Learning through teaching: factors influencing teachers' mathematics knowledge

Understanding mathematics teacher knowledge is an international endeavour, seen by researchers as a key part of improving pupil learning. Within the last few decades, several conceptions of teacher knowledge have been proposed within the literature including Mathematical Knowledge for
Teaching (Ball and colleagues) and the Knowledge Quartet (Rowland and colleagues). However, multiple criticisms of these conceptions exist, prompting the introduction of a new approach to considering teacher knowledge within this thesis. Rather than seeking to categorise a knowledge unique to teaching different than the mathematical knowledge required for other professions, this research aims to examine how knowledge changes within the context of trainee secondary teachers in England. The poor mathematics results of school leavers in the UK as well as a shortage of
mathematics teachers, has influenced government policies on teacher training. Bursaries differentiated by degree class and the introduction of government-sponsored ‘subject knowledge enhancement’ (SKE) courses (to graduates from numerate disciplines) attempt to increase the quality and
supply of teachers. By examining how knowledge changes over a teacher training course, with emphasis on the divide between SKE and non-SKE course participants, it is proposed that further insights into the knowledge useful for teaching and how this knowledge needs to be organised can be
gleaned. This mixed methods study employs questionnaires, interviews and observations to track the knowledge change of a sample of Postgraduate Certificate in Education (PGCE) students over their year-long course.
Results of the current study suggest that changes in the quality rather than quantity of knowledge take place over a PGCE course, in other words, a change in the organisation of knowledge. In addressing the research questions, this study also: raises questions about what the Mathematical
Knowledge for Teaching items measure; suggests potential changes to the Knowledge Quartet codes; evaluates the proposed alternative approach to knowledge; and, discusses implications for teacher training policy.