Beliefs and practices of secondary teachers crossing subject boundaries to teach mathematics out-of-field

Out-of-field teaching of mathematics is a reality in many secondary schools in the world. The incidence of out-of-field teaching generally occurs in low socio-economic communities and, in Australia, in schools located in rural and remote locations. The theory of boundary crossing enables positive perspectives of teaching out-of-field to be explored. In this paper, we explore changes in out-of-field mathematics teachers' beliefs and practices about teaching mathematics over 3 years and the way in which their in-field teaching influenced and was influenced by their out-of-field mathematics teaching. Out-of-field teachers from schools in three Australian states participated in the study. The findings show that initially the majority of these teachers held instrumentalist beliefs about the mathematics discipline and its teaching and learning. Those who continued to teach mathematics out-of-field beyond the first year of the study presented evidence of some shifts in their beliefs about the teaching and learning of mathematics by including more student-centred or problem-solving approaches. Exploring the factors that enable continuity of discourse across subject boundaries is important not only for supporting and retaining teachers of mathematics in schools with a high incidence of out-of-field teaching but also for fostering interdisciplinary approaches to teaching and learning.