Remember the frustration of holding up your hand, waiting to be called on? One of the great things about Twitter is that it allows for multiple strands of conversation to occur in real time. It can also be a fantastic forum for people who are still building confidence expressing themselves verbally and have ideas they feel more comfortable sharing in writing.
If your school doesn't have access to technology, you can create your own Twitter-style chat on a whiteboard or wall. Encourage your students to write their thoughts on the "Twitter wall" throughout the day, especially if they have a question that wasn't answered during lessons or discussions. This gives students a chance to get up, move around and express their voice. It allows several conversations to occur simultaneously. It gives you and your students a record of thoughts and questions that emerged. And it is practice for using social media in productive and responsible ways.