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Abstract As with many mathematics teacher educators, I purposefully set about challenging the curriculum and pedagogical status-quo; I wanted my Bachelor of Education pre-service teachers (PSTs) to experience learning and teaching mathematics in a connected and powerful way. I initiated was Roundtable Reflective Inquiry (RRI) sessions as one key practice that enabled PSTs to reflect on their mathematics teaching experience in an ongoing, structured manner. PSTs generated discussions based on critical events and interactions, and my aim was for PSTs to learn through their own experience rather than mine. My role was to facilitate, synthesise and challenge (often) firmly held assumptions. However, as this chapter will reveal, an often unexpected outcome of pre-service teacher education is teacher educator enrichment, knowledge and transformation. While my intention, and indeed the initial focus of my self-study was to enhance PST learning and teaching in mathematics, it soon became evident that I was learning as a teacher educator and my new approach was contributing to my own pedagogical development as a teacher educator. Learning in mathematics teacher education is about coming to know and self-study enabled me as teacher educator researcher to notice, to challenge my assumptions and to name new knowledge. [ABSTRACT FROM AUTHOR]

The discussion in this final chapter focuses on a key imperative associated with self-study of teacher education practices: that of moving from personal, contextual and localised learning about the development of teacher educator pedagogy, to one which considers possible implications and recommendations for a broader educational/ professional context. As such, this chapter represents possibilities for ways forward in teacher education. These possibilities have arisen from the close scrutiny and critical reflection of, and in my practice as, a mathematics teacher educator. I begin this chapter with a discussion of the key areas of connection to learning about teaching and conclude with six recommendations which emerged as a result of my self-study. [ABSTRACT FROM AUTHOR]

Learning through self-study is the focus for the discussion within this chapter as it captures for me the salient aspects of ‘coming to know' as a teacher educator. Identifying and challenging taken-for-granted assumptions about teaching and learning provided a lens for me to examine my practice. This chapter reveals the ways in which exploring assumptions has contributed to the development of my pedagogy as a teacher educator. [ABSTRACT FROM AUTHOR]

This chapter explores issues of authority and power. I have presented my learning in four sections. The first section highlights and examines a pivotal interaction that occurred early in the study which raised issues associated with negotiation, power and authority of experience. The second section is my retrospective analysis of talk during RR sessions and attempts to clarify more about the connection between talk and the development of pre-service teacher authority of experience. The third section I discuss relates to teacher educator talk and examines my talk over time, and establishes the challenges for me in deciphering the intended from the actual in terms of my practice. The final section of my discussion summarises my learning and what it means for me to hold the assumption that pre-service teachers and their teacher educator can be reconceptualised as co-learners. In my introduction I refer to my initial attempts to negotiate the LTM unit with a cohort of pre-service teachers. I begin by describing a critical interaction which provided the stimulus for researching the ways in which power and authority were being interpreted, constructed and understood by both the pre-service teachers and me, through the vehicle of unit negotiation. [ABSTRACT FROM AUTHOR]

This chapter examines a third assumption which reflects my belief that pre-service teachers who contributed verbally to the reflective discourse would be maximising their learning opportunities. This third assumption frames the analysis in this chapter. The process of examining this assumption began with my recognition of, and curiosity about, the role of dominant voices during Roundtable Reflection sessions. I begin with a brief summary of the literature related to the ways in which silence has been conceptualised in teacher education. This is followed by an examination of the theme of silence as it emerged in my practice and the ways in which silence was recognised, experienced and interpreted by the pre-service teachers/teacher educator. The examination of silence and of that which remains unsaid explicates more about the (re)construction of self as a teacher educator and raises questions about how an increased awareness of silence can influence our awareness of all learners and contribute to new ways of being a teacher educator. [ABSTRACT FROM AUTHOR]

This chapter explores my assumption that the practice of Roundtable Reflection would not only provide structured opportunities for pre-service teachers to share their teaching experiences, but also challenge their taken-for-granted beliefs about learning and teaching mathematics. I begin this chapter with a brief overview of the literature related to the examination of voice in pre-service teacher education. [ABSTRACT FROM AUTHOR]

