Discursive possibilities: Re -imagining reform and equity in elementary mathematics.

摘要

Much of the research on preservice education has focused on finding and remediating the problematic beliefs and inadequate knowledge of individual beginning teachers. Research on children engaged in elementary mathematics has generally been seen as a separate body of work. This dissertation seeks to explore the work of preservice education by drawing the lines around it differently. First, it uses discourse as a theoretical frame, which locates practices like teaching, problem-solving and understanding mathematics, outside of individual heads and disperses them into multiple, but always interacting, fields. Second, it uses children's interactions with elementary mathematics as a catalyst for thinking in new ways about how we might educate those who teach them.;To explore these issues, I spent a year in a third-grade urban classroom, primarily during math class, where I observed the students, the teacher, and the student teacher. I also observed the elementary mathematics methods course that the student teacher attended during the first semester of the year. Throughout this dissertation, I draw on my experiences in these two classrooms, as well as on relevant written documents, such as curricula, state standards, and academic writing in mathematics education.;In particular, this dissertation is intended to respond to two prominent strands within the conversation about preservice education in elementary mathematics: those about equity and reform-oriented teaching. In addition, the dissertation is also designed to respond to current calls for "evidence-based" or "scientific" education research by drawing on ethnographic, genealogical, and rhetorical research traditions. By highlighting different research traditions in different chapters, the dissertation makes it possible to see the analytical affordances of each of these research strands. In particular, the ethnographic chapter argues that students who do not share the linguistic, cultural or ethnic background of their teacher may have more difficulty answering open-ended questions in competent ways. The chapters that draw on genealogical and rhetorical traditions examine the role that metaphors of hierarchy have played in defining the ways that we think about student learning in mathematics, the persuasive powers of different kinds of problems commonly used in mathematics classrooms, and the purposes that multiple genres of teaching may play in the mathematics classroom. The overarching argument of the dissertation is that the current narrowly-focused consensus on the definitions of equity and reform-teaching limits, rather than expands, possibilities for students.