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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 theories. 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 An Online Journal for Teacher Research Networks: Vol. 19, Issue 1 ISSN 2470-6353 Summer 2017 Betts, McLarty, & Dickson 2 project on the use of inquiry learning in mathematics classrooms, which extended beyond the end of the course into their final teaching practicum. Paul participated in this project as both their teacher and mentor. This paper reports on what Krysta, Michelle, and Paul learned from participating in this action research project on inquiry. Our action research led us into a consideration of possible linkages between the theory and practice of using inquiry learning in mathematics classrooms. The teacher education literature has clearly described the polarizing of theory and practice in the learning experiences of pre-service teachers (e. g., MacDonald, Falkenberg, & Goodnough, 2012). Pre-service teacher education programs, by their very nature tend to silo theoretical understandings from practical experience (Russell & Dillon, 2015; Zeichner, 2010). It is common in traditional teacher education programs to assume that teacher candidates apply the theory they learn in course work during their practicum experience (Russell & Dillon, 2015). For teacher candidates, the university is positioned as imparting theories of education, which may or may not be helpful as they learn how to teach in their practicum placements. The practice of teaching in schools is perceived as more useful by teacher candidates, and theory is only useful when it “applies” to practice. But the relationship between theory and practice is richer than linear and one-directional application of theory to practice (Betts & Block, 2013; Zeichner, 2010). A more nuanced understanding of the possible linkages between the theory and practice of inquiry-based teaching was triggered by our action research project. Theoretical Framework for this Paper We used three theories in this paper, namely, action research, inquiry learning, and the relation between theory and practice in teacher education. Action research was the methodology, inquiry learning was the math teaching pedagogy we sought to understand further, and the relation between theory and practice was the theoretical framework used to interpret what we learned from our action research project. In this section, we describe literature on each of these theories that are relevant to our project, and close by noting connections between these theories.

An Action Research Project by Teacher Candidates and their Instructor into using Math Inquiry: Learning about Relations between Theory and Practice