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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. Doctor of Philosophy This research seeks to understand and interpret the beliefs of 10 high school geometry teachers that resolve apparent inconsistencies between what teachers say they believe and what they do in the classroom. 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. It was identified that teachers consistently and inconsistently enact their stated beliefs, but there are also instances when teachers both consistently and inconsistently enact their stated beliefs. When teachers appear to inconsistently enact their stated beliefs, it was found that teachers have logical reasons why they do so, and these reasons relate to specific teaching practices. It was also found that teacher beliefs interact with each other in different ways. Teachers' beliefs can limit or prevent the enaction of their other beliefs. In addition, school level constraints can override the enaction of some teacher beliefs. This research shows that some beliefs are held by different teachers from vastly different schools which suggests that some geometry teacher beliefs are held socially. The findings from this research have implications for teacher education.

The purpose of this study was to determine the understandings and perceptions that teachers in one elementary school in Virginia had about the teacher evaluation system. Participants were recruited from one elementary school in Virginia. All of the teachers and specialists were asked to participate and 12 participants volunteered. General education teachers made up 25% of the participants while specialists who taught in areas such as Music, Art, Physical Education, or Special Education made up 75% of the participants. Participants were interviewed individually and were asked the same questions about the teacher evaluation process. Interviews were transcribed and primary codes were developed from the data. Interview questions asked participants to describe both their understandings of the evaluation system under which they worked and the perceptions they had about their experiences with evaluation. Even though there were no questions dealing with emotions and feelings, emotional language was prevalent throughout the data. The overall findings from this study indicated that teachers had a limited knowledge about a problematic evaluation system. The fact that elementary teachers have unique responsibilities means that they may need multiple ways to TEACHER UNDERSTANDINGS AND PERCEPTIONS OF EVALUATION iii show their effectiveness. Other findings suggested that inconsistent evaluation practices in this school caused teachers to see no benefit from the process. Finally, findings also suggested that there was a misalignment between the evaluation instrument and the jobs of teachers, particularly those of specialist teachers. Implications for future research include studies which focus on teacher learning over time in order to support teachers at any level of experience. Future research also needs to be conducted with elementary classroom teachers and specialist teachers to discover ways that may create a more aligned and fair process. Further research would also include studying the perceptions of evaluators and how they carry out the evaluation process and make decisions about its use. Ph. D.