TLRP: Repertoires of aspiration, narratives of identity, and cultural models of mathematics in practice, chapter 2.
In this chapter we will draw on work from our project, Opening doors to mathematically-demanding programmes in Higher Education 1 and in particular on four of the project’s recent papers (Black, Davis, Hernandez-Martinez, Pampaka, Wake, & Williams, under review; Hernandez-Martinez, Black, Williams, Davis, Pampaka, & Wake, 2008; Williams, 2007; Williams, Black, Hernandez-Martinez, Davis, Hutcheson, Nicholson, & Wake, 2007) to demonstrate three distinct methodological frameworks, based on ‘discursive psychology’, a narrative approach to identity, and cultural-historical activity theory (CHAT) respectively. The first two of these papers analysed interview data to gain insight into how different students formulate different aspirations and identities in regard to mathematics. The latter two increasingly draw on a broader set of case study data that includes observations of classrooms and interviews of observed students and their teachers, and indeed managers and principals in the colleges where the learners were studying. In addition to grounding these three methodological approaches in the project’s data, we aim to evaluate the adequacy of these approaches to understanding and explaining how identity is produced in practice. Although the substance of our results are of interest to mathematics educators, our main aim in this paper is to illustrate the different theoretical and methodological approaches and what they can offer researchers interested in identity. We finally will argue the need for discursive and narrative methodologies to be complemented by ethnographic-style case studies of social practice in order to produce ‘explanations’ of trajectories of identity. In particular, we argue that this requires a ‘boundary’ concept between the activity of doing mathematics (the mathematical practice) and the activity of storying one’s self (narrating a biography) and accounting for one’s aspirations. We show how we use ‘cultural models’ in this regard: indeed we show how cultural models arising from classroom mathematical practice can be instrumental in students’ accounting for their aspirations and in their narrative identity work. ISBN 978-90-8790-715-0 (paperback) ISBN 978-90-8790-716-7 (hardback) ISBN 978-90-8790-717-4 (e-book) Full chapter available on Sense url, listed above.