Chapter 8: Playing the Field(s) of Mathematics Education: A Teacher Educator’s Journey into Pedagogical and Paradoxical Possibilities

There is promising research on how inquiry-based classroom discourse in mathematics leads to enhanced student engagement and conceptual understanding (Walshaw & Anthony, 2008). While the notion of an inquiry-based classroom (what it looks and feels like) is interpreted in diverse ways across a variety of contexts, there are a few distinguishing features common to most. In general, inquiry-based pedagogy is an alternative view of teaching and learning, based primarily on theories of constructivism and characterized by classrooms where the focus is on constructing mathematical understanding through student investigation, collaboration, and communication (Cheeseman, 2008; Leikin & Rota, 2006). In university teacher education, however, mathematics educators struggle in their work with prospective teachers to help bring about a shift from traditional teacher-directed approaches to such inquiry-based classroom discourses (Makar, 2007; Manouchehri, 1998; Wilson, Cooney, & Stinson, 2005). This is due, in part, to the fact that the paradigm shift to inquiry-based classrooms also demands a tolerance for ambiguity, uncertainty, and negotiation—skills not generally acquired through years of traditional school mathematics experiences. Thus, mathematics teacher educators are confronted with numerous challenges and complexities as they work to inspire prospective teachers to embrace inquiry-based pedagogies, while also seeking to deconstruct what are perceived as firmly entrenched stereotypes and ideas about teaching (Weber & Mitchell, 1995).

My current scholarship as a mathematics teacher educator and researcher involves introducing prospective middle years teachers to alternative, inquirybased pedagogy in mathematics. In recent research (Nolan, 2006), I proposed the existence of several classroom discourses that act to regulate the teaching and learning of mathematics, with the discourses often being in direct opposition to reform recommendations to effect change in mathematics classrooms. As Brown (2008) suggests, such regulative discourses can act as “cover stories” for why theories of alternative forms of pedagogy are not having a noticeable impact on classroom practice and new teacher development. At issue, of course, is the prospective teachers’ own lack of experience as students with alternatives to traditional teacher-directed approaches in teaching and learning mathematics. Mathematics reform and teacher education initiatives must begin by acknowledging that the first step to changing the way prospective teachers teach is to change the way prospective teachers learn (Pereira, 2005). In other words, “unless teachers directly experience inquiry learning for themselves it is quite unlikely that they will be able to implement it in their classroom” (Carter & Richards, 1999, p. 70). In addition, I would argue that when prospective teachers have positive and self-affirming experiences with learning mathematics through alternative, inquiry-based pedagogy, they are less inclined to resist the traditional, familiar (and regulating) discourses of what it means to teach and to “cover” mathematics content.

The belief that prospective teachers require experience learning through (not merely about) inquiry-based pedagogy led me to design and teach a new course in a university undergraduate teacher education program. The course, entitled Curricular Topics in Mathematics, is a compulsory course taken by prospective middle years teachers in their second year of a four-year teacher education degree at a Canadian university. In the design of the course, I selected the content to focus on middle years and secondary school topics in geometry and statistics, while the pedagogy included a variety of inquiry-based approaches, such as mathematical investigations, problem-based learning, technology-integrated learning modules, and collaborative problem posing/ solving. The discussions in this chapter are based on data from a research project designed as a self-study narrative of my experience teaching this new course, using my own journal reflections (as the designer and instructor for the course), as well as the journal writings and assignments of the students enrolled in the course. In addition to journals, data included student autobiographical “inventory” (survey) responses and final course evaluations. In this chapter, I present a reflexive narrative on my experience teaching this course, constructed through my own lens as a teacher (acknowledging my vulnerability in the face of student resistance and dissatisfaction) and through the lens of identifying with new teachers as they face similar student and classroom discourses of resistance. What makes this story unique is its candid approach to exploring why current mathematics teacher education programs generally have a superficial and temporary impact on reforming the teaching and learning of school mathematics. The story, told from my perspective as a mathematics teacher educator, highlights the need for a reconceptualized mathematics teacher education program that embraces the dynamic relationship between research, teaching, and learning.

Encouraging prospective mathematics teachers to make personal and professional transitions from traditional didactic teaching practices to inquirybased approaches presents many challenges. While there has been valuable research to date on the nature of the transitions required for becoming teachers (Garcia, Sanchez, Escudero, & Llinares, 2006; Jaworski & Gellert, 2003; Klein, 2004; Ritchie & Wilson, 2000), the area is still relatively under-documented and under-explored in the research literature. In this chapter, I claim that the transitions of prospective teachers call for a drastic change of script in storylines for what it means to teach and learn mathematics. I propose that one way to understand and unpack the transitions is using Bourdieu’s social field theory. In the following pages, I draw on aspects of Bourdieu’s theory to explore the pedagogical and paradoxical possibilities of inquiry-based pedagogy in mathematics (teacher) education.