This action research study examined my attempts during a six-lesson unit of instruction to implement five practices developed by Stein, Engle, Smith, and Hughes (2008) to assist novice teachers in orchestrating meaningful mathematical discussions, a component of inquiry-based teaching and learning. These practices are anticipating student responses to a mathematical task, monitoring student responses while they engage with the task, planning which of those responses will be shared, planning the sequence of that sharing, and helping students make connections among student responses. Although my initial anticipations of student responses were broad and resulted in unclear expectations during lesson planning, I observed an improvement in my ability to anticipate student responses during the unit. Additionally, I observed a high-level of interaction between my students and me while monitoring their responses but these interactions were generally characterized by low-levels of mathematical thinking. The actual sharing of student responses that I orchestrated during discussions, and the sequencing of that sharing, generally matched my plans although unanticipated responses were also shared. There was a significant amount of student interaction during the discussions characterized by high-levels of thinking, including making connections among student responses. I hypothesize that task quality was a key factor in my ability to implement the five practices and therefore recommend implementing the five practices be accompanied by training in task selection and creation.

This dissertation focuses on the development and testing of a conceptual framework for student motivation in mathematical discussion. Specifically, this document integrates Yackel and Cobb's (1996) framework with aspects of Self-Determination Theory (SDT), as described by Ryan and Deci (2000). Yackel and Cobb articulated the development of students' mathematical dispositions through discussion by facilitating student autonomy, incorporating appropriate social norms and co-constructing sociomathematical norms. SDT mirrors these factors and describes a similar process of self-regulation through fulfillment of the individual needs of autonomy, social relatedness, and competence. Given the conceptual overlap, this dissertation examines the connection of SDT with mathematical discussion with two studies. The first study examined the effect of student frequency of explaining mathematics on their perceived autonomy, competence and relatedness. Results of HLM analyses found that more frequent explanation of mathematics had a positive effect on students' perceived mathematics autonomy, mathematics competence, and relatedness. The second study used a triangulation mixed methods approach to examine high school geometry students' classroom discourse actions in combination with their perceived autonomy, competence, and relatedness. Results of the second study suggest a higher perceived sense of autonomy is indicative of more engagement in mathematical talk, but a measure of competence and relatedness are needed for such engagement to be fully indicative of mathematical discourse. Rather, students who lacked a measure of perceived competence or relatedness would cease participation in mathematical discussion when challenged by peers. While these results need further investigation, the results of the second study provide evidence that indicates the necessity of fulfilling all three SDT needs for engagement in mathematical discussion. Evidence from both the first and second studies presented in this dissertation provides support for the conceptual framework presented. / Ph. D.