Coherent Dynamic Accounts Of Prospective Secondary Mathematics Teachers Knowledge Of And Beliefs About Mathematics

Coherent, Dynamic Accounts of Prospective Secondary Mathematics Teachers' Knowledge of and Beliefs about Mathematics

This thesis presents accounts of the mathematical knowledge and beliefs of eight prospective secondary mathematics teachers (PSTs) as they progressed through a six-week unit on division of fractions that was designed to bring about change in their knowledge of and beliefs about mathematics. These accounts capture the sense that the PSTs made of their experiences during the unit and investigate how their knowledge and beliefs interacted to both facilitate and prevent change. One of the pressing problems currently facing mathematics education reform efforts is that PSTs frequently leave college with critical gaps in their understanding of secondary school mathematics topics and with traditional beliefs about mathematics, teaching and learning. Efforts to better prepare PSTs have only been partially successful, in part because teacher educators do not have a clear understanding of PSTs' knowledge of and beliefs about mathematics and how PSTs perceive of their experiences in classes designed to influence their knowledge and beliefs. This study used qualitative methods, including grounded theory, teaching experiment methodology, and case studies to investigate PSTs' knowledge of and beliefs about mathematics as they participated in the division of fractions unit. The PSTs' initial knowledge of division of fractions consisted mostly of procedural expertise, with only limited conceptual understanding. They tended to perceive of secondary school mathematics as an interrelated, consistent set of rules, procedures, facts and definitions. This interrelated rules perspective toward mathematics persisted for a short period after the PSTs began the unit. However, through a series of mathematical explorations, the PSTs were able to develop new understandings for division of fractions. This new conceptual knowledge led PSTs to rethink how they would teach division of fractions and to reconsider how they perceived mathematics. They began to view mathematics as a collection of rules and procedures that were supported by underlying concepts. Nevertheless, they continued to see rules and procedures as the major landmarks in the mathematical landscape, which in turn limited the mathematical understandings they were able to develop during the unit.

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