This chapter explores our learning about teaching through reflection. My discussion is framed around my assumption that through the integration of multiple reflective practices in the Learning and Teaching Mathematics units, pre-service teachers would be encouraged to reflect critically on their learning. Reflective practices included an introduction to multiple reflective tools (the ALACT cycle of reflection, Freewrites and Critical Incident Questionnaires) and I discuss why and how reflective tools were introduced and utilised; what we learnt from their implementation and examine the ways in which my initial assumption was supported and/or challenged. I begin this chapter with a brief review of the literature relating to the impact of reflective practice in teacher education programs and the ability (or inability) of programs to succeed in the development of critical reflection, in particular. [ABSTRACT FROM AUTHOR]

In this chapter I describe the ways in which I structured, organised and analysed my data. I illustrate the ways in which I designed specific data gathering tools as a matter of need in order to more deeply understand aspects of practice (for example, my development of the multiple perspectives tasks which were designed as a tool through which I gained a deeper understanding of the multiple perspectives on particular roundtable interactions). [ABSTRACT FROM AUTHOR]

Self-study is an approach to research which enables teacher educators (and other professionals) to reflect on, and scrutinise practice and assumptions about learning, so as to improve pedagogy and to challenge the status-quo within the profession. Underpinning all of this is the intention to further explore deeper understandings of the why of practice (Feldman, 2002). However, as with notions of reflection and reflective practice, defining the nature of self-study research remains complex and "open to individual interpretation" (Schuck, 2002, p. 327). Self-study is defined in multiple ways: as a process to research teacher educator practice and pre-service teachers' perspectives from the"inside" (Hamilton & Pinnegar, 1998); as a distinct and unique methodology employed by teacher educators to research practice (Hamilton & Pinnegar, 1998); and as systematic and rigorous inquiry into practice, often instigated by a problem, which then leads to the theorising of practice and a deeper understanding of the why of teaching and learning about teaching and learning (Loughran, 2003; Tidwell & Fitzgerald, 2004). Self-study may involve study of an individual, a program or an institution but common to all studies is a challenging of the status-quo in teacher education through rigorous and systematic inquiry into professional practice. A further requirement of self-study is dissemination of research outcomes to the educational community for critique and appraisal (Loughran, 2004a; Loughran & Northfield, 1996; Schuck, 2002). [ABSTRACT FROM AUTHOR]

When I introduce new mathematical concepts with pre-service teachers, I inevitably ask "What is the big idea?" and our exploration leads to a discussion that highlights multiple understandings about how big ideas are both perceived and articulated. As I write about understanding more about the underbelly of my thinking, I am drawn to once again ask "What is the big idea?" when discussing the role of theory when needing to articulate knowledge about my practice. With relation to a discussion about a new professionalism in education, perhaps it becomes pertinent to ask more about the nature of theory that is relevant to teacher educators and then examine the connection between teacher educator's behaviours and their inner beliefs. In positioning teacher educators as producers of knowledge then we need to challenge traditional ideas of how knowledge is produced and disseminated (Berry, 2004b, 2007) and the foundation for this process is on the having of experience. As a primary teacher, I rarely had recourse to reflect on theory and the ways in which theory had explicitly or implicitly influenced my teaching. I did things because I did them in much the same way as I believed things because I believed them; they just were. I did not have reason to challenge the status-quo. Teaching, for me, was a doing profession with both immediate and urgent needs and in retrospect, this belief transferred to my teacher education classrooms. In my discussion in this chapter of the role of theory, I will begin to untangle the ways in which my beliefs influenced what I thought pre-service teachers should know and understand about theory and developing knowledge, and about the ways in which articulating my own philosophy of learning began to influence my practice and beliefs as an educator. [ABSTRACT FROM AUTHOR]

My self-study, presented in this book, describes my proactivity as a teacher educator in a Bachelor of Education program and offers an indepth account of how I questioned the culture of teacher education; from the inside. It is an account of my practice as a mathematics teacher educator; how I came to understand more about the nature of taken-for-granted assumptions about teaching and learning and, the impact of those assumptions on pre-service teacher learning; the development of professional knowledge; the impact of reflective practice; and, the importance of relationships in teaching, and learning about teaching. I began to examine what Whitehead (1993) referred to as "living contradictions". In one sense, the problem as I defined it was quite simple - I wanted to teach so that pre-service teachers could learn about teaching through their experiences, not mine. In seeking a solution, which required a deliberate challenging of the statusquo, complexities associated with teaching and learning about teaching were further exposed. [ABSTRACT FROM AUTHOR]