Mathematical knowledge for teaching

Jason Silverman and Patrick W. Thompson have written an interesting article entitled Toward a framework for the development of mathematical knowledge for teaching. This article was published online in Journal of Mathematics Teacher Education on October 14. In the article, they draw upon the research that has been done in the area of Mathematical Knowledge for Teaching (MKT), and they try to navigate towards a framework for this. Silverman and Thompson present a framework that is "not only informed by the work of mathematics teaching, but also a developmental trajectory for mathematics learning and the learning sciences" (from their concluding comments).

Here is the abstract of their article:
Shulman (1986, 1987) coined the term pedagogical content knowledge (PCK) to address what at that time had become increasingly evident—that content knowledge itself was not sufficient for teachers to be successful. Throughout the past two decades, researchers within the field of mathematics teacher education have been expanding the notion of PCK and developing more fine-grained conceptualizations of this knowledge for teaching mathematics. One such conceptualization that shows promise is mathematical knowledge for teaching—mathematical knowledge that is specifically useful in teaching mathematics. While mathematical knowledge for teaching has started to gain attention as an important concept in the mathematics teacher education research community, there is limited understanding of what it is, how one might recognize it, and how it might develop in the minds of teachers. In this article, we propose a framework for studying the development of mathematical knowledge for teaching that is grounded in research in both mathematics education and the learning sciences.