I actually started out teaching when I was in high school. Stuyvesant (High School) had a math team, and one of the responsibilities being the captain of the math team was to teach, every morning, five days a week, for an hour, to all the other people on the math team. So by age 14 or 15 I was teaching. When I was in college — actually when I was a senior in high school — I took a summer National Science Foundation Math Program, which was a wonderful program. I went back to teach in that for four summers after that, and that was a wonderful experience. I taught six days a week, six hours a day, for six weeks. When you teach like that, you can’t prepare lesson plans. You’ve got to know what you’re doing and go with the flow. I loved it, because the students were some of the best high school math students in the country, and you’d start off teaching a course on something, but halfway through the students would say, “We’d rather study something else.” In fact, we gave a problem set one night, and the students got so enthusiastic about it that at 11 o’clock, when they were all going home, they said, “Why don’t we instead make the course on this?” And they full well expected that tomorrow morning we would have the course switched over to that, and so we did. So in fact, by the time I got around to teaching as a professional, as a professor, I had had hundreds of hours of teaching under my belt, and I’m so grateful for that, because I think the experiences of teaching in those ways, teaching where you have to go with the flow, is something that young professors, young teachers, don’t get enough of. When I look at graduate students today, I find that they get a couple of hours TA-ing — teaching assistants — in a course. And how in the world can you learn the really complicated business of teaching without a tremendous amount of trial and error, and just experience?