‘Ours is not to reason why, just invert and multiply’: an insight into Irish prospective secondary teachers’ conceptual understanding of the division of fractions

This paper reports on an investigation into the conceptual knowledge, through the domain of fraction division, of prospective secondary mathematics teachers in their final/fourth year of undergraduate initial teacher education. The aim of the study is to assess if levels of conceptual knowledge in this domain are sufficient in order for these prospective teachers to teach for understanding. Some impact of conceptual understanding on teaching approaches is also explored. The content of the teacher education program and its suitability for preparing prospective mathematics teachers is also considered. The results indicate that in spite of four years of mathematics teacher education, these prospective mathematics teachers hold a fragmented and limited conceptual understanding of dividing fractions. To address this issue and to ensure the effective implementation of Project Maths, it is argued that initial teacher education programs need to be revised to include an emphasis on school mathematics.