I think they think that zero point something is less than zero: Investigating pre-service teachers' responses to mathematical tasks

It is generally accepted in education research that effective teaching of mathematics requires a combination of content knowledge and pedagogical content knowledge. What is less evident, however, is the relationship between these two types of knowledge and the impact this has on the learner. This paper reports on an investigation into pre-service teachers' mathematical content knowledge and their ability to interpret students' responses to tasks 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 cohort of final year pre-service primary teachers. From this group, a selected sample were given a number of hypothetical student work samples and asked to analyse the mathematical thinking and make suggestions as to appropriate teaching approaches. The results indicated that a lack of mathematical content knowledge did impact on the pre-service teachers' ability to both recognise and address students' mathematical errors. This study adds to the limited field of research by providing evidence that the types of knowledge required for effective teaching of mathematics are inextricably linked, with mathematical content knowledge being particularly influential. Furthermore, the results showed that the participants were often unaware that they lacked this knowledge and the impact this had on their teaching practice.