In theories of learning that adopt a situated stance to knowledge the notion of identity is vital; how learners position themselves in relation to, and are mutually positioned by, the situation within which they are learning will have a strong bearing on the learning outcomes. One of the challenges for learning mathematics in school is that learners position themselves, and are positioned, as pupils rather than as mathematicians. This paper focuses on discussion boards designed for secondary school mathematics students, and we use Wenger's (1998) model of communities of practice, building on earlier work by the authors (Back and Pratt 2007; Pratt and Kelly 2007) in which 'idealised communities' are constructed and used, to consider a case study of one participant who engages in developing his identity as a mathematician doing mathematics, as well his identity as a learner and a teacher of mathematics.

In this article, we address the methodological implications of analysing online discussion boards with a focus on participants' changing identities. More specifically, we propose the use of a Communities of Practice framework as a heuristic method for considering how participants' contributions to online discussion play a role in changing who they become, as opposed to what they learn. We argue that many analyses of online communication fail to take account of learning as a change in identity -what/who the learner is (becoming) -and focus mainly on the opportunity for cognitive development -what they know. In doing so, we use a single case study from a discussion board for secondary-aged students of mathematics which acts as a 'telling case' before demonstrating what this might say about other contexts for online learning. We argue that this has important implications for both research into, and the design of, online education.

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