Suggests that strategy choice is a misleading characterization of efficient mental calculation and that teaching mental calculation methods as a whole is not conducive to flexibility. Proposes an alternative in which calculation is thought of as an interaction between noticing and knowledge. Presents an associated teaching approach to promote…

In this paper, I explore two beliefs about learning and teaching that I argue are prevalent among educators. The first is the belief that subject matter expertise is sufficient for success in teaching. The second belief is that to learn a specific content area, one needs to begin with an understanding of the formal structure and abstract…