Out-of-field teachers knowing, learning and doing mathematics

This thesis considers how out-of-field teachers of mathematics conceptualise knowing and learning mathematics and why they value doing it. Out-of-field teachers are those whose degree and professional qualifications are in subjects other than the one they are teaching. This thesis addresses the gap in the knowledge of how they conceptualise the subject they are teaching, paying particular attention to the complex work they undertake recontextualising knowledge as they cross boundaries. A two-dimensional framework was developed to analyse how out-of-field teachers conceptualise mathematics. The philosophical dimension considers how they know, learn and value doing mathematics, respectively their ontology, epistemology and axiology. Mathematics, defined as a discipline of patterns and connections used to model our complex world, is treated as heterogeneous, with four forms forming the second dimension (school, academic, everyday and pedagogical mathematics). The bricolage as methodology provides a critical complex perspective. Data was collected through semi-structured interviews, employing a range of tools, including images and mathematical objects. Data collection and analysis was designed to adopt an opportunity model, give the out-of-field teacher a voice and acknowledge the complexity of their work as they adapt flexibly to take advantage of their context.

Out-of-field teachers of mathematics participating in this study tended to conceptualise mathematics as school mathematics through the lens of learners. The boundaries where they recontextualised their knowledge were generally between school and pedagogical mathematics. Participants’ work was both complex and critical, privileging students above mathematics and blurring their own experiences as learners of school mathematics with that of their students.

The conceptual framework developed for this thesis provides a tool for researchers seeking to understand conceptualisations of out-of-field teachers of any subject. The findings of this study have implications for out-of-field teachers and school leaders in recognising the complexity of the work of out-of-field teachers and the opportunities offered for and by them.