One of my first essays ever (I've been writing these essays since the late 80's) was on the subject of analysis, sort of. I believe that self criticism (or analysis) and creative thought are opposite thoughts and cannot both be present in a person's mind at the same time. By their very nature, they oppose each other. I believe that you can't be creative and critical at the same time.
If this is true, when should you be witch?
After studying the subject of genius, I learned that most people achieve genius through an alternation between creative thought and critical thought. People who have manic depressive tendencies have this process built into their personalities, thus the common association between manic depression and genius (Beethoven being the most popular example).
So I have made an effort to switch modes at certain, key times. For example, performances REQUIRE complete creative thought with the absence of critical (analytical) thought. Practice time tends to need more critical thought than performance time, with two major exceptions. The first exception is that it takes a creative process to discover solutions to problems (the very problems discovered during the critical thoughts). The second exception is that it becomes important to practice being creative before you actually get to the performance. But aside from those two exceptions, practicing should be a primarily critical (analytical) process and I find that when I'm practising I shift between the two "modes of thought" at the times when that switch is most necessary.
In applying this to teaching, I see my responsibility as a teacher as being someone who encourages creative thought when it's necessary and critical thought when it's necessary. But I should say that criticism is one of the major responsibilities of a teacher. I believe that we go to teachers expecting them to know more about what we are doing than we do. And not only that, we rely on them to hear the things that we cannot hear from where we are. There are lots of things which we think we are doing right but need a teacher to point out our short comings, simply because we cannot hear them. But I should stress that a teacher who is ONLY critical can stifle a student, encouraging only that one kind of thought.
One more thing, I believe that teaching by example is one of the most important styles of teaching. And this doesn't only apply to the playing. What I mean is that the teacher is a role model when it comes to creativity and criticism. If the teacher is always critical, that will influence the student. The same is true for the other side, if the teacher is always creative, never critical, that will influence the student.
Eddie "Tiger" Lewis