'I Use IBL in This Course' May Say More about an Instructor's Beliefs than about Their Teaching

Inquiry-Based learning (IBL) is a fairly well-known term in the United States (US) describing a range of student-centered or active pedagogical approaches in mathematics. However, the 'big tent' definitions of IBL mean that there is much variation in IBL users' instructional practices, variation which we set out to codify. Cluster analysis of self-reported data from a survey of postsecondary calculus instructors across the US reveals three instructional profiles among self-declared users of IBL: (a) heavy users of group work; (b) users of a variety of mixed approaches; and (c) heavy users of didactic lecture. The instructional profile of this third group is indistinguishable from that of calculus instructors who report never having heard of IBL. We further investigate the relationship of these instructional profiles to certain beliefs about teaching and learning. All groups agree that inquiry supports learning; the groups who spend a minority of time in didactic lecture disagree with statements that there are benefits to lecturing. Implications for research and adoption of IBL are discussed.