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Johnson, K. A. (2011). The effect of Twitter posts on students’ perceptions of instructor credibility. Learning, Media and Technology, Vol 36(1): 21-38.

full text pdf

A small-scale study that shows an increase in students’ perceptions of instructor credibility (competence, trustworthiness & caring) as a function of self-disclosure on Twitter. Specifically there was evidence for an increase in ratings of credibility if the instructor used the microblogging platform to tweet about personal information.

Interestingly, there was no evidence of an effect between social-only tweets (greatest credibility of all) and a combination of social and instructional tweets, or instructional-only tweets and the combination of social and instructional tweets.

I like this explanation: 

No longer do teachers need to use class time to reveal bits of personal information about themselves: instead, this revelation of information can take place outside of class in a forum where students can choose whether to look at it.