This paper reports on what two teacher candidates and their instructor learned from an action research project into the use of inquiry to teach mathematics. We use a model of the relation between theory and practice in teacher education to interpret what we learned about inquiry. This model describes three modes for teacher candidates to learn about teaching: (1) applying theory to practice; (2) interpreting theory and practice, and (3) building/refining personal, practical and professional

more »

... ries. We learned to (1) apply the 4D-Cycle Model of inquiry, (2) interpret what it means for inquiry to be flexible, and (3) build a theory of teaching with inquiry based on non-linear and community-based dispositions of teachers toward learning. We conclude by suggesting that this model could constitute a developmental pathway by teacher candidates for experiencing the linkages between theory and practice. We are action researchers. Paul is an associate professor who teaches mathematics teaching methods to prospective K-8 teachers. Michelle and Krysta have completed their pre-service teacher education, but were teacher candidates at the time of the action research reported in this paper. We are passionate about teaching mathematics. Krysta and Michelle aspire to be dynamic and cutting edge teachers of mathematics. Paul encourages his students to take-up reform-based approaches to teaching mathematics. In his second of two mathematics teaching courses in a two-year generalist elementary teacher education program, Paul used principles of action research to inscribe the major assignment for the course; an invitation for teacher candidates to become action researchers of the teaching of mathematics. When Michelle and Krysta took this course, they saw the assignment as an opportunity to conduct a collaborative action research