How I Use It
I use twitter to communicate with students. I created an account @GPNphysics that the students follow. When they have homework or a project due I tweet that out (in addition to verbal and written reminders within the classroom). In addition, I tweet when I see something that is interesting about physics that I see outside of the classroom. As students see me do this, they start tweeting to me about things that they notice in their worlds about physics.
In addition to the classroom use, I have used Twitter to create my own Personal Learning Network (PLN) where I've connected to educators of all sorts all over the country. I read posts from people who's opinion I value (even when they are different from my own) and have learned so much from my PLN.
Lastly, I have used it to create a culture of connectedness within my PD - both the workshops that I attend and the workshops that I lead. Teachers can share their thoughts and see others thoughts (in real time). These are indexed and can be reviewed laster.
This is not a pedagogical tool. It is a way to create a classroom culture where the students are communicating with you and thinking about your class and content when they are outside of your classroom.
I love it. It has opened me up to a world of like minded educators and has enhanced the PD experiences within and outside of the district.
I follow teachers in my building who I don't have any other contact with and have gotten to know them through twitter.