| Beginning mathematics teachers enter their classrooms with a network of conceptions about mathematics and how they will go about teaching it. These conceptions are based on a set of beliefs and body of mathematical knowledge. They are robust and deeply ingrained, and they influence how teachers approach the teaching and learning of mathematics. When teacher educators examine the relationship between teachers' conceptions and their practices, they are able to better understand how teachers define their practice. This understanding, then, can inform their work in preservice and inservice teacher education.;This study focused on the conceptions of three first-year secondary mathematics intern teachers and examined how these conceptions were manifested in their classroom practices. Using case study methodology, I observed the participants in their classrooms weekly, and they participated in ongoing mentorship during the year. Their university mathematics methods course provided opportunities for them to engage in reflective discourse regarding any connections made between their experiences in the course and in their classrooms. The data collected was analyzed to document the teachers' conceptions and how these conceptions were influenced and reshaped by their classroom, mentoring, and methods course experiences.;The participants initially entered their classrooms and taught in the traditional manner of lecture/demonstration of new problems. Then students practiced similar problems as the teacher walked around and offered help. This routine persisted for one of the participants throughout the year, but for two participants, classroom events triggered a reaction to the status quo of this classroom routine. A different set of conceptions were manifested, and with the support of mentoring and the mathematics methods course, these two participants implemented changes in their practices.;The findings of this study suggest that beginning mathematics teachers enter their classrooms with a set of implicitly acquired conceptions of mathematics from their personal experiences as learners of mathematics. The findings also suggest that when their conceptions were classroom tested and challenged during their methods course and mentorship, these teachers were able to make explicit the basis of their conceptions, expose them to critique and analysis, and reshape them or develop new conceptions. |
