<So if a master mathematician can maintain the perspective of what it feels like NOT to understand some mathematical concept, there's every reason to believe she will be an excellent mathematics teacher>
Mike - Interesting observation. I never really *liked* mathematics until I took geometry in high school. Geometry was so exciting to me - it was so obvious and so clear. Interestingly enough when I began teaching, I was a much better algebra teacher than geometry teacher. I had made every possible mistake an algebra student could make, so I could guide and prod and extend their learning. Geometry was much much harder for me to teach. It WAS intuitively obvious to me. It was difficult to step back and find some steps to help the students find their understanding. I think several have said it - you need both - an understanding of the content and an understanding of how to teach.
Please, please, please can we move on from the personal attacks now and concentrate on the focus of the forum.