My reaction to my limited trial of twitter:
In education, Twitter communication would work great in a department or team situation where you have an established circle of people that want to be in touch but may not have time for face-to-face. I can imagine a teacher writing “Science water lab from the kit did not work. Who has had success with it?” or “In writing, used a fishbone graphic organizer helped students to see cause and effect. Worked well” Short nuggets of success or concerns.
I see Twitter as disjointed as early email non-threaded conversations were. As times I feel like I standing in the middle of a busy intersection watching the cars go by. They are going in every direction (from serious to silly). So far, I have not find a car that is worth the time of following.