Designing videos for undergraduate mathematics

TL;DR

This paper discusses the design of pedagogical videos for teaching elementary differential equations to undergraduates, emphasizing the importance of rigorous content tailored to the medium's specificities.

Contribution

It introduces a pedagogical approach for creating mathematical videos that balance rigor and accessibility, highlighting their role beyond traditional oral or classroom methods.

Findings

Videos provide rigorous mathematical content tailored for undergraduates.

Pedagogical videos should be distinct from oral manuals or standard lessons.

The approach enhances understanding of differential equations through tailored visual content.

Abstract

This article presents some technical and pedagogical considerations about a series of videos made by the authors to teach elementary theory of differential equations. Intended to be a pedagogical support for undergraduate students of scientific curricula, these videos provide rigorous mathematical contents in a form that takes into account the specificities of the tool. Videos for teaching mathematics should be seen as a specific way for providing rigorous scientific content to learners, and should not be reduced to oral manuals or standard classroom lessons. Research Contribution: Arij Bouzelmate and Beno{\^i}t Rittaud are searcher and teacher in mathematics. Arij Bouzelmate is a specialist in partial differential equations and director of LaR2A. Beno{\^i}t Rittaud is a specialist in discrete mathematics and is involved in popularization of mathematics.