There are hundreds of articles, chapters, and videos about breathing for singers. How about breathing for the teacher? Specifically, how about breathing while the teacher is listening to the student?
When I have observed Jeannette Lovetri teaching, I and those around me have always been aware of the peace that pervades the room. She is calm and relaxed, and therefore calming and relaxing for the student. In her pedagogy classes, she stresses this attitude as a skill that teachers need to develop.
I have been experimenting with this for the last year and a half. It is not easy at first. A student who is calm and singing well makes it easy. But a student who is struggling, with either singing or emotions, can encourage me to react with a rise of anxiety and tension, which can affect my breathing, posture, vocal demonstrations, and ability to listen productively.
Often I find myself breathing when my student breathes, as if I’m silently singing along (which I often am). I am more effective when I break the cycle, so I try to breathe in while the singer is singing out. It helps me to accept and hear the singing better. Then when I go into correction mode, I have more to say because I have heard more.
When I take the time to “breathe in” the singer’s sound, I hear more, talk less, and probably have something more productive to say. At least I am likely to say it in a more calm way. Just changing the speed and tone of the delivery makes a big difference. I can never know exactly how the singer reacts to this, but I know that this is what I prefer as a student, so it makes sense to pass it along.