Investigating the structure of discourse for reform -based mathematics classroom

One of the key ideas in mathematics education reform today is the need to support discourse in classrooms. Despite the importance of this goal however, research has shown that realizing this vision of discourse can be hard to achieve. To address this issue, this dissertation introduces a framework that can be used to study and implement discourse in mathematics classrooms. Data come from two second-grade classrooms in which instruction was based on a reform-based curriculum.;The dissertation is organized as two related studies. The first study examines the character of the discourse that occurred in these two classrooms. Specifically, it first identifies six distinct discourse structures that were used as building blocks for talking about students' solutions to mathematical problems. The structures vary in the level of mathematical reasoning addressed ranging from answering and explaining the problem to going beyond the problem situation and to generalizing. The study also identifies three broad patterns in the ways these structures were used to define interactions in the classrooms. These patterns vary in the level of complexity from getting discourse started to increasingly complex patterns where students were engaging in extended and more mathematically complex discussions.;The second study focuses on one of these classrooms and looks closely at one of the interaction patterns identified above---a focus on comparisons of drawings. The study explores how comparisons were used in the classroom and changes in its use over time. It then examines strategies that the teacher used to facilitate this notion of investigating by comparing.;This dissertation contributes to current research in several ways. First, it contributes to our understanding of the nature and development of discourse in mathematics classrooms. In particular it offers insights concerning how to characterize discussions around mathematical problems and situations. The study also demonstrates that classroom interaction patterns can be described based on these characterizations. Second, it identifies specific ways in which the discourse structures and patterns address important goals of mathematics education reform. Finally the dissertation contributes to our existing base of research concerning strategies that teachers might use to implement discourse.