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LeGresley, Sarah E.; Delgado, Jennifer A.; Bruner, Christopher R.; Murray, Michael J.; Fischer, Christopher J. – Physical Review Physics Education Research, 2019

Here we demonstrate the benefits of a new curriculum for introductory calculus-based physics that motivates classical mechanics using a modified version of Hamiltonian mechanics. This curriculum shifts the initial focus of instruction away from forces and the associated vector mathematics, which are known to be problematic for students, to the…

Descriptors: Undergraduate Students, College Science, Science Instruction, Introductory Courses

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

Schutera, Stefanie; Schnierle, Marc; Wu, Mathilde; Pertzel, Tim; Seybold, Jonathan; Bauer, Patricia; Teutscher, Dennis; Raedle, Matthias; Heß-Mohr, Natascha; Röck, Sascha; Krause, Mathias J. – Education Sciences, 2021

Learning content in mathematics, such as vector geometry, is still predominantly taught in an abstract manner, as the visualization and interaction of three-dimensional problems are limited with classical forms of teaching such as blackboard lessons or exercise sheets. This research article proposes the use of augmented reality (AR) in mathematics…

Descriptors: Mathematics Instruction, Computer Simulation, Geometry, Visual Aids

Martin-Gonzalez, Anabel; Chi-Poot, Angel; Uc-Cetina, Victor – Innovations in Education and Teaching International, 2016

Augmented reality (AR) is one of the emerging technologies that has demonstrated to be an efficient technological tool to enhance learning techniques. In this paper, we describe the development and evaluation of an AR system for teaching Euclidean vectors in physics and mathematics. The goal of this pedagogical tool is to facilitate user's…

Descriptors: Teaching Methods, Mathematics Instruction, Physics, Science Instruction

Mutambara, Lillias; Bansilal, Sarah – African Journal of Research in Mathematics, Science and Technology Education, 2019

This exploratory study investigated 10 pre-service mathematics students' understanding of vector subspaces at a university in Zimbabwe. The study involved an in-depth document analysis of the students' written responses to five items based on the vector subspace concept. An APOS (Action--Process--Object--Schema) approach was used to identify the…

Descriptors: Preservice Teachers, Mathematics Teachers, Mathematical Concepts, Concept Formation

Craig, Tracy S. – International Journal of Mathematical Education in Science and Technology, 2017

The notation for vector analysis has a contentious nineteenth century history, with many different notations describing the same or similar concepts competing for use. While the twentieth century has seen a great deal of unification in vector analysis notation, variation still remains. In this paper, the two primary notations used for expressing…

Descriptors: College Mathematics, Mathematics Instruction, Mathematical Concepts, Algebra

Dewi, Irmawati Liliana Kusuma; Zaenuri; Dwijanto; Mulyono – European Journal of Educational Research, 2021

This research is motivated by a linear equations system, which is the basis for studying necessary linear algebra materials, such as rank, range, linear independent/dependent, linear transformations, characteristic values and vectors. There are still prospective mathematics teachers who have difficulty solving linear equations system and…

Descriptors: Foreign Countries, Preservice Teachers, Mathematics Education, Mathematical Concepts

Johansson, B. Tomas – International Journal of Mathematical Education in Science and Technology, 2019

A method based on oblique projection is presented for construction of sundials. The derived formulas are classical, but usage of vectors and projections renders a coherent presentation rather than a number of special cases. The presented work is aimed to be useful for those taking a beginning module on vector algebra.

Descriptors: Mathematics Instruction, Algebra, Computation, Mathematical Formulas

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

The Characterization and Evolution of Strategies about Vector Equations in the Game "Vector Unknown"

Mauntel, Matthew; Levine, Benjamin; Plaxco, David; Zandieh, Michelle – Digital Experiences in Mathematics Education, 2021

We present results of a grounded analysis of individual interviews in which students play Vector Unknown -- a digital game designed to introduce visualizing vectors, scaling vectors, vector addition, and vector equations, attending to the geometric and algebraic representations of vectors. The game was designed to be used at the beginning of a…

Descriptors: Mathematics Education, Mathematics Activities, Educational Games, Computer Games

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

Kwon, Oh Hoon – ProQuest LLC, 2012

This dissertation documents a new way of conceptualizing vectors in college mathematics, especially in geometry. First, I will introduce three problems to show the complexity and subtlety of the construct of vectors with the classical vector representations. These highlight the need for a new framework that: (1) differentiates abstraction from a…

Descriptors: Mathematics Instruction, Geometric Concepts, Geometry, Teaching Methods

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

Singh, I.; Khun, K. Khun; Kaur, B.; Kaur, H.; Singh, T. – Physics Education, 2021

This paper describes a way to simulate and visualise 3D representations of the resultant electric field vector propagation for plane, circular and elliptically polarised waves. These polarisation states are obtained by the superposition of two coherent linearly polarised waves oscillating in two mutually perpendicular directions. The required data…

Descriptors: Computer Simulation, Visualization, Physics, Scientific Concepts

Saracoglu, Hanife; Kol, Özge – Asia-Pacific Forum on Science Learning and Teaching, 2018

In this study, it is aimed to reveal math teachers' knowledge level and misconceptions about vectors. The study was conducted with the participation of 66 teacher candidates in different nine universities. As for data collection tool, a questionnaire of 6 open-ended questions was used, related to basic knowledge about vector magnitude, addition,…

Descriptors: Preservice Teachers, Mathematics Teachers, Algebra, Geometric Concepts