There are two questions relating to Twitter and education:
1. Should we teach students how to use Twitter?
2. Can Twitter be used in education?
Here I want to concentrate on the second, largely based on University level education in my own area of Computing.

Twitter is a micro-blogging site in which users can post messages of up to 140 characters, this character limit means that it would be difficult to deliver the equivalent to the traditional lecturer. It is hard to imagine explaining the syntax and semantics of a statement in a programming language in 140 characters. However I have seen and heard of Twitter having a use in a less formal context and these are things that seem to work in educational settings:

+ Back channel. Setting up a hash tag that matches a module/course code (for example we use #CS2TX6 for our Business Programming) gives students and staff a chance to share opinions, questions, responses via tweets. Getting a hash tag that doesn't clash with other institutions would be more problematic if modules/courses use common codes like C101 - in which case it would need to be combined with something identifying the institution.

+ Feeds. We feed tweets from willing people into our school's social media site (RedGloo) this allows anyone to get a flavour of what goes on in Twitter. We use the tag #norg (no RedGloo) which stops a tweet appearing, so that tweeeters can control what is seen.

+ Lists. Lists are a great way of bringing together people with shared interests, so a list of all known twitters in a university can help in introductions, we have a list of University of Reading people. Lists can also help in creating links between students and graduates/potential employers.

+ Mentions. Seeing who people you respect follow, mention, recommend is a way many twitters build their networks and it certainly works in educational settings. I've often noticed that people within a circle start following someone who is mentioned in a relevant tweet.

The number of people who actively tweet in an academic community is small, less than 10% in my school. But those who do have seen benefits, which include:
+ answers to quick questions
+ help with bigger problems
+ bringing students to the attention of employers
+ brokering sub-projects
+ getting students involved with research projects

And one student told me the other day Twitter had saved her degree.

So while twittering isn't for everyone, if you are part of a real academic community but feel you aren't getting enough out of it you may find that there are other people tweeting about things that interest you near you.