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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
Kontorovich, Igor'; Li, Tianqing – International Journal of Science and Mathematics Education, 2023
Research into didactics of calculus has maintained a long-standing interest in students' grasp of the relations between definite integrals and areas. This study comes to contribute to this line of research by unpacking how students use the concept of area to find definite integrals. Specifically, we focus on mathematical situations where the…
Descriptors: Undergraduate Students, Calculus, Graphs, Mathematical Models
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)
Imre Kocsis; Sandor Hajdu; Robert Mikuska; Peter Korondi – IEEE Transactions on Education, 2025
We have introduced a novel approach to competency-based education in mechatronics from the undergraduate to the postgraduate level. What distinguishes this approach is the integration of modeling and control of sampled systems right from the beginning of the undergraduate education. It is achieved by changing the structure of the first-semester…
Descriptors: Competency Based Education, Undergraduate Study, Electromechanical Technology, Calculus
Jaleh Rezaei; Nasim Asghary – International Journal of Mathematical Education in Science and Technology, 2025
Mathematical modelling is an interlinking process between mathematics and real-world problems that can be applied as a means to increase motivation, develop cognitive competencies, and enhance the ability to transfer mathematical knowledge to other areas of science, such as engineering disciplines. This study was designed to investigate the effect…
Descriptors: Calculus, Mathematical Models, Mathematics Instruction, Problem Solving
Jennifer Czocher; Elizabeth Roan; Sindura Subanemy Kularajan – PRIMUS, 2024
We studied aspects of undergraduate STEM majors' mathematical reasoning as they engaged in mathematically modeling a predator-prey scenario. The study used theoretical viewpoints on quantitative reasoning to inform scaffolding moves that would assist modelers in overcoming blockages to their mathematization of real-world problems. Our contribution…
Descriptors: Undergraduate Students, Mathematical Models, Scaffolding (Teaching Technique), Calculus
Kalman, Dan – PRIMUS, 2023
In the precalculus curriculum, logistic growth generally appears in either a discrete or continuous setting. These actually feature distinct versions of logistic growth, and textbooks rarely provide exposure to both. In this paper, we show how each approach can be improved by incorporating an aspect of the other, based on a little known synthesis…
Descriptors: Mathematics Education, Calculus, Teaching Methods, Mathematical Models
T. Clark – PRIMUS, 2024
A standard element of the undergraduate ordinary differential equations course is the topic of separable equations. For instructors of those courses, we present here a series of novel modeling scenarios that prove to be a compelling motivation for the utility of differential equations. Furthermore, the growing complexity of the models leads to the…
Descriptors: Mathematics Instruction, Undergraduate Study, College Mathematics, Equations (Mathematics)
Jennifer A. Czocher; Elizabeth Roan; Abigail Quansah; Andrew Baas – International Journal of Mathematical Education in Science and Technology, 2024
Students exit calculus with understandings of change that want for conceptual depth and are disconnected from real-world contexts. In this paper, we present a problem that will develop their skills in using "change" concepts for learning differential equations through modelling. The problem comes from a qualitative study of how STEM…
Descriptors: STEM Education, Calculus, Undergraduate Students, Modeling (Psychology)
Minchul Kang – International Journal of Mathematical Education in Science and Technology, 2024
Since the introduction by Kermack and McKendrick in 1927, the Susceptible-Infected-Recovered (SIR) epidemic model has been a foundational model to comprehend and predict the dynamics of infectious diseases. Almost for a century, the SIR model has been modified and extended to meet the needs of different characteristics of various infectious…
Descriptors: Calculus, Communicable Diseases, Prediction, Mathematics Activities
Christian Farkash; Michael Storm; Thomas Palmeri; Chunhui Yu – Mathematics Teaching Research Journal, 2024
Several studies indicate that exploring mathematical ideas by using more than one approach to prove the same statement is an important matter in mathematics education. In this work, we have collected a few different methods of proving the multinomial theorem. The goal is to help further the understanding of this theorem for those who may not be…
Descriptors: Undergraduate Students, College Mathematics, Mathematics Skills, Mathematical Models
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
Using Physical Simulations to Motivate the Use of Differential Equations in Models of Disease Spread
Elizabeth G. Arnold; Elizabeth A. Burroughs; Owen Burroughs; Mary Alice Carlson – International Journal of Mathematical Education in Science and Technology, 2024
The SIR model is a differential equations based model of the spread of an infectious disease that compartmentalises individuals in a population into one of three states: those who are susceptible to a disease (S), those who are infected and can transmit the disease to others (I), and those who have recovered from the disease and are now immune…
Descriptors: Calculus, Communicable Diseases, Disease Control, Simulation
López-Reyes, Luis Javier – World Journal on Educational Technology: Current Issues, 2022
This paper presents a didactic proposal designed through the active methodology of collaborative learning to analyse the effect of the use of numerical simulation of a mathematical model on the learning of differential equations in engineering students. A mathematical model of a vibrating string was used, and the Octave Online platform was used…
Descriptors: Cooperative Learning, Calculus, Engineering Education, Mathematical Models