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Anna McAllister; Mark McCartney; David H. Glass – International Journal of Mathematical Education in Science and Technology, 2024
Discrete time models, one linear and one non-linear, are investigated, both with a herbivore species that consumes a basal food source species. Results are presented for coexistence of the species and to illustrate chaotic behaviour as parameters are varied in the non-linear model. The results indicate the benefit of fertilization in terms of the…
Descriptors: Lesson Plans, Mathematics Activities, Mathematics Instruction, Mathematical Models
Peter Rowlett; Chris Graham; Christian Lawson-Perfect – International Journal of Mathematical Education in Science and Technology, 2025
Partially automated assessment is implemented via the 'Printable worksheet' mode in the Numbas e-assessment system to create a mathematical modelling worksheet which is individualised with random parameters but completed and marked as if it were a non-automated piece of coursework, preserving validity while reducing the risk of academic misconduct…
Descriptors: Automation, Worksheets, Mathematical Models, Computer Assisted Testing
Mehmet Pakdemirli – International Journal of Mathematical Education in Science and Technology, 2025
The hanging rope problem is considered. The rope is subject to rotation with the rotation axis being parallel to the rope. Using a continuum model and the basic principles of dynamics, the differential equation governing the motion is derived. The dynamic equilibrium case without vibrational motion is assumed in deriving the equation. The equation…
Descriptors: Mathematical Models, Calculus, Motion, College Mathematics
Leao, Aline A. S.; Oliveira Filho, Adaiton M.; Toledo, Franklina M. B. – International Journal of Mathematical Education in Science and Technology, 2023
The purpose of this note is to describe a classroom activity that can be used in introductory Operations Research courses. It consists of modelling a one-dimensional puzzle using mathematical programming to produce glider models. The exercise is designed to motivate the students in solving a problem with the opportunity of producing by themselves…
Descriptors: Puzzles, Programming, Class Activities, Introductory Courses
Adrianne L. Jenner; Pamela M. Burrage – International Journal of Mathematical Education in Science and Technology, 2024
Mathematics provides us with tools to capture and explain phenomena in everyday biology, even at the nanoscale. The most regularly applied technique to biology is differential equations. In this article, we seek to present how differential equation models of biological phenomena, particularly the flow through ion channels, can be used to motivate…
Descriptors: Cytology, Mathematical Models, Prediction, Equations (Mathematics)
Yves Nievergelt – International Journal of Mathematical Education in Science and Technology, 2024
On 24 June 1994 at Fairchild Air Force Base, during practice for an air show, a low-flying B-52H aircraft banked its wings vertically and crashed. Emphasizing the activity of modeling drag and gravity, these notes examine the possibility of recovery with several models. First, with algebra, historical data lead to a model where in a free fall near…
Descriptors: Air Transportation, Mathematical Models, Prevention, Calculus
Lie Group Method for Constructing Integrating Factors of First-Order Ordinary Differential Equations
Feng, Yuqiang; Yu, Jicheng – International Journal of Mathematical Education in Science and Technology, 2023
This paper introduces the basic knowledge of integral factors of first-order ordinary differential equations and Lie symmetry analysis. It then discusses the principle of constructing an integral factor of the first-order ordinary differential equation by the Lie symmetric method. Finally, it presents some examples to show the process of…
Descriptors: Equations (Mathematics), Mathematical Concepts, Problem Solving, Algebra
Ismael Cabero; Carl Winsløw – International Journal of Mathematical Education in Science and Technology, 2025
The notion of function is central in all of the secondary curriculum, and indeed functional models appear in almost all higher education that is based on mathematics. However, in secondary education, functions usually appear in restricted and somewhat sterile forms. In this (mostly theoretical) paper, we present a proposal -- exemplified by a…
Descriptors: Mathematics Instruction, Mathematical Models, Teaching Methods, Secondary School Mathematics
Cumber, Peter – International Journal of Mathematical Education in Science and Technology, 2023
The dynamics of a simple pendulum are often presented to undergraduate engineering students in introductory courses in dynamics. It is usually the first dynamic system considered by students that is modelled by a differential equation. This paper presents the standard material given to students. It is fair to say that students are accepting this…
Descriptors: Motion, Scientific Concepts, Undergraduate Students, Engineering Education
Milici, Pietro; Plantevin, Frédérique; Salvi, Massimo – International Journal of Mathematical Education in Science and Technology, 2022
We propose an original machine that traces conics and some transcendental curves (oblique trajectories of confocal conics) by the solution of inverse tangent problems. For such a machine, we also provide the 3D-printable model to be used as an intriguing supplement for geometry, calculus, or ordinary differential equations classes.
Descriptors: Computer Peripherals, Printing, Geometry, Geometric Concepts
G. R. Fulford – International Journal of Mathematical Education in Science and Technology, 2024
Mathematical modelling has great potential to motivate students towards studying mathematics. This article discusses several different approaches to integrating research work with a second-year undergraduate, mathematical modelling subject. I found sourcing papers from the areas of epidemiology and ecology to be a fruitful source area,…
Descriptors: Mathematical Models, Undergraduate Students, College Mathematics, Case Method (Teaching Technique)
Forest Mannan – International Journal of Mathematical Education in Science and Technology, 2024
This article considers starting with an existing SIMIODE modeling scenario [Winkel, B. (2015). 1-031-CoolIt-ModelingScenario. SIMIODE (Version 2.0). "QUBES Educational Resources." https://doi.org/10.25334/3WG8-EC31] that develops Newton's law of cooling by considering data on the cooling of a beaker of water in a room, and expanding upon…
Descriptors: Calculus, Mathematical Models, Programming, Heat
Kerri Spooner – International Journal of Mathematical Education in Science and Technology, 2024
Gaining useful insight into real-world problems through mathematical modelling is a valued activity across several disciplines including mathematics, biology, computer science and engineering. Differential equations are a valuable tool used in modelling. Modelling provides a way for students to engage with differential equations within a…
Descriptors: Mathematical Models, Relevance (Education), Learning Experience, Calculus
Brian John Winkel – International Journal of Mathematical Education in Science and Technology, 2024
We present a complete, soup to nuts, modeling activity of a falling column of water. Many colleagues have used this material in teaching applications of first order separable differential equations. We describe how the material can be presented with students collecting their own data from online videos. One can then either offer the differential…
Descriptors: Calculus, Learner Engagement, Video Technology, Mathematical Concepts
Nelson, Mark Ian – International Journal of Mathematical Education in Science and Technology, 2021
A textbook model of a contagious disease, the dynamics of which are represented by the SIS epidemic model with saturating treatment, is considered. I show that this model, as originally formulated, is not dimensionally consistent. The model can be fixed by including a dimensional constant [alpha] of value one (with units individuals[superscript…
Descriptors: Textbooks, Models, Communicable Diseases, Epidemiology