This paper draws on the biographical narratives of two mathematics teachers who describe themselves as 'traditional' and 'connectionist' teachers respectively. Holland et al.'s amalgam of Bourdieu, Vygotsky and Bakhtin, including 'figured worlds', 'positionality', 'self-authoring', and 'world-making' is used to examine these narratives. Differences between the two narratives include (i) their histories of compliant or oppositional identities as learners, and subsequently as teachers; (ii) their different experiences of 'understanding' and 'tricks', and (iii) their different use of figures as role models or anti-heroes in their self-authoring as teachers. It is argued that these narratives might 'make worlds' and provide future teachers in turn with figures for their own professional identity work. © 2011 British Society for Research into Learning Mathematics.