A non-specialist teacher of mathematics is a school teacher who qualified to teach in a subject other than mathematics yet teaches mathematics to students in secondary school. There is an emerging interest internationally in this population, a brief report of which is given in the paper. Because of concerns about the quality of non-specialists' mathematics teaching, in-service courses for these teachers have been provided by some educational jurisdictions, including within the United Kingdom (UK). This paper reports on a research project based on designing and teaching such courses in London. The paper operationalises "Mathematics Teacher Identity" by adapting Wenger's (1998) social ecology of identity to give a framework of "Modes of Belonging" for a teacher of mathematics, which is then used to analyse qualitative data of different types. Analysis of the data identifies (1) aspects of non-specialists' mathematics teacher identity in terms of indicators and (2) through two case studies, "trajectories" towards development of a mathematics teacher identity.