Mathematical knowledge for teaching and the teaching of mathematics

This paper reports on a review of 12 empirical studies framed to address the problem of whether and in what ways mathematical knowledge for teaching influences teaching practice. From a larger review of literature on mathematical knowledge for teaching, this qualitative synthesis examines the theoretical foundations, methods applied and claims made. Most of the studies reviewed are small-scale qualitative studies. There is variability in the language to describe teaching and in how focused the studies are on teaching. We suggest that the tendency has been to focus on the question of the knowledge that teachers need, but that it would be more useful to focus on the mathematical entailments of doing teaching, which will require more detailed and shared conceptualizations of the mathematical work of teaching.