Knowledge for teaching secondary school mathematics: what counts?

Abstract

This article discusses key issues surrounding the nature and development of professional knowledge for effective teaching of mathematics, especially at the secondary school level. In the education research community it is generally accepted that teachers need more than knowledge of the content they will teach; an additional construct, pedagogical content knowledge, has been proposed to describe the knowledge teachers need in order to make the content comprehensible to learners. Studies demonstrate that mathematical content knowledge (MCK) and pedagogical content knowledge (PCK) predict students’ mathematics achievement gains, and that PCK has the greater influence on achievement. However, the relationship between these two types of knowledge, and how their development might be influenced by studying university level mathematics, remains unclear. The article reports on an Australian study of the knowledge for teaching mathematics of prospective secondary school teachers, which found that MCK is a statistically significant predictor of PCK, and vice versa, although in each case only a small proportion of the variance in the outcome variable was explained. A higher level of prior mathematical experience was also associated with higher levels of MCK, but not PCK. These results suggest that although university level study of mathematics may be beneficial in developing secondary school MCK, it does not have a significant influence on PCK and is therefore inadequate, on its own, for preparing effective teachers of secondary school mathematics.