Multivariable Calculus Instructors' Reports of Resource Use

Given the challenge of visualizing the main constructs of two-variable functions and their differential and integral calculus, it is essential to consider instructional resources' use and perceived potential to contribute to students' understanding. This case study considers how four instructors selected and used digital and physical resources in multivariable calculus and their motivations for doing so. We use the teaching triad of "sensitivity to students," "mathematical challenge," and "management of learning" to consider the reasons for resource adoption, studying how these instructors think about the resources they use. We also consider how instructors, students, and resources are reported to interact in multivariable calculus. Findings suggest that the instructors' concern for students' learning and their conviction that visualization is crucial in multivariable calculus moved them to explore and adopt different resources, especially ones that were free and easy to use. However, visualization was not the only spatial literacy aspect considered. As the instructors gained more experience with the instructional resources they were using, they reported adopting more student-centered use of these resources that allowed them to do more than facilitate visualization during a lecture. The resources began serving as referents for students as they communicated and reasoned about tasks with the instructor as well as among themselves.