The shortage of mathematics teachers in the UK has led to a number of government initiatives aiming to increase the supply of teachers of mathematics (e.g., DfE 2014). One set of initiatives concerns up-skilling teachers who are already employed at a school or college and who are teaching some mathematics, but who initially trained to teach in a subject other than mathematics. These non-specialist teachers of mathematics have come for in-service training at the university where they learn more mathematics relevant to the school curriculum. The participants in such courses expect to transfer their pedagogical knowledge from their initial specialism into the context of mathematics teaching as a result of developing their mathematical subject knowledge. We have run such courses for four years and this report draws on some of the data collected over this period. The particular finding that we report on here concerns participant aspiration and resistance. For instance, gaining certification at the end of the course that indicated their new specialism in mathematics teaching was a goal to which many of the teacher participants aspired, also reported in Crisan and Rodd (2011, 2014). However, some teacher participants resisted changing their conceptions about the teaching of mathematics; for instance, ‘understanding a topic’ was construed by some as an instrumental facility with a mathematical procedure sufficient to answer standard questions. We used many forms of data from the course participants: mathematical work, interviews, teaching observations, written narratives, and used a ‘communities of practice’ framework (Wenger 1998) for analysis of data. The issues of aspiration and resistance are considered in terms of the participants’ developing mathematics teacher identity in terms of ‘engagement, imagination and alignment’ or lack of it. Keywords: out of field teaching; communities of practice; identity; engagement

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