Probing teachers' pedagogical content knowledge: lessons from the case of the subtraction algorithm

In this paper we present a framework for investigating teachers? mathematical pedagogical content knowledge (PCK). The components of the framework permit identification of strengths and weaknesses in the PCK held by various teachers on different topics. It was applied to teachers? written and interview responses addressing a student?s difficulties with the standard subtraction algorithm. This enabled comparison of the PCK held by individual teachers, together with analysis of the teachers? PCK as a group. Most understood the issues and knew suitable representations, but occasionally lacked key understanding of students? misconceptions and how to help students recognise them.