Hi Joann,
When people refer to acting in the teaching context I believe they are referring to how a professional educator has to "act" as the class leader. That is it may be the tendency of a personality type to come into a setting and not talk much in a group. As the teacher this is not possible since as class leader you have to be prepared, organized and ready to offer the course content. So even though one's personality may be a bit on the shy side you have to develop a teaching style that will get you to put your personality out there in front of the students. You are right about being phony as an actor, that won't work for the students at all. So be yourself in the context of being a the class manager, model and motivator and you will do fine.
Gary