Date of Award

9-16-2009

Document Type

Dissertation

Degree Name

Doctor of Education (Ded)

Department

Professional Studies in Education

First Advisor

Monte G. Tidwell, Ph.D.

Second Advisor

George R. Bieger, Ph.D.

Third Advisor

Dr. Janet M. Walker

Abstract

This study addressed the inherent and age-old quandary of learning mathematical proof. The aim of the study was to explore the nature of the learning of mathematical proof by undergraduate mathematics majors through the lens of discourse. Additionally, the study investigated mathematics majors’ sense of a learning community in relation to their participation in a seminar on learning mathematical proof utilizing small-group discourse. A communicational approach to cognition—or commognition—provided the theoretical and research perspective for the study. The setting of the study was a zero-credit seminar focusing on mathematical proof for freshman and sophomore mathematics majors. The primarily qualitative study had nine participants. A multiple methods strategy of data collection was employed. First, audio recordings of small-group discourse on mathematical proof were collected along with participants’ related work. Participants additionally completed the Classroom Community Scale survey. Finally, interviews were conducted. Focal and preoccupational analyses were performed on the audio data to determine the object-level and meta-level features of the mathematical discourse/learning. Descriptive statistics and typological analysis were used respectively to summarize the survey and interview data. A synthesis of these analyses revealed the complexity of learning mathematical proof; that is, of becoming a more expert participant in the discourse of mathematicalproof. Small-group discourse appears to be a comfortable way for novice interlocutors to approach a more expert discourse on proof. Moreover, there may exist in discourse between novice interlocutors natural opportunities, called discursive entry points, in which experts could intervene to steer the discourse towards increasing sophistication. Additionally, the study revealed several complex and interrelated factors related to learners’ thinking (communication) of mathematical proof. The factors include: discursive contributions/role of interlocutors, discursive foci of interlocutors, difficulty/familiarity of mathematical content, negotiating effective communication, commognitive conflict, and power. Finally, interlocutors had a sense of community in the seminar on mathematical proof utilizing small-group discourse. The discourse may also have contributed to the connectedness that participants felt with their fellow math majors both inside and beyond the seminar walls. Moreover, the participants viewed being able to communicate about mathematical proof as the conduit to a universal math community.

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