Date of Award
Program or Major
Doctor of Philosophy
Karen J Graham
The purpose of this study was to investigate and describe how middle school mathematics teachers make meaning of proofs and the process of proving in the context of their classroom practices. A framework of making meaning, created by the researcher, guided the data collection and analysis phases of the study. This framework describes the five central aspects of the process of making meaning: knowledge, beliefs, utilization of knowledge, interconnections of practice and knowledge, and making sense of past knowledge and current experiences. The utilization of a qualitative research methodology that combined ethnographic fieldwork and discourse analysis allowed the researcher to consider the interplay of individual knowledge and action with contextual influences.
Data was gathered through participant observations, conducted in grade levels 5-8 classrooms, and interviews were conducted with teachers and administrators. The participants in the study include six middle grades teachers and two administrators from a New Hampshire public school. The teachers' decision making processes, understandings of proofs, and the connections formed between their past knowledge and current experiences were analyzed. Data analysis was conducted using open coding, the creation of episodic threads, and the development and examination of themes.
Findings from this study suggest that: (1) these teachers use proofs and the process of proving in their classrooms often and in meaningful ways, (2) the teachers hold a dual understanding of proofs and the process of proving: one related to their own education experiences and one related to their students' education, (3) the teachers use alternative resources to make meaning of proofs and the process of proving in relation to their professional experiences, and (4) the use of alternative resources has allowed the teachers to disconnect their view of proofs and the process of proving in relation to their students education from their own past experiences, which they view as negative.
Implications for future research related to teachers' knowledge of proofs and the process of making meaning, as well as implications for the education and professional development of middle school mathematics teachers are presented and discussed.
Paddack, Megan, "The process of making meaning: The interplay between teachers' knowledge of mathematical proofs and their classroom practices" (2009). Doctoral Dissertations. 500.