A colleague and I recently planned a lesson on developing a need for factoring when solving quadratic equations. It was totally unexpected. He walked into my room after school and we started talking. Two hours later, we had the framework of a lesson.
Two teachers. Two hours. One lesson (sort of).
What struck me was that the bulk of the time was spent anticipating student responses to questions we wanted to ask during the course of the lesson. We went back and forth about the roles of the distributive and zero product properties and how students might interpret these ideas in context. How could we use their responses to bridge an understanding of solving linear equations to solving quadratic equations? We didn’t want to shape how they answered, but simply craft questions that would naturally guide them to worthwhile discussions and new understandings. Whatever question we toyed with throughout the two hours, it always came back to the same criteria.
How might the kids answer? How will their response draw them nearer to the goal? How can their thinking help the lesson tell a story?
Subconsciously, I think I do this. Just not enough. This experience connected well with the principles of my current book as well as providing me a nice reminder to plan the critical points of a lesson so that they pivot on student thinking.