(2008) Journal of Teacher Education, v. 59, no. 5, 389-407
Deborah Loewenberg Ball
Mark Hoover Thames
University of Michigan
This article reports the authors’ efforts to develop a practice-based theory of content knowledge for teaching built on Shulman’s (1986) notion of pedagogical content knowledge. As the concept of pedagogical content knowledge caught on, it was in need of theoretical development, analytic clarification, and empirical testing. The purpose of the study was to investigate the nature of professionally oriented subject matter knowledge in mathematics by studying actual mathematics teaching and identifying mathematical knowledge for teaching based on analyses of the mathematical problems that arise in teaching. In conjunction, measures of mathematical knowledge for teaching were developed. These lines of research indicate at least two empirically discernible subdomains within pedagogical content knowledge (knowledge of content and students and knowledge of content and teaching) and an important subdomain of “pure” content knowledge unique to the work of teaching, specialized content knowledge, which is distinct from the common content knowledge needed by teachers and nonteachers alike. The article concludes with a discussion of the next steps needed to develop a useful theory of content knowledge for teaching.
Keywords: mathematics; teacher knowledge; pedagogical content knowledge
Deborah Ball and her colleagues have been working for some time to further explicate teachers' content knowledge for teaching, and have helped to shed some light on the often invoked but somewhat ethereal notion of pedagogical content knowledge (PCK; Shulman, 1986). In this piece, the authors state what I have come to understand through my work in this area over the past few years: "the filed has made little progress on Shulman's initial charge: to develop a coherent theoretical framework for content knowledge for teaching" (p. 394). Researchers often cite and implicitly agree (without explication) on the idea that teachers must have some "deep understanding" of their subject area that is unique to the teacher and not necessarily understood by the content area expert. But what that understanding looks like and how it relates to teachers' pedagogical knowledge is not well understood. "Instead of taking pedagogical content knowledge as given, however, we argue that there is a need to carefully map it and measure it" (p. 404). This is, in part, the aim of my work with the Flexible Application of Student-Centered Instruction (FASCI) survey.
The research program of Ball and her colleagues is focused on defining the nature of content knowledge for teaching in a methodologically precise manner (e.g. see work on the Mathematical Knowledge for Teaching (MKT) measures and associated validity arguments in the special issue of Measurement: Interdisciplinary Research and Perspectives, vol.5 issue 2-3, 2007). In defining two empirically discernible subdomains within PCK (knowledge of content and students, and knowledge of content and teaching), and the subdomain of content knowledge--common content knowledge--this work helps to map out what PCK is and how it could be more useful.
In the conclusion, a three-fold rationale is presented for this work: helping to discover which aspects of teacher knowledge are predictive of student achievement, how different approaches to teacher development have an effect of these aspects of teacher knowledge, and third, how a better definition of these knowledge constructs and sub-constructs may inform teacher education and professional development. The last of these is a particularly motivating factor for my own work in this area.