Twitter, Web 2.0 and education

Last night I read a comment on a blog ~ a teacher was wondering how Twitter could be used in an educational setting... perhaps you could open a single twitter account and share the details with your students. At random moments you could 'twitter' a challenging question and the students could 'twitter' their responses. You could provide rewards based on their responses including a prize for the first correct response. A tally of results could be kept for each of the following twitter challenge activitities. I wonder if this will work? I will give it a go.