I Know You Have to Put Down a Zero, But I'm Not Sure Why': Exploring the link between pre-service teachers' content and pedagogical content knowledge

This paper reports on an investigation into pre-service teachers' mathematical content knowledge and their ability to interpret students' responses to a multi-digit multiplication task and make subsequent appropriate teaching decisions. Using a combination of quantitative and qualitative methods, the researchers tested aspects of the mathematical knowledge held by a volunteer group of twenty final year preservice primary teachers. A volunteer sample of seven pre-service teachers were involved in a follow-up interview, where they were provided with hypothetical student work samples, including one using the long multiplication algorithm, and asked to analyse the student's mathematical thinking and make suggestions as to appropriate teaching approaches. The results indicated that the pre-service teachers in the study had an instrumental understanding of the long multiplication process that impacted on their ability to both recognise and address students' mathematical errors. This study provides an insight into the lack of content knowledge of a small sample of pre-service teachers with respect to multiplication of two and three digit numbers and subsequent lack of pedagogical content knowledge for teaching this topic.