My first real teaching was in the army where, as a twenty one year old lieutenant in the artillery, I needed to teach my charges — mostly Puerto Rican high school drop-outs who were as old or older than I was– how to prepare howitzers to fire at objects which were miles away. It was an important and practical form of geometry, a subject at which I had not been very successful in school. By now I was good at it, but I feared that learning would be too difficult for them, and then we would all fail. I learned then that most teachers need to learn before they can teach. They have to learn about their students, and especially about what is relevant to them. My students were determined not to hit the wrong target; they struggled with the guns’ sights’ calibrations until they got them right. They took care of the ammunition so that it wouldn’t grow too wet or too dry. They followed all the safety precautions as if they had written the manual themselves. Where they came from, what learning difficulties they had, how different their childhoods had been from mine, even what language they spoke