Date of Award

Spring 2011

Project Type

Dissertation

Program or Major

Mathematics Education

Degree Name

Doctor of Philosophy

First Advisor

Sharon McCrone

Abstract

Over the past decade, mathematics educators and researchers have become increasingly aware of the impact of social interactions on students' learning (NCTM, 2000; Bowers & Nickerson, 2001; Forman, 2003). Current research indicates that the classroom environment, including the activities and discussions that take place, can have a significant effect on the ways students make sense of mathematical concepts (Yackel, 2001). Understanding mathematics involves knowing how to make sense of key concepts through the processes of reasoning and justification. Educators and researchers agree on the importance of providing students with opportunities in class to explore, conjecture, and prove in order to promote mathematical understanding beyond procedural knowledge (Lakatos, 1976; Rasmussen & Marrongelle, 2006).

Although there are a number of studies that investigate many different aspects of classroom discourse and students' learning, there remains a need for more understanding (Franke, Kazemi & Battey, 2007). This study is aimed at investigating the nature and impact of social interactions, both teacher-student and student-student, in classroom discourse. In particular, the study seeks to gain understanding of how interactions influence students' engagement in proof and reasoning activities. In addition, the study analyzes students' argumentation schemes as they occurred in classroom discussions and during student group work.

Through the perspective that learning is both a social and an individual activity, this research focuses on the social component of the learning process as it occurs in the classroom. Ethnographic techniques of participant observation and interviews provided methods of data collection, and analysis of discourse and argumentation structures provided a way to interpret the data. This study contributes to the existing research by highlighting certain types of interactions that resulted in students contributing to proof construction and collective reasoning.

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