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.

KEYWORDS:

• Mathematics textbooks
• university
• calculus
• instruction
• teaching
• inquiry

MSC:

• 97D99
• 97U20

Acknowledgements

The University of Michigan is located on the traditional territory of the Anishinaabe people. In 1817, the Ojibwe, Odawa, and Bodewadami Nations made the largest single land transfer to the University of Michigan. This was offered ceremonially as a gift through the Treaty at the Foot of the Rapids so that their children could be educated. Through these words of acknowledgment, their contemporary and ancestral ties to the land and their contributions to the University are renewed and reaffirmed. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We thank Casey for participating in the study and his suggestions on the early findings of this paper. We also thank Thomas Judson, Yannis Liakos, and Yue Ma for their support in several aspects of the research reported here.

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Notes

1 Active Calculus is not the only calculus textbook designed for teaching with inquiry (e.g., IBL Calculus: Concepts and Applications [Greene & Shorter, n.d.]; Calculus for Team-Based Inquiry Learning: 2023 Early Edition [Clontz & Lewis, 2023]). However, because we used Active Calculus in our larger study, we had the opportunity to study how this one inquiry-oriented textbook was used.

2 There are also departmental and systemic efforts to promote inquiry-based methods of teaching mathematics, specifically calculus, in U.S. colleges (e.g. Bennoun & Holm, 2021; Carreon et al., 2018).

Additional information

Funding

Funding for this work has been provided by the National Science Foundation’s IUSE program, USA [grant number 1624634, 1821509].