Preservice Teachers’ Pedagogical Content Knowledge: Instructional Explanations

Abstract

Many research studies have documented that the mathematical understanding preservice teachers bring from schooling and university mathematics courses was inadequate for teaching primary school mathematics (Even, 1993; Tirosh, 2000). In these studies, while preservice teachers generally knew how to carry out a procedure, they could not produce mathematical explanations for the underlying meaning. To become a mathematics teacher, preservice teachers need to develop profound subject matter knowledge, pedagogical content knowledge and knowledge of students‟ cognition (Shulman, 1986; Ball, 1990a; Ma, 1999). These three types of knowledge should be considered as parts of a larger system on which teacher relies on as they plan and implement instruction (Verschafel, Janssens, and Janssens, 2005). Pedagogical content knowledge, which depends on subject matter knowledge (McDiarmid, Ball, and Anderson, 1989), consists of knowledge of ways of representing and explaining mathematics to make it understandable, and knowledge of students‟ cognition. Knowledge of representation and knowledge of students‟ mathematical thinking are two main components of this knowledge type. The purpose of this study was to investigate the nature of explanations they provide for mathematical situations and the knowledge of these mathematical situations.