AFTER EXTENSIVE PLANNING, I presented what should have been a masterpiece lesson. I worked several examples on the overhead projector, answered every student’s question in great detail, and explained the concept so clearly that surely my students understood. The next day, however, it became obvious that the students were totally confused. In my early years of teaching, this situation happened all too often. Even though observations by my principal clearly pointed out that I was very good at explaining mathematics to my students, knew my subject matter well, and really seemed to be a dedicated and caring teacher, something was wrong. My students were capable of learning much more than they displayed.
ALISON YIN/EDSOURCEIn data science classes, students write computer programs to help analyze large sets of data. High school math, and algebra, in