Thesis (Ph.D.) - Indiana University, School of Education, 2010Abstract: Through the lens of Schegloff¡®s (1996) Action Theory, this study examined the dynamics of four groups of fifth-grade students as they learned to talk about academic mathematical reasoning over the course of a school year using Freeze Frame Analysis (Leander & Rowe, 2006) to help map ¨Dtalking spaces¡¬ and Critical Discourse Analysis to understand the discursive turns that helped students to become more effective in small- group settings. In this study, I theorize, if teachers understand how and why students position each other within small-group discussion-based mathematics (Boaler & Greeno, 2000), they can create conditions for increased student engagement in mathematics. While the results of this study were mixed, several conditions or factors, which both supported and hindered mathematical discussions arose. Discursive actions, which supported mathematical discussions, included the use of common ground, positive assessment, transmediation, and teacher confidence in student abilities. Discursive actions, which hindered effective mathematical discussion, were over use of negative assessment turns, ratification, use of rules, facts, and formulas as arguments, and using physical or political power over peers. Teacher discourse and physical positioning, which supported student engagement, was divided into three categories; teacher guidance, teacher redirection, and teacher listening. Included in chapter eight, are suggestions for why the use of discussion-based mathematics was difficult to incorporate into traditional mathematics settings and recommendations for teachers attempting to shift to discussion-based mathematics or inquiry based collaborative learning in mathematics.