The field of mathematics teacher education is researched extensively from diverse perspectives and using multiple theories to better understand the processes involved in becoming a teacher. This includes research concerned with identity constructions in becoming a mathematics teacher (Brown & McNamara, 2011; Williams, 2011) as well as research focusing on the theory-practice transitions of student teachers (Jaworski & Gellert, 2003). Recently, the field of mathematics teacher education has been paying close attention to the specific aspect of teacher education programs known as the school practicum or field experience.  The research discussed in this presentation is a self-study of my practice as a faculty supervisor for secondary mathematics student teachers during their four-month school field placement. In studying my practice, I draw on a blend of self-study methodology, the conceptual tools of Bourdieu’s sociological theory, and a mathematics graph theory network analogy to unpack the structures of the field and my role within that field.  The overall purpose of the research study is to explore how the network of relations in (the field of) field experience shapes me as a supervisor and as a mathematics teacher educator, including how my own habitus and identity is being (re)produced. In this overview of my proposed presentation, I not only introduce my research in the field of teacher education, but also the key components of a new theory-methodology conceptualization.

In my university's four-month field experience (internship), each student teacher (intern) is paired with a cooperating (mentor) teacher in a school and assigned a university faculty supervisor. Typically, my supervisory role positions me in the back of a high school classroom, observing an intern’s mathematics lesson from start to finish, taking notes on field experience observation forms. This note-taking task is preceded and followed by brief pre- and post-conferences with the intern. Research indicates this is a common portrayal of supervision in teacher education programs (Britzman, 2009) and that the model is problematic and deficient for a number of reasons, not the least of which is how superfluous, even token, the role of the university supervisor is. In essence, my research seeks to understand how I might move beyond tokenism in the field, thus contributing to knowledge about transitions in the field of teacher education and field experience. I do this by designing and studying a new internship model that includes a digitally-enhanced learning community approach. While data from this new internship research study is important for this presentation, the deeper purpose lies in discussing the research data in the context of a newly proposed theory-methodology-analysis conceptualization. That is, in this presentation, I trace the evolution of a new tool for educational research: a form of discourse analysis shaped by conceptual tools from both sociology (Bourdieu’s social field theory) and mathematics (graph theory) and applied, in this case, to my self-study research as a faculty supervisor and mathematics teacher educator. I refer to this new analytical tool (or framework) as Bourdieu-informed discourse analysis (BIDA) for self-study. 

While the research study is conducted in a Canadian context, the applications of this novel analytical tool are by no means confined to that specific context. In fact, the combinations of conceptual tools being introduced in this work are highly relevant to the European teacher education context and, in fact, even beyond the field of teacher education. Its applicability in the European context is confirmed by the fact that an expanded version of this research will be published as a chapter in a forthcoming book edited by M. Murphy & C. Costa (entitled, Theoryas method in research: On Bourdieu, social theory and education).

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