Current reform in mathematics teaching and learning is rooted in a changing vision of school mathematics, one that includes constructivist learning, student-centered pedagogy, and the use of worthwhile tasks (National Council of Teachers of Mathematics, 1989, 1991, 2000). This changing vision not only challenges teachers‘ beliefs about mathematics instruction but their philosophies of mathematics as well (Dossey, 1992). This study investigates the processes that four teachers‘ go through as they implement a new task-based mathematics curriculum while exploring their personal philosophies of mathematics. The participants were part of a graduate-level course that examined, through the writings of Davis and Hersh (1981), Lakatos (1976), Polya (1945/1973), and others, a humanist/fallibilist philosophy of mathematics. These participants shared, through reflective writings and interviews, their struggles to, first, define mathematics and its purpose in society and in schools, and second, to reconcile their views of mathematics with their instructional practices. The study took place as the participants, two classroom teachers and two instructional coaches, engaged in the initial implementation of a reform mathematics curriculum, a reform based in social constructivist learning theories.

Using narrative analysis, this study focuses on the unique mathematical stories of four experienced educators. Each of the participants initially expressed a traditional, a priori view of mathematics, seeing mathematics as right/wrong, black/white, a subject outside of human construction. The participants‘ expressed views of mathematics changed as they attempted to align their personal philosophies of mathematics with their (changing) classroom practices. They shared their personal struggles to redefine themselves as mathematics teachers through a process of experimentation, reflection, and adaptation. This process was echoed in their changing philosophies of mathematics. These participants came to see mathematics as fluid and a human construct; they also came to see their philosophies of mathematics as fluid and ever-changing, a process more than a product.