to engage. I didn't and still don't want to incorporate Twitter into my graded assignment structure, so I don't really feel the need to make Twitter a course requirement at this point. This is not to say that Twitter can't work wonderfully inside and outside of the classroom and I've seen a number of examples of this (check out Prof Hacker for some examples like this one in a Shakespeare course).
I have not however given up on Twitter and the classroom. Instead this fall I am continuing to tweet class related tidbits and I have picked up a few followers. But I have also started collecting my tweets with Storify and have posted the links to these collections on my course web pages, so non-Tweeps can access them as well. So we'll see how it goes this semester!
If you want to see what I'm tweeting about feel free to check out my course hash tags on Twitter or the collected versions at Storify.com.
My ancient sports course tweets can be found with #CLCV2780
My classical myth tweets via #CLCV1550
My upper level Latin courses, in which we are reading Augustus' Res Gestae and Suetonius' Divus Augustus, get their tweets via #LATIN4610