A few thoughts on ignorance and exploration in teaching
Unless something like this ignorance-awareness-honesty happens in the classroom, one's teaching will not allow the teacher himself to learn from his own ignorance and from the responses of his students. Exploration means meeting the unknown with what one knows (or thinks one knows). One of the most thrilling things I experience in the classroom is when new ideas emerge in my mind in real time through the act of teaching. It must be akin to the joy a great jazz improviser (such as Sonny Rollins) feels when he finds open sky and ascends accordingly.
The kind of ignorance I am considering is not that of being ill-prepared for class; rather, it pertains to how a well-educated and well-prepared pedagogue comports himself in light of what he does not know. That sort of ignorance is nothing to be ashamed of and nothing to hide.