Graduate Thesis Or Dissertation
 

Teaching mathematics for understanding : intentions and practices of an expert middle school mathematics teacher in the context of a reform-based curriculum

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  • The movement to reform mathematics teaching and learning in schools began in the 1980s. After dedicating vast resources to support reform efforts since then, the transition to improve mathematics teaching and learning in schools has not occurred. In the majority of mathematics classrooms teachers still rely on traditional teaching strategies despite the use of reform-based curricula aimed at improving student learning of mathematics. The purpose of this study was to investigate the intended instructional objectives and practices of an expert middle school mathematics teacher in the context of a reform-based mathematics curriculum. Data collected from interviews, audio recording of whole class discussions, classroom observations, and detailed analyses of several lesson segments were used to create a case study for the teacher to describe a model of her practice as an expert mathematics teacher. The theoretical framework used for this study was Schoenfeld's (1998) model of teaching-in-context that defined key contributories to teachers' practice: beliefs, intentions or goals, and their content and pedagogical content knowledge. The research questions in the study considered the teacher's intentions, her conceptions about mathematics and teaching and learning, the instructional strategies she frequently used, the curricula with which she practiced, and the impact of the classroom and school communities. The practices of the teacher in this study were reform-based. She used an active, process-oriented, collaborative approach to teaching and learning. She was given the freedom to choose the curricula from which she taught. She chose reform-based curricula for her mathematics classes, and her practices followed these curricula most closely, emphasizing connection making, pattern recognition, and problem solving in collaborative environments. Explaining solutions and consensus building among alternative strategies to solve problems dominated the discourse during whole class and small group activities. The teacher rarely used computing technologies in her teaching. Her own beliefs and corroborating opinions from collaborating middle and high school mathematics teachers were the main reasons for this, although access to the computing technologies at the school was limited. The teacher's collaboration with the members of the school community was strong and this collaboration had a significant impact on her intentions and practice. This study resulted in a proposed model of expert mathematics teachers' practice in reform-based curriculum situations. This model included the teacher's strong and expanding content knowledge, her career-long commitment to participating in professional development programs and improving her practice, and her enthusiasm about students and the teaching profession as key factors that played an important role with respect to the her decision-making process and the actions she took as she taught in her mathematics classes.
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