I don’t facebook at all. However in case you don’t know, you can have your settings such that the page is extremely bland. Seen many professionals whose pages are thus.
I'm fine with teachers taking an interest in students, being mentors, offering advice, etc. I just see Facebook as a bad and often counterproductive medium for doing that.
Curiously, kids are moving away from Facebook to smart phone share apps that are more immediate and more shallow.