Primary teachers' representations of division: Assessing mathematical knowledge that has pedagogical potential

This article reports on a study that was conducted with 378 primary teachers from Catholic schools in Victoria who participated in the first year of a 2-year research and professional learning program in mathematics. One aim of the program was to enhance teacher knowledge in mathematics in its many forms. As part of the larger study, the teachers were assessed at the beginning and the end of school year (February and October, respectively) on their Mathematical Knowledge for Teaching (MKT), through the use of a questionnaire involving teachers’ responses to hypothetical teaching, planning, or assessment scenarios. We report here the results from one item that assessed teachers’ MKT in relation to representations of division. Results indicated that teachers were more familiar with partitive than quotitive division, and found connecting appropriate story problems with a given form of division difficult. Teachers’ relating their understanding of the forms of division to the context of division by a decimal number was also challenging. There were interesting variations in the data across primary grade levels, particularly in relation to change over time. Professional learning on these topics and other support within the project appeared to improve teachers’ MKT in this area.