Twitter is a great device for teaching concise writing. Come on. Think about it. Say what you want to say using no more than one hundred forty characters. Characters not words. Even if you don't want to 'tweet' try writing something, anything, in a hundred forty characters or less. We are a quite verbose society. We don't say much nor do we have much to say generally but we take up a lot of space saying it. Twitter puts an end to all of that. Say what you have to say in as few characters (or okay words) as possible.
Give it a try.