Search

When designing lessons and units of study, teachers prepare problems that will make learning accessible, challenging, and targeted to goals. Experienced teachers often can predict classroom dialogue. This sense of déjà vu is even stronger when they teach the same course several times a day. The questions from the students are familiar and almost on cue. A lesson that goes as planned is incredibly satisfying for teachers. It reinforces the belief that they have thought of "everything" that might occur and that the students will be able to reach the learning goals that have been set. This article provides an account, however, of one instance in which the author's lesson took an unexpected turn. This departure strengthened the students' understanding of the true nature of mathematics.