OBSERVING SUBJECT KNOWLEDGE IN PRIMARY MATHEMATICS TEACHING

The mathematics subject matter knowledge of primary school teachers has in recent years become a high profile issue in the UK and beyond. This paper describes a videotape study of mathematics lessons prepared and conducted by trainee teachers. The aim was to identify ways in which their subject knowledge, or the lack of it, was evident in their teaching. We set out a framework which has emerged from the data, in which classroom events and episodes can be viewed as representative of one (or more) of four broad categories. CONTEXT The seminal work of Lee Shulman conceptualises the diversity of the knowledge required for teaching. His seven categories of teacher knowledge include three with an explicit focus on ‘content ’ knowledge: subject matter knowledge, pedagogical content knowledge and curricular knowledge. Shulman (1986) notes that the ways of discussing subject matter knowledge (SMK) will be different for different subject matter areas, but adds to his generic account Schwab’s (1978) notions of substantive knowledge (the key facts, concepts, principles and explanatory frameworks in a discipline) and syntactic knowledge (the nature of enquiry in the field, and how new knowledge is introduced and accepted in that community). For Shulman, pedagogical content knowledge (PCK) consists of “the ways of representing the subject which makes it comprehensible to others…[it] also includes an understanding of what makes the learning of specific topics easy or difficult … ” (Shulman, 1986, p. 9). PCK is particularly difficult to define and characterise, but seems essentially to conceptualise the hitherto missing link between knowing something for oneself and being able to enable others to know it. In 1998, the UK government specified for the first time a curriculum for Initial Teacher Training (ITT) in England (DfEE, 1998), setting out what was deemed to be the “knowledge and understanding of mathematics that trainees need in order to underpin effective teaching of mathematics at primary level”. There is now a growing body of research on prospective primary teachers ’ mathematics subject knowledge, which has undeniably been facilitated by the necessity of some process of audit and remediation within ITT (e.g. Rowland, Martyn, Barber and Heal, 2002; Goulding an