If not for educational purpose, communication between students and teachers via social media is not a good idea because of two reasons:
First, personal conversation between a teacher and a student is uncalled for -- unless the teacher also acts as a guidance counselor, which is unlikely. Besides, personal conversation is kept in private cubicles in guidance centers.
Second, teachers and students need privacy. Students, and perhaps some teachers, normally go to the social media to "be social" by disclosing 'hidden' aspects of their lives and personalities. When teachers are given access to students' "personal sides" and when students get to step on the imaginary boundary that separates teachers from them through the social media, more personal relationships could possibly develop. And that could later result in the blurring of identities, in which teachers could lose its status as being "teachers" who are seen more on a professional level, not on personal side.
In one way or another, a more personal conversation could lead to some sort of "information leak", e.g. how teachers evaluate student performance, how students perceive their teachers' capability, how other teachers teach, how they both perceive the dean's leadership, etc. Social media is for "social" networking, and part of it is personal disclosure which seems inappropriate and unnecessary in any teacher-student relationship.
I taught in a university for over 11 years, and I did not attempt to accept any Facebook invitation from any of my students because of these reasons I cited; when I left the academe and went to the social media industry, most of my former students became my friends in FB... :-)
Great article, thanks for sharing!