Chapter 10: Deconstructing Discourses in a Mathematics Education Course: Teachers Reflecting Differently

What should a mathematics classroom look like? And what should mathematics teachers do? Over the past 30 years, theNational Council of Teachers of Mathematics (NCTM) has produced a collection of documents that provide suggestions for these politically charged questions (see NCTM, 1989, 1991, 1995, 2000; Kilpatrick, Martin, & Schifter, 2003). Most mathematics teachers, educators, and policymakers would agree that these documents describe a different mathematics classroom than that which is experienced by most students in schools in the USA, and throughout schools in English-speaking countries (see Hiebert, 2003, for a discussion of “traditional” curricula and pedagogy). It has also been argued that these documents are the catalyst for the “math wars” armed by two opposing camps: the traditionalists and the reformers (Schoenfeld, 2004). The traditionalists’ camp fears that the NCTM reform-oriented, “standards-based” curricula are superficial and undermine “classical” mathematical values, whereas the reformers’ camp claims that the reform-oriented curricula reflect a deeper, richer view of mathematics (p. 253). The purpose of this chapter is to explore how postmodern theory might assist mathematics teachers (educators and policymakers) who position themselves in either camp (or somewhere in between) to begin to ask different questions regarding teachers and students of mathematics, and what it means to practice “good” mathematics teaching.

Although the impact of the NCTM documents in actually reforming mathematics teaching has been somewhat limited (see Wilson & Goldenberg, 1998), research has shown that these documents have had an impact on how mathematics teachers define and practice good mathematics teaching (Wilson, Cooney, & Stinson, 2005). Wilson, Cooney, and Stinson’s research on the perspectives of seasoned mathematics teachers about good teaching suggests that efforts to reform mathematics teaching are seldom all-or-nothing affairs. Their research illustrated that even as seasoned teachers reformed (some of) their teaching practices, most often, they continued to maintain a belief in the teacher-centered classroom and the infallibility of mathematics. It has been argued that the latter of these beliefs is counter to reform-oriented mathematics teaching, thus securing the continuation of traditional practices (see Davis & Hersh, 1981; Ernest, 1998). To make it possible for teachers to create mathematics classrooms that are consistent with the constructivist, studentcentered objectives of reform-oriented mathematics teaching, we believe that teachers must be provided an opportunity to challenge and “trouble” both traditional mathematics teaching and the reform efforts themselves.

Here, we broadly define reform-oriented education from a Deweyian experiential prospective (see Dewey, 1916, 1998), in that the aims of “effective” teaching must be an outgrowth of experience, provide flexibility to meet various circumstances, and represent a freeing of activities (Dewey, 1916). Specifically, within the context of mathematics education, we draw upon Davis and Hersh (1981), who stated: “Ideally, mathematical instruction says, ‘Come, let us reason together’” (p. 282), and Ernest (1998), who reminded us that mathematics “for all its wonder . . . remains a set of human practices, grounded, like everything else, in the material world we inhabit” (p. xii). In understanding the mathematics classroom as a pedagogical space for teachers and students to reason together through the socially constructed discipline of mathematics, we believe that postmodern theory provides a different theoretical framework for teachers to trouble both traditional and reformoriented mathematics teaching as they explore their own pedagogical philosophies and practices.

The value of postmodern theory is found in its awareness of and tolerance toward social differences, ambiguity, and conflict; it requires developing new languages, conventions, and skills to address the moral and political implications of knowledge (Seidman, 1994). In short, postmodern theory requires shifting the “focus from foundations and familiar struggles of establishing authority toward exploring tentativeness and developing scepticism of those principles and methods that put a positive gloss on fundamentals and certainties” (Walshaw, 2004b, pp. 3–4). Gordon (1980) marked the beginning of postmodern theory in the mid-to-late 1970s, characterizing the immediate years after the failed Student and Worker’s Revolt of 1968 in Paris as an unusual, fascinating, and confused period in which new lines of investigation and critique emerged on the intellectual scene. Some of these new lines of investigation and critique can be found in Foucault’s (1972) reinscription of discourse, Derrida’s (1997)deconstruction of language and cultural practices, and Deleuze and Guattari’s (1987) characterization of the rhizome.