Teacher practice in primary mathematics classrooms: A story of positioning
The past twenty-five years have seen a dramatic increase in the interest given to dialogue between teachers and students, and students and students during mathematics teaching and learning. This interest is evident within the growing body of research and the call for the increased quality and quantity of student discourse in curriculum and policy documents. Recent research in mathematics education is underpinned by the belief that students learn best when they have the opportunity to participate in their own and others’ mathematical talk, text, and actions in purposeful and meaningful ways. This study explores how teachers position themselves and students in their lowest and highest mathematics strategy groups and how that positioning influences the sharing of mathematical know-how. Mathematical know-how within this study comprises teacher and student independence, judgement, and creativity. Social-constructivist theories of teaching and learning underpin the focus of this study. The importance of teachers and students constructing and co-constructing individual and shared mathematical understandings through dialogically rich interactions with each other and the environment are considered. Positioning theory provides the theoretical lens through which mathematical know-how will be analysed and understood. The constructs of positioning theory important to this research were the teachers’ and students’ positions, enacted as their rights and duties, the storylines that develop through the positions, rights, and duties and the teachers’ and students’ social acts which come to have significance and be a social force within the teaching and learning. The decision to employ qualitative case study methodology arose naturally from the subjective social phenomenon of teaching and learning. The analysis of data generated through video and audio recordings, transcriptions, participant observations, and documents and archival records supported the development of the two cases: teacher affording positioning, and teacher constraining positioning. The particularised and investigative design of qualitative case study supported the development of an emerging taxonomy of teacher affording and constraining positioning. The taxonomy contributed to the growing body of knowledge regarding student participation by categorising new thinking in regards to the phenomenon of teachers and positioning in mathematics. Teachers in this study afforded the sharing of mathematical know-how from the position of appropriator, procurer, and provoker. The positions of controller, proprietor, and protector were found to constrain the sharing of mathematical know-how. Significant differences were revealed in how teachers positioned themselves and how their positioning influenced opportunities for student engagement. Higher levels of student talk, text, and actions were evident when teachers positioned themselves to ensure the mathematics was visible, fluid, and contestable. Collaboration between teachers and students, and students and students, was a strong feature of the emerging taxonomy.