Resolving Apparent Inconsistencies in the Belief Systems of High School Geometry Teachers

This qualitative research seeks to identify and understand the beliefs of 10 high school geometry teachers that help resolve apparent inconsistencies between their espoused and enacted beliefs. Data was collected using an initial interview, classroom observations, and a follow-up interview to gather evidence of teacher beliefs based on what they say, do, and intend respectively. Open coding, analytical coding, cluster identification, coding memos, and analytical memos were used to analyze the data and write summaries of the teachers' explanatory beliefs with beliefs as the unit of analysis. It was identified that teachers consistently and inconsistently enact their espoused beliefs, but there are also instances when teachers both consistently and inconsistently enact particular espoused beliefs. This endeavor necessitates a shared understanding of terms, and it was found what it means to "understand" needs to be clarified with a definition and examples from teachers. When teachers appear to not enact their espoused beliefs, explanatory beliefs were pinpointed that resolve the conflict and found the explanatory beliefs exist in at least seven macro clusters. These explanatory beliefs interact with espoused beliefs by overriding, limiting, or preventing the espoused beliefs to resolve the apparent inconsistency in teachers espoused and enacted beliefs. The explanatory beliefs with limiting and overriding interactions were found to coexist for some teachers around a teaching practice as overriding interactions are connected to constraints on the classroom whereas limiting interactions are not. It was also found that belief clusters are nested within clusters of beliefs, and these clusters allow for beliefs to cluster in isolation in different ways. This work also shows empirically that some geometry teacher beliefs are socially constructed due to the presence of common cultural artifacts and influence from mathematics teacher educators. This work has implications and future research directions in the areas of using beliefs as the unit of analysis, mapping teacher's belief systems, considering the social construction of beliefs and role of community, connecting beliefs to specific teaching practices, and educating teachers.