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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)

Aysel Sen Zeytun; Bulent Cetinkaya; Ayhan Kursat Erbas – International Journal of Mathematical Education in Science and Technology, 2024

This study investigated the sources of difficulties experienced by prospective teachers in mathematical modelling in the context of a semester-long course on mathematical modelling for teachers. The data reported in this study were collected from six prospective teachers through in-depth semi-structured interviews supported by audio and videotaped…

Descriptors: Mathematical Models, Preservice Teachers, Mathematics Instruction, Teacher Education Programs

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

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

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)

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

Glenn Ledder; Stefano Manzoni – International Journal of Mathematical Education in Science and Technology, 2024

Decomposition of organic matter controls the flow of carbon and nutrients in terrestrial and aquatic ecosystems. Several kinetic laws have been proposed to describe decomposition rates, but they neglect adaptation of the microbial decomposer to environmental conditions. Here we formalise decomposition as an optimal control problem by assuming that…

Descriptors: Microbiology, Calculus, Undergraduate Students, Barriers

Mark McCartney – International Journal of Mathematical Education in Science and Technology, 2024

Using the sawtooth map as the basis of a coupled map lattice enables simple analytic results to be obtained for the global Lyapunov spectra of a number of standard lattice networks. The results presented can be used to enrich a course on chaos or dynamical systems by providing tractable examples of higher dimensional maps and links to a number of…

Descriptors: Maps, Mathematics Instruction, Mathematics Activities, Matrices

Aaron E. Naiman – International Journal of Mathematical Education in Science and Technology, 2024

We automate and randomize the building of linear systems with a parameter, appropriate for assigning to students. When the parameter takes on a specific value, the system has no solutions. When the parameter takes on a different value, the system has an infinite number of solutions.

Descriptors: Mathematics Instruction, Advanced Courses, Teaching Methods

Fabiana Zama – International Journal of Mathematical Education in Science and Technology, 2024

This paper describes a teaching experiment in a Numerical Methods course for Master of Science students. The experiment uses scientific papers to develop modelling studies in the context of wine fermentation microbial interactions. The course involves theoretical and laboratory classes that focus on implementing numerical methods using Matlab for…

Descriptors: Masters Programs, Mathematical Models, Graduate Students, Microbiology

Michael A. Rother – International Journal of Mathematical Education in Science and Technology, 2024

A straightforward experimental set-up, requiring a two-liter bottle, a ruler and a stopwatch, is used to provide data appropriate for modelling with Torricelli's Law in the simplest case, and a more sophisticated differential equation when losses are taken into account and a pipe extension is considered. With only an exit hole included in the…

Descriptors: Science Experiments, Science Education, Scientific Principles, Equations (Mathematics)

Alonso Ogueda-Oliva; Padmanabhan Seshaiyer – International Journal of Mathematical Education in Science and Technology, 2024

In this paper, we introduce novel instructional approaches to engage students in using modelling with data to motivate and teach differential equations. Specifically, we introduce a pedagogical framework that will execute instructional modules to teach different solution techniques for differential equations through repositories and notebook…

Descriptors: Mathematical Models, Equations (Mathematics), Mathematics Instruction, Learning Modules

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

Ana Isabel Sacristán; Marisol Santacruz-Rodríguez – International Journal of Mathematical Education in Science and Technology, 2024

This paper reports some results of a study on how Colombian primary-school teachers, experienced in the use of technological tools, integrate digital resources into their practice. Specifically, we investigate the processes of selection and integration (including appropriation and orchestration) of these resources in the teaching of geometry. We…

Descriptors: Foreign Countries, Elementary School Teachers, Grade 1, Grade 5

Nour Awni Albelbisi; Ahmad Samed Al-Adwan; Akhmad Habibi; Shahid Rasool – International Journal of Mathematical Education in Science and Technology, 2024

The present paper aims at investigating the relationship between students' attitudes toward online homework use and mathematics anxiety among secondary school students. In this study, a model has been proposed by integrating the technology acceptance model (TAM) with mathematics anxiety theory. Three hundred and forty-five secondary school…

Descriptors: Student Attitudes, Anxiety, Homework, Secondary School Students