Refining Calculus Pedagogy
Parthasarathy Srinivasan

TL;DR
This paper proposes integrating computational tools like Gaussian quadrature and series analysis into calculus teaching to enhance understanding and accessibility, especially in multivariable contexts.
Contribution
It introduces easy-to-develop computational tools and methods, such as Gaussian quadrature, to improve calculus pedagogy and address gaps in student comprehension.
Findings
Gaussian quadrature can be developed using basic linear algebra.
The method extends to higher-dimensional integration.
Series discussed may be more useful than traditional ones.
Abstract
There have been several modifications of how basic calculus has been taught, but very few of these modifications have considered the computational tools available at our disposal. Here, we present a few tools that are easy to develop and use. Doing so also addresses a different way to view calculus, and attempts to fill the gaps in students' understanding of both differentiation and integration. We will describe the basics of both these topics in a way that might be much more useful and relevant to students, and hence possible ways in refining calculus pedagogy to make calculus more accessible to them. For integration, an elementary development of Gaussian quadrature using basic linear algebra is presented. This numerical method can be extended to integrate functions over various domains in higher dimensions, a subject that is not currently well covered in multivariable calculus or…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematics Education and Teaching Techniques
