Investigating the different dimensions of preservice mathematics teachers’ understanding – the case of factorisation

This paper reports on a study designed to investigate preservice teachers’ understanding of factorisation, a topic not explicitly taught within their teacher education programme, but one they will be required to teach when they graduate. We query if the knowledge they bring from secondary school, prepares them sufficiently to teach their future students for understanding. 83 preservice secondary school mathematics teachers’ procedural and conceptual understanding of quadratic factorisation were assessed using Usiskin’s Framework for understanding mathematics (2012) which identifies several dimensions of understanding. The study provides evidence that the preservice mathematics teachers have a strong procedural understanding, and while some conceptual understanding does exist, there was very limited conceptual understanding within most of the dimensions of the framework (Usiskin, 2012). We conclude the paper by considering how teacher educators can address the issues of preservice teacher knowledge and understanding of content not formally covered within their teacher education programmes.