Multiple meanings of mastery in mathematics education: a Q methodology study

This thesis investigates diversity in views teachers hold about mastery in mathematics. Mastery, in relation to teaching and learning of mathematics, remains poorly-defined and under-researched, yet mastery programmes attract generous government funding in England. This research employs a Q methodology to quantitatively evaluate the subjective opinions of 45 specialist mathematics teachers. Unlike conventional Q methodology research, which utilises a high degree of researcher-participant interaction within an interpretivist paradigm, this study collected anonymous data online and took a postpositivist position.

The findings identified a set of mastery pedagogies, which combine progressive educational aims with traditional educational practices, that could fulfil the aim of ‘all children achieving a deep understanding of mathematics’. Adopting this approach requires changes to mathematics teacher training and development, and the practices of school mathematics departments. This approach could address retention of mathematics in England which is currently of national concern.

The research revealed four distinct viewpoints, or factors, labelled ‘travel far, travel together’, ‘know your subject, follow the teacher’, ‘create a curriculum for interconnected understanding’ and ‘variety in teaching, learning and assessment’. A teacher’s view of mastery depends on their combined beliefs in student potential and how much a student’s learning journey should be explicitly crafted by the teacher. The teachers’ competence and confidence in mathematics, and their previous experiences in teaching and professional development were distinctly different across the factors.

This research realised the potential for Q methodology, which balances the rigour and precision of large-scale randomised controlled trials with the relevance and richness of smaller studies, to be utilised more in educational research, within and beyond mastery in mathematics.