Mathematical Discussion and Self-Determination Theory
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.