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College calculus plays an important role in STEM students’ degree and career aspirations. One of the key factors considered in assessing a student’s ability to be successful in calculus is their proficiency in topics from prior mathematics courses such as algebra and precalculus. This study set out to examine the impact of students’ precalculus proficiency on their achievement in introductory calculus based on their classroom environment. Results from the implementation of the Modeling Practices in Calculus (MPC) model, an innovative, active learning approach, are presented. Using a randomized-controlled trial research design, students were randomly assigned to MPC and traditional, lecture-based calculus sections. The Precalculus Concept Assessment inventory was administered to gauge students’ precalculus proficiency. We found that students exposed to the MPC model were more likely to be successful in their calculus course, even if they began with low precalculus proficiency. Also, students enrolled in the MPC sections saw significant growth in their precalculus proficiency from the beginning to the end of the semester. Additionally, we observed this model providing support for students in key demographics (low proficiency, female, underclassmen) in terms of the development of their proficiency that they may not receive in traditional classrooms.
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Exterior Calculus in Graphics: Course Notes for a SIGGRAPH 2023 Course
The demand for a more advanced multivariable calculus has rapidly increased in computer graphics research, such as physical simulation, geometry synthesis, and differentiable rendering. Researchers in computer graphics often have to turn to references outside of graphics research to study identities such as the Reynolds Transport Theorem or the geometric relationship between stress and strain tensors. This course presents a comprehensive introduction to exterior calculus, which covers many of these advanced topics in a geometrically intuitive manner. The course targets anyone who knows undergraduate-level multivariable calculus and linear algebra and assumes no more prerequisites. Contrary to the existing references, which only serve the pure math or engineering communities, we use timely and relevant graphics examples to illustrate the theory of exterior calculus. We also provide accessible explanations to several advanced topics, including continuum mechanics, fluid dynamics, and geometric optimizations. The course is organized into two main sections: a lecture on the core exterior calculus notions and identities with short examples of graphics applications, and a series of mini-lectures on graphics topics using exterior calculus.
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- Award ID(s):
- 2239062
- PAR ID:
- 10500504
- Publisher / Repository:
- ACM
- Date Published:
- Journal Name:
- SIGGRAPH '23: ACM SIGGRAPH 2023 Conference Proceedings
- ISBN:
- 9798400701450
- Page Range / eLocation ID:
- 1 to 126
- Format(s):
- Medium: X
- Location:
- Los Angeles California
- Sponsoring Org:
- National Science Foundation
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