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This article examines the relations between content, resource use, and the pedagogy of instructors in multivariable calculus. Content included topics that typically appear in multivariable calculus which were grouped into these general areas: introductory ideas, differential calculus, integral calculus, and vector calculus. The resources used included digital resources, 3D-printed models, and other physical resources. Pedagogy practices included both collaborative and individual in-class learning activities, instructor demonstrations, and homework. We also consider the instructor’s assessment of the activities they use. Data were obtained from three instructors working at three different types of institutions in the United States: a community college, a small selective undergraduate college, and a large comprehensive research university. The results provide information about instructional needs, as instructors implement resources in multivariable calculus, and about patterns related to the content they cover, the technology they use, and their pedagogical practices.
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Instructors’ resource use in multivariable calculus: A case study
This case study examines the relations between the instructional resources, the instructors’ pedagogy and the multivariable calculus content. The resources used included digital resources, 3D-printed models and other physical resources. Pedagogy practices included both collaborative and individual in-class learning activities, instructor demonstrations and homework. Content included topics that typically appear in multivariable calculus. The 35 specific topics were grouped into the general areas of introductory/foundational ideas, differential calculus, integral calculus and vector calculus. We also consider the instructor’s assessment of the activities they use. Data were obtained from three instructors working at three different types of institutions in the United States. The study finds that instructors use digital resources primarily for demonstrations; 3D-printed materials are more likely to be used in collaborative vs. individual learning opportunities; instructors design more activities for the introductory/foundational and differential calculus topic areas of the course; the integral calculus, and to an even greater degree, the vector calculus portions of the course are lacking in resource-supported activities and instructors sharing materials could be beneficial to others who are just beginning to incorporate the use of resources in their multivariable calculus teaching. The study suggests instructional needs and informs about instructor practices for multivariable calculus topics.
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- PAR ID:
- 10661778
- Publisher / Repository:
- International Journal of Mathematical Education in Science and Technology
- Date Published:
- Journal Name:
- International Journal of Mathematical Education in Science and Technology
- ISSN:
- 0020-739X
- Page Range / eLocation ID:
- 1 to 22
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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This article examines the relations between content, resource use, and the pedagogy of instructors in multivariable calculus. Content included topics that typically appear in multivariable calculus which were grouped into these general areas: introductory ideas, differential calculus, integral calculus, and vector calculus. The resources used included digital resources, 3D-printed models, and other physical resources. Pedagogy practices included both collaborative and individual in-class learning activities, instructor demonstrations, and homework. We also consider the instructor’s assessment of the activities they use. Data were obtained from three instructors working at three different types of institutions in the United States: a community college, a small selective undergraduate college, and a large comprehensive research university. The results provide information about instructional needs, as instructors implement resources in multivariable calculus, and about patterns related to the content they cover, the technology they use, and their pedagogical practices.more » « less
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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.more » « less
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Given the challenge of visualizing the main constructs of two-variable functions and their differential and integral calculus, it is important to consider the use and perceived potential of resources to contribute to students’ understanding of multivariable calculus. This case study considers how four instructors attempt to utilize resources in their multivariable calculus teaching and their motivations to do so. We study how these instructors think about the digital and non-digital resources that they use to foment students’ understanding. We also look at their reporting of the ways that instructors, students, and resources interact in multivariable calculus to determine if resource use is meant to facilitate visualization, reasoning, or communication. With this, the study proposes to contribute to the discussion of resource use in multivariable calculus.more » « less
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Given the challenge of visualizing the main constructs of two-variable functions and their differential and integral calculus, it is important to consider the use and perceived potential of resources to contribute to students’ understanding of multivariable calculus. This case study considers how four instructors attempt to utilize resources in their multivariable calculus teaching and their motivations to do so. We study how these instructors think about the digital and non-digital resources that they use to foment students’ understanding. We also look at their reporting of the ways that instructors, students, and resources interact in multivariable calculus to determine if resource use is meant to facilitate visualization, reasoning, or communication. With this, the study proposes to contribute to the discussion of resource use in multivariable calculus.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1080/0020739X.2025.2532172
