Making sense of fraction division: domain and representation knowledge of preservice elementary teachers on a fraction division task

The mathematical domain of fraction division continues to be an area of great difficulty for many teachers and preservice teachers (Lo and Luo, Journal for Mathematics Teacher Education 15:481-500, 2012; Newton, American Educational Research Journal 45:1080-1110, 2008; Rizvi and Lawson, International Education Journal 8(2):377-392, 2007; Young and Zientek, Investigations in Mathematics Learning 4(1):1-23, 2011). In this study, preservice teachers were given a fraction division task that sought to investigate their own personal approaches to solving a fraction division problem. Their results were contrasted with their ability to interpret student work on the same task. The purpose was to uncover information and gain greater insight into conceptualizations of fraction division they used and links or connections they made among verbal, diagrammatic, and algebraic representations as they solved the task themselves and then analyzed sample student solutions to the same task. Our findings have implications for future research and instruction on fraction division.