Pre-service Teachers’ Explanations of Two Mathematical Concepts

There has been growing interest in the role played in mathematics teaching by teachers’ pedagogical content knowledge. This form of teacher knowledge goes beyond mastery of the subject to incorporate how subject matter is actually used in teaching. In particular, it includes knowledge of how to explain concepts and what models can be used to facilitate students’ understanding. In this study two items were used to investigate aspects of teachers’ mathematical pedagogical content knowledge. Pre-service primary and secondary mathematics teachers were asked to give written reasons to (a) justify the procedure of “adding a zero” onto the end of a whole number when multiplying by 10, and (b) explain the equivalence of 3/8 and 37.5%. Both cohorts of pre-service teachers found the first task difficult, with many struggling to find appropriate language for their explanations. For the second task there was a variety of successful strategies and models, with the pre-service primary teachers having a greater range of pictorial models and the pre-service secondary teachers having more computational strategies. The implications of these results for the preparation of both primary and secondary mathematics teachers will be discussed.