This book is about a collaboration between two mathematics teachers. It offers a historical narrative of their joint research into what is involved in becoming a teacher of mathematics. This is a story of change and the process of change. Laurinda Brown and Alf Coles have collaborated for over 10 years, researching strategies for the teaching of mathematics. Their work is valued in both the research and teaching communities: …worldwide research projects in the development of teaching in mathematics education tend to encourage models of critically reflective practice …[t]his type of research is well illustrated by the work of Coles and Brown. (from Nickson, M. (2003) ‘A review of BSRLM research, 1995-2002’ (ed. J. Winter), British Society for Research into Learning Mathematics, Monograph Series: Number 1, Totton, Hampshire 2003). Laurinda Brownteaches at the University of Bristol, Graduate School of Education, having previously been a mathematics teacher and a curriculum developer. Alf Coles teaches at Kingsfield School, South Gloucestershire.He is also doing a part-time PhD at the University of Bristol, taking on the ideas of ‘listening’ that are detailed in the last chapter of this book.