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Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita – International Journal of Mathematical Education in Science and Technology, 2018

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…

Descriptors: Calculus, Algebra, Geometric Concepts, Mathematics Instruction

Kaplan, Samuel R. – PRIMUS, 2015

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…

Descriptors: Undergraduate Study, College Mathematics, Mathematics Instruction, Calculus

Bollen, Laurens; van Kampen, Paul; De Cock, Mieke – Physical Review Special Topics - Physics Education Research, 2015

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…

Descriptors: Foreign Countries, Calculus, Electronics, Magnets

Schermerhorn, Benjamin P.; Thompson, John R. – Physical Review Physics Education Research, 2019

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…

Descriptors: Physics, Science Instruction, Student Attitudes, Calculus

Burkholder, Eric W.; Murillo-Gonzalez, Gabriel; Wieman, Carl – Physical Review Physics Education Research, 2021

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…

Descriptors: Physics, Science Instruction, Introductory Courses, Calculus

Wang, Jinhui – Physics Teacher, 2020

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…

Descriptors: Physics, Magnets, Calculus, Mathematical Logic

Ponce Campuzano, J. C.; Roberts, A. P.; Matthews, K. E.; Wegener, M. J.; Kenny, E. P.; McIntyre, T. J. – International Journal of Mathematical Education in Science and Technology, 2019

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…

Descriptors: Visualization, Computer Simulation, Calculus, Mathematical Concepts

Añino, María Magdalena; Merino, Gabriela; Miyara, Alberto; Perassi, Marisol; Ravera, Emiliano; Pita, Gustavo; Waigandt, Diana – International Journal of Mathematical Education in Science and Technology, 2014

This paper describes an action-research experience carried out with second year students at the School of Engineering of the National University of Entre Ríos, Argentina. Vector calculus students played an active role in their own learning process. They were required to present weekly reports, in both oral and written forms, on the topics studied,…

Descriptors: Action Research, Foreign Countries, College Students, Mathematical Concepts

Glynn-Adey, Parker – International Journal of Mathematical Education in Science and Technology, 2021

In this classroom note, we describe the use of a wiki to aggregate student solutions to calculation-based mathematics problems. We outline the setup of the wiki used to support this project, the administrative issues involved in running a wiki, and student reaction to the wiki project. We will describe how students participated, and were assessed,…

Descriptors: Teaching Methods, Mathematics Instruction, Collaborative Writing, Educational Technology

Spotts, Jeffrey D.; Gutierrez de Blume, Antonio P. – SAGE Open, 2020

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…

Descriptors: Teaching Methods, Mathematics Instruction, Pilot Projects, Calculus

Carli, Marta; Lippiello, Stefania; Pantano, Ornella; Perona, Mario; Tormen, Giuseppe – Physical Review Physics Education Research, 2020

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.…

Descriptors: Mathematics Tests, Science Tests, Multiple Choice Tests, Calculus

Ting, Fridolin Sze Thou; Shroff, Ronnie H.; Lam, Wai Hung; Chin, David C. W. – Journal on Excellence in College Teaching, 2020

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…

Descriptors: Flipped Classroom, STEM Education, Mathematics Instruction, Instructional Effectiveness

Voigt, Matthew; Fredriksen, Helge; Rasmussen, Chris – ZDM: The International Journal on Mathematics Education, 2020

While the number of studies of flipped classrooms has increased, they have primarily addressed the efficacy of using such an approach on student outcomes, often failing to account for the classroom activities and learning theories used to design the curriculum. This study begins to fill this gap in the literature by uniting the at-home video and…

Descriptors: Foreign Countries, Blended Learning, Curriculum Design, Heuristics

Yaacob, Yuzita; Wester, Michael; Steinberg, Stanly – International Journal for Technology in Mathematics Education, 2010

This paper presents a prototype of a computer learning assistant ILMEV (Interactive Learning-Mathematica Enhanced Vector calculus) package with the purpose of helping students to understand the theory and applications of integration in vector calculus. The main problem for students using Mathematica is to convert a textbook description of a…

Descriptors: Textbooks, Problem Solving, Calculus, Computer Assisted Instruction

Padyala, Radhakrishnamurty – Physics Teacher, 2020

The family of paths of ideal projectiles shot from a point with a common value of speed and at different angles to the horizontal has several interesting properties associated with it. For example, Chapou et al. have shown that an ellipse passes through the apexes of these parabolic paths. This observation encouraged us to further explore this…

Descriptors: Physics, Motion, Mechanics (Physics), Science Instruction