It'm quite surprised to find that "conatcting my teacher" with a Conversation message is not a very straightforward thing to do from the course context. From what I have observed, only by visiting the Inbox can a student intiate a message (email) to their teacher. Compare this to the multiple opportunities that a teacher has to contact students by Conversations (listed often as email).
I suggest that the course home page feature a permanent link/button (with the View Course Stream and View Course Calendar buttons) that intiates a Conversations email message to the teacher (or as suggested in Allow students to email 'All Teachers' -- all of them).
Places other than the course home where such a link/button would be useful? Grades. There could be others. Thanks!