The evolution of pre-service secondary mathematics teachers' beliefs about and understandings of mathematics: Toward a community of learning

This study examines the nature of pre-service teachers' evolution of beliefs about and understandings of mathematics. Through surveys of a mathematics education cohort, trends in pre-service teachers' beliefs and attitudes about mathematics are identified and compared to a larger population of undergraduate mathematics students. These data serve as background information for an interview study that examines more closely pre-service teachers' beliefs about and understandings of mathematics. Initial interviews of seven participants aided in the development of a model through which to examine the relationships between one's beliefs about mathematics and one's understandings of mathematics. The Interaction-Enriched Learning Community (IELC) model focuses on the community of interactions in an individual's learning environment and serves as a model through which to discuss the pre-service teachers' advanced mathematical thinking. Interviews with three pre-service teachers—Erin, Beth and Greg—contribute to a greater understanding about how beliefs about mathematics and understandings of mathematics are related. The study found that the types of interaction in the process of social construction influenced greatly the conceptual learning of mathematics for these three pre-service teachers. Moreover, the types of interaction and the richness of those interactions afford greater opportunities for movement towards a broader understanding of mathematics.; The results of this study contribute to a growing body of research that seeks to understand how belief structures and conceptual understandings of mathematics influence pre-service teachers and, in turn, all of mathematics education. The study embraces the cyclical complexity of the influence of beliefs about and understandings of mathematics—building a diagram model of the community of interactions which comprise the mathematical learning environment, and which point towards the social construction of knowledge. In summary, the study addresses the constructivist notion that metacognition influences learning, and further posits that metacognition also influences teaching.