"Although today's kids are 'writing more than ever before in history," it may not look like the writing of yesterday. The focus of today's writing is "more about instantaneous communication." It's also about audience.
Stanford University's Andrea Lunsford found that
(Haven)
Twitter allows students to connect with three important groups:
Experts
The Teacher
Peers
Sample assignments
Opinion sharing: The teacher asks for an opinion
Favorites: The teacher posts her favorite line from today's reading, asking students to do the same.
Content: Students post their thoughts on an assigned topic. The teacher responds.
Teachers can create an ambient scholarly buzz that will help students feel connected to class discussions and reading, as well as to the teacher herself.
Digitally breaking the ice
Phatic Communication
"Merely looking at a stranger's Twitter or Facebook feed isn't interesting, because it seems like blather. 
Follow it for a day, though, and it begins to feel like a short story;
follow it for  month, and it's a novel." 

-Clive Thompson
Phatic communication acts like a power grid
the lines are already set up, sometimes only transmitting a fraction of full capacity
when something happens, the grid is already set up
because the grid is there, substantive communication is possible quickly, complete with the phatically-established context.
Scholarly proprioception
Notes-sharing
peer review
questions about class
Sample assignments:
Students post arguments, thesis statements, etc., and comment on their peers' posts.
Students post a link to the full text of their paper, and peers (assigned a certain number to read) comment on their full drafts.
Students post examples of a literary device, writing style, etc. Comments required.
Students can find other students researching similar topics and collaborate.
Post and Comment
Links
Examples
Group work
It's like proprioception, your body's ability to know where your limbs are. That subliminal sense of orientation is crucial for coordination: It keeps you from accidentally bumping into objects, and it makes possible amazing feats of balance and dexterity. Twitter and other constant-contact media create social proprioception. They give a group of people a sense of itself, making possible weird, fascinating feats of coordination. (“Social Sixth Sense”)
Twitter is not just a service for prioritizing Twitter information, 
but a tool to organize the information of the entire Internet
Twitter brings to real-time the academic practice of citing sources and engaging in a conversation.
Sample assignments:
Comparison: Read two opinions. Tweet the better written opinion. Tweet the opinion you agree with.
Follow: Find Twitter streams of people who are interested in your issue. Follow them. Interact with them.
Feedback: Students tweet their thesis statements and ask for feedback from "the twittersphere."
Students see that their issues matter
Twitter is a series of digital road signs directing traffic to the most relevant information
Fred Wilson calls it "the power of the passed link" (Schonfeld).
to the outside world
Ethos
President Obama's huge success with the youth vote in the 2008 election suggests that following his example might teach us a thing or two about connecting with our students.
The Pedagogy of Twitter