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Brandt, Keith – PRIMUS, 2012

This article points out a simple connection between related rates and differential equations. The connection can be used for in-class examples or homework exercises, and it is accessible to students who are familiar with separation of variables.

Descriptors: Equations (Mathematics), Calculus, Mathematics Instruction, Teaching Methods

Fisher, Robert J. – Chemical Engineering Education, 2019

Our exponentially increasing knowledge base creates many new technology challenges. Academia must therefore respond emphatically. Educating rising professionals to successfully confront these future difficulties requires innovative curricula challenges. A successful adaptation integrates STEM program protocols into core courses. Embracing…

Descriptors: Science Instruction, Teaching Methods, Mathematical Concepts, Engineering Education

Debnath, L. – International Journal of Mathematical Education in Science and Technology, 2013

This article deals with a short historical introduction to determinants with applications to the theory of equations, geometry, multiple integrals, differential equations and linear algebra. Included are some properties of determinants with proofs, eigenvalues, eigenvectors and characteristic equations with examples of applications to simple…

Descriptors: Equations (Mathematics), Geometry, Calculus, Algebra

Bollen, Laurens; van Kampen, Paul; De Cock, Mieke – Physical Review Physics Education Research, 2018

We have developed, implemented, and assessed a teaching-learning sequence that aims to enhance students' understanding of the divergence and curl of electromagnetic fields. We designed guided-inquiry worksheets based on student difficulties we identified during semiquantitative and qualitative studies and discussions in the literature. A multiple…

Descriptors: Energy, Magnets, Teaching Methods, Concept Formation

Kose, Emek; Kunze, Jennifer – College Mathematics Journal, 2013

Students in college-level mathematics classes can build the differential equations of an energy balance model of the Earth's climate themselves, from a basic understanding of the background science. Here we use variable albedo and qualitative analysis to find stable and unstable equilibria of such a model, providing a problem or perhaps a…

Descriptors: College Mathematics, Mathematics Instruction, Equations (Mathematics), Climate

Winkel, Brian – International Journal of Mathematical Education in Science and Technology, 2012

We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course. This situation crosses falling body modelling in an upper level differential equations course into a modest discrete dynamical systems unit of a first-year mathematics course. (Contains 1 figure.)

Descriptors: Mathematics Instruction, Undergraduate Study, College Mathematics, Equations (Mathematics)

Kovacs, Zoltan – International Journal for Technology in Mathematics Education, 2010

The use of difference and differential equations in the modelling is a topic usually studied by advanced students in mathematics. However difference and differential equations appear in the school curriculum in many direct or hidden ways. Difference equations first enter in the curriculum when studying arithmetic sequences. Moreover Newtonian…

Descriptors: Equations (Mathematics), Computer Uses in Education, Computer Software, Mathematics Instruction

Camacho-Machín, M.; Guerrero-Ortiz, C. – International Journal of Mathematical Education in Science and Technology, 2015

The aim of this paper is to present and discuss some of the evidence regarding the resources that students use when they establish relationships between a contextual situation and an ordinary differential equation (ODE). We present research results obtained from work by seven students in a graduate level course in mathematics education, where they…

Descriptors: Equations (Mathematics), Mathematics Instruction, Graduate Students, College Science

Walsh, Jim; McGehee, Richard – College Mathematics Journal, 2013

A dynamical systems approach to energy balance models of climate is presented, focusing on low order, or conceptual, models. Included are global average and latitude-dependent, surface temperature models. The development and analysis of the differential equations and corresponding bifurcation diagrams provides a host of appropriate material for…

Descriptors: College Mathematics, Mathematics Instruction, Energy, Climate

Rasmussen, Chris – North American Chapter of the International Group for the Psychology of Mathematics Education, 2016

A challenge in mathematics education research is to coordinate different analyses to develop a more comprehensive account of teaching and learning. I contribute to these efforts by expanding the constructs in Cobb and Yackel's (1996) interpretive framework that allow for coordinating social and individual perspectives. This expansion involves four…

Descriptors: Mathematics Education, Teaching Methods, Mathematics Instruction, Mathematical Concepts

Bollen, Laurens; van Kampen, Paul; Baily, Charles; De Cock, Mieke – Physical Review Physics Education Research, 2016

Many students struggle with the use of mathematics in physics courses. Although typically well trained in rote mathematical calculation, they often lack the ability to apply their acquired skills to physical contexts. Such student difficulties are particularly apparent in undergraduate electrodynamics, which relies heavily on the use of vector…

Descriptors: Science Instruction, Magnets, Energy, Semi Structured Interviews

Raychaudhuri, Debasree – International Journal of Mathematical Education in Science and Technology, 2013

There are numerous theories that offer cognitive processes of students of mathematics, all documenting various ways to describe knowledge acquisition leading to successful transitions from one stage to another, be it characterized by Dubinsky's encapsulation, Sfard's reification or Piaget's equilibration. We however are interested in the following…

Descriptors: Undergraduate Students, College Mathematics, Mathematical Concepts, Calculus

Raychaudhuri, Debasree – International Journal of Mathematical Education in Science and Technology, 2014

Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of "reducing abstraction" maps the abstract nature of mathematics to the nature…

Descriptors: Abstract Reasoning, Equations (Mathematics), Mathematics Education, Undergraduate Students

Deakin, Michael A. B. – International Journal of Mathematical Education in Science and Technology, 2011

An earlier paper discussed the case of a flexible but inextensible membrane filled to capacity with incompressible fluid. It was found that the resulting shape satisfies a set of three simultaneous partial differential equations. This article gives a more general derivation of these equations and shows their form in an interesting special case.

Descriptors: Equations (Mathematics), Calculus, Mathematics Instruction, Mathematics Education

Beynon, Kenneth A.; Zollman, Alan – Investigations in Mathematics Learning, 2015

This mixed-methods study examines the conceptual understanding of limit among 22 undergraduate engineering students from two different sections of the same introductory differential equations course. The participants' concepts of limit (concept images and personal concept definitions) were examined using written tasks followed by one-on-one…

Descriptors: Undergraduate Students, Engineering Education, Community Colleges, Mixed Methods Research