The purpose of this study was to investigate the knowledge base and instructional practices of two highly qualified experienced secondary mathematics teachers within the context of their classrooms during a unit in a geometry class. Data collected from interviews, classroom observations, pre and post-observation questionnaires, and detailed analyses of several lesson segments were used to create case studies for each teacher, which were compared to reveal any patterns in their instructional practices. The theoretical framework used for this study was Schoenfeld's (1998) model of teaching-in-context that included three factors that affected teachers' decisions during instruction: beliefs, goals, and their knowledge bases. The supporting questions that were investigated in this study dealt with teachers' conceptions of mathematics and teaching and learning mathematics, instructional goals, instructional strategies and curricular materials used during the unit, and any modifications made to instruction. Both teachers in this study used a more traditional lecture and discussion style of instruction that closely followed an explicit model of teaching instead of a more reform-based style of teaching. The teachers incorporated the processes of mathematics such as proof and reasoning and representation into their instruction through modeling instead of incorporating activities into instruction designed to engage students in the processes. Although both teachers were aware of and had used reform-based methods, they perceived that the traditional instructional methods were more efficient and effective. Contextual factors played a dominant role in the decisions the teachers made about their instruction. The contextual factor that had the greatest effect on instruction for these two teachers was the pressure to teach all of the topics in the required curriculum to prepare their students for the state standardized high stakes test. Other contextual factors were large class sizes, limited physical space, and limited access to technology. The results of this study indicated that although the teachers had strong content knowledge and knowledge of both traditional and reform-based pedagogy, they chose a more traditional instructional style and this decision was affected by contextual factors such as high stakes testing, a required curriculum, and the demands of their jobs. / Graduation date: 2006

The purpose of this research was to estimate (1) the extent to which institutional inbreeding is prevalent among mathematics faculty at colleges and universities throughout the United States; (2) the extent of institutional inbreeding among mathematics faculty at American colleges and universities classified according to institutional genre; (3) the extent of institutional inbreeding among mathematics faculty classified according to gender; and (4) the extent of institutional inbreeding among mathematics faculty in American colleges and universities classified according to regions of the country. Institutional inbreeding was defined as faculty employment at the institution from which one received the highest earned degree. An exhaustive review of the literature on inbreeding was used to develop this research. All public-supported and private-supported American universities that offer a doctorate in mathematics were identified by consulting the 1991 American Mathematical Society Professional Directory. Catalogs for the academic year 1991-1992 were requested from each institution. One-hundred sixty-seven institutions of higher education which offer the Ph.D. degree in mathematics and 5,961 faculty members were identified. The results of the analyses found a mean proportion of inbred mathematics faculty of 3.46 percent, which is one-tenth of the most recent study examining mathematics faculty. A chi-square goodness of fit test using specified frequencies, found a statistically significant difference between rates of institutional inbreeding among mathematics stratified according to gender. A chi-square goodness of fit test using specified frequencies was used to test the association between mathematics faculty when stratified by Carnegie classification and regions of the country. No association was found between rates of institutional inbreeding of mathematics faculty when institutions were stratified according to the Carnegie classification and regions of the country. This research indicates institutional inbreeding is on the decline among mathematics faculty in American Colleges and Universities.

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