Asking good questions remains a challenge for all of us. In our professional development sessions and while visiting teachers in their classrooms, this is a major focus of our work.
Developing pedagogy based on questioning is a real challenge for teachers. In our professional development sessions, as teachers are working on a particular math problem in small groups, we begin by sitting down with them and asking questions to hear what they are thinking and how they are approaching the problem. We model this as a major strategy for getting at the mathematics of a lesson. Later, during a discussion of teaching strategies, we have a direct discussion about how teachers see the role of questioning in their classes. When we visit the teachers' classes we model this same type of questioning in our interactions with students. Our goal is for teachers to be able to distinguish between questions that expect a certain answer and those that are intended to further mathematical discourse.
Once teachers begin to develop an awareness of the effectiveness of questioning in supporting students' learning and understanding of mathematics, they want to know how to develop the skill of asking appropriate questions. Different questions are necessary for different students depending on how they are looking at a particular problem. This skill is essential in heterogeneous classes where great variations exist in students' mathematical understanding.