CAROLINE BRAYER EBBY LEARNING TO TEACH MATHEMATICS DIFFERENTLY: THE INTERACTION BETWEEN COURSEWORK AND FIELDWORK FOR PRESERVICE TEACHERS ⋆ (Accepted October 4, 1999) ABSTRACT. Understanding how preservice teachers integrate coursework and fieldwork as they learn to teach is critical to understanding how to prepare teachers to implement the kind of instruction envisioned by current reforms in mathematics education. This article explores the connections that 3 preservice elementary teachers made between their exper- iences as learners of mathematics in a masters-level university methods course and their experiences as teachers of mathematics in the fieldwork classroom. Three case studies are presented in order to illustrate different ways that the experience of engaging in mathemat- ical inquiry influences the way in which elementary preservice teachers construct their understanding of themselves as mathematics teachers. Taken together, the case studies suggest that we need to expand our perspective as teacher educators to encompass learning from the fieldwork experience as well as preservice teacher learning beyond the conclusion of the semester. In particular, I conclude that the goals of a methods course should include developing and nurturing particular habits of mind that help preservice teachers learn from their own teaching. The traditional school curriculum represents mathematics as a static collection of facts, rules, and procedures to be passively learned by students through drill and practice (Romberg, 1992). In contrast, the current reform movement in mathematics education, as represented by recent reform documents, builds on a conception of mathematics as a dynamic, socially constructed, and inquiry-driven field (National Council of Teachers of Mathematics, 1989). The image of teaching as a process of inquiry that follows from these reform-oriented views stands in sharp contrast to the linearity and predictability of traditional mathematics instruction. Given that prospective teachers are inclined to teach as they were taught (Ball, 1990; Brown, Cooney & Jones, 1990), a critical issue for mathe- matics teacher educators is how to help prospective teachers develop a ⋆ This research was conducted as part of the author’s Ph.D. dissertation completed at the University of Pennsylvania under the direction of Betsy McNeal. An earlier version of the report was presented at the annual meeting of the American Educational Research Association in San Diego, 1998. The author thanks Janine Remillard and Betsy McNeal for their helpful comments and suggestions on earlier drafts of this report. Journal of Mathematics Teacher Education 3: 69–97, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands.