Important ideas in mathematics: What are they and where do you get them?

In recent years, there has been greater attention in research and professional development work to discussion of the kinds of knowledge teachers need to teach effectively in the mathematics classroom. It seems reasonable that in planning at the school level, teaching team level and then specifically for a given lesson, teachers might have a sense of the most important mathematical ideas on which they wish to focus. In this article, we discuss written statements by teachers in surveys regarding the most important ideas on which they intended to focus in their next teaching topic. There was considerable variation in teachers capacity to articulate these important ideas. We discuss the implications of this for teacher professional learning and planning.