The role of textbooks for supporting instruction with inquiry: the case of Active Calculus

Abstract

In this case study, we investigate how an inquiry-oriented interactive calculus textbook supported one U.S. college instructor’s classroom teaching. We utilized analytical inquiry-oriented frameworks on observation data from a small classroom to capture textbooks’ influence on the instruction conceptualized by the Teacher-Mathematics-Student face of the socio-didactical tetrahedron [Rezat, S., & Sträßer, R. (2012). From the didactical triangle to the Rezat and Sträßer’s tetrahedron model socio-didactical tetrahedron: Artifacts as fundamental constituents of the didactical situation. ZDM - Mathematics Education, 44(5), 641–651. https://doi.org/10.1007/s11858-012-0448-4]. Operationalizing specific inquiry-oriented processes allowed us to examine the depth of the interactions conceptualized by the tetrahedron. The instructor’s reliance on the textbooks, their activities, and their supplemental materials created opportunities for meaningful classroom interactions about calculus, supporting a shift towards inquiry. We conclude by suggesting further research on the role of textbooks in supporting undergraduate mathematics instruction with inquiry and discussing implications for practice.