What Did Jenny Need to Know to Do What She Did? Pedagogical Content Knowledge for Mathematics in Action

Abstract

Building on Shulman’s (1986, 1987) construct of Pedagogical Content Knowledge (PCK), Ball and colleagues (Ball, Thames & Phelps, 2008) created a model of mathematical knowledge for teaching that differentiates between subject matter knowledge and PCK. The model categorises different types of knowledge within these two domains. In this research Ball et al.’s framework was used to code the knowledge used and connected by a teacher, Jenny, as she taught geometry to her class of 10-11-year-old students over six lessons. The categories of the framework were useful in classifying the knowledge Jenny used though specialised content knowledge was difficult to demark from common content knowledge. There was high connectivity between the Specialised Content Knowledge (SCK), Knowledge of Content and Students (KCS) and Knowledge of Content and Teaching (KCT) Jenny activates. Her responsive teaching style impacted on the nature of the knowledge she needed and on her learning about her students. The article demonstrates that the risk of categorising knowledge, and attempting to measure forms of it, may result in the neglect of the connective and transformative nature of how this knowledge is activated in action.