Calculus is traditionally tested, at least in part, by a closed book written examination taken under secure conditions. In March 2020, two-thirds of the way through a vector calculus course, our institution went into lockdown and all teaching and assessment had to shift online. While some teachers insisted that remotely written non-proctored…

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

Previous work has looked at the relationship between high school preparation and student performance in calculus-based introductory mechanics (physics 1) courses. Here, we extend that work to look at performance in introductory calculus-based electricity and magnetism (physics 2), and we look at the significance of what college math courses have…

Dynamic visual tools such as MATLAB have inbuilt features which are believed to be able to empower students to learn through the visualisation of three-dimensional objects. While student learning through MATLAB has been investigated regarding students in urban settings, only a handful of studies have investigated how MATLAB can assist students in…

Vector calculus and multivariable coordinate systems play a large role in the understanding and calculation of much of the physics in upper-division electricity and magnetism. Differential vector elements represent one key mathematical piece of students' use of vector calculus. In an effort to examine students' understanding of non-Cartesian…

Recreating the social aspects of face-to-face teaching in an online environment became more challenging in the midst of the COVID-19 pandemic. With limited or no face-to-face interaction with students, lecturers had to explore alternative ways to recreate aspects of an engaging and supportive face-to-face learning environment. This article focuses…

Classic stock portfolio analysis provides an applied context for Lagrange multipliers that undergraduate students appreciate. Although modern methods of portfolio analysis are beyond the scope of vector calculus, classic methods reinforce the utility of this material. This paper discusses how to introduce classic stock portfolio analysis in a…

In this paper we present two simulations designed with GeoGebra that illustrate dynamically a key concept in Vector Calculus: line integrals of vector fields, along with other associated mathematical properties and applications. Students are not required to know the GeoGebra environment: a user-friendly interface with buttons, functionalities and…

The distant magnetic field of a magnetic dipole is usually derived via the magnetic vector potential and substantial vector calculus. This paper presents an alternate proof that is less mathematically intensive, and that ties together various problem-solving tricks (the principle of virtual work, observation that only instantaneous quantities…

Articulated pedagogical and didactic strategies allow improving academic quality and strengthen individual and institutional cognitive processes such as student retention. Mathematical modelling, articulated with complementary actions, contributes to teaching and learning processes within situations that go beyond the classroom since they are…

Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven…

This article explores the conceptual challenges that engineering students encounter with double integrals in a vector calculus course. Drawing on previous literature and utilising APOS (Activity- Process- Objects- Schema) as a theoretical framework, this study investigates the difficulties that students face in understanding and applying double…

A more effective math education has never been more pressing than in today's world. However, it is no mystery that students continue to struggle with basic mathematics concepts, let alone more advanced math such as Pre-Calculus. Thus, in the present study, two Pre-Calculus math classrooms were randomly assigned to either a flipped classroom model…

This study aimed to better understand the effect that the flipped method of instruction has on students' learning approaches using interactive math lecture videos in a second-year vector calculus course. Three hypotheses were tested to determine if students' perceptions of their level of active engagement, the number of interactive lecture videos…

In this article, we discuss the development and the administration of a multiple-choice test, which we named "Test of Calculus and Vectors in Mathematics and Physics" (TCV-MP), aimed at comparing students' ability to answer questions on derivatives, integrals, and vectors in a purely mathematical context and in the context of physics.…