There are some excellent tools, such as http://www.tweetchat.com which you can use to set up Twitter in your classroom as a back channel communication. I prefer to use my Moodle page, however. Twitter + Moodle = Twoodle.
The reasons are purely practical, I don’t want to have to split screens, and I don’t have two data projectors on hand. If I am displaying the back channel chat on a screen, I cannot then also display course content. By placing a twitter feed discretely on my Moodle page, any back channel chat will automatically display directly onto the course Moodle page. In this way the back channel becomes a part of the ICT infrastructure of my classroom, and can continue operating even after the physical class is over. If students are using their Moodle page after school, the chat goes on!
Because I am an ICT Teacher and I teach in an IT Room and my students all have computers in front of them, I don’t have to worry about displaying tweets to the back row or anything like that. My students will usually be logged on to their Moodle page as they work, and will be able to send tweets and monitor replies as they work.
Another reason for preferring to have a Twitter feed permanently placed on my Moodle page is that, by editing the search settings in the feed, I can use the feed for different purposes, either following a certain keyword relating to the theme of the unit of work being studied, or a class hashtag, enabling a back channel in that class. the following video shows how you can set up a Twitter feed on Moodle, and how you can edit it.