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Jean Marie Linhart – International Journal of Mathematical Education in Science and Technology, 2024
The historic total global human population dataset is available on Wikipedia and provides an opportunity for modelling with simple models such as the exponential and logistic differential equations for population. Using the per-capita population growth rate (PPGR) predicted by these two models and estimated PPGR from the data, we are able to…
Descriptors: Calculus, Population Growth, Mathematical Models
Samuel Cuthbertson; Mark Ian Nelson – International Journal of Mathematical Education in Science and Technology, 2025
We adapt the Lanchester combat model to represent conflict between vampires and humans. It is assumed that vampires attack humans during the hours of darkness whilst humans attack vampires during the hours of light. The right-hand side of the differential equation model therefore depends upon the hour of the day. A key insight is that to answer…
Descriptors: War, Mathematical Models, Calculus, Problem Solving
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
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
Viktoria Savatorova; Aleksei Talonov – International Journal of Mathematical Education in Science and Technology, 2024
We present an example of one of the modelling projects we assign to students in our differential equations classes. Students are asked to determine how to run a cost-efficient hot water heating system. We consider a cylindrical tank filled with water and heated by a heating element immersed in it. Together with students we discuss physical laws…
Descriptors: Mathematics Instruction, Calculus, Mathematical Models, Heat
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
Oehrtman, Michael; Simmons, Courtney – International Journal of Research in Undergraduate Mathematics Education, 2023
Prior research on students' productive understandings of definite integrals has reasonably focused on students' meanings associated to components and relationships within the standard definition of a limit of Riemann sums. Our analysis was aimed at identifying (i) the broader range of productive quantitative meanings that students invoke and (ii)…
Descriptors: Mathematics Skills, Mathematical Models, Mathematical Concepts, Calculus
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
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
Puleng Motseki; Kakoma Luneta – African Journal of Research in Mathematics, Science and Technology Education, 2024
Among the problems identified at Technical and Vocational Education and Training (TVET) colleges, low achievement in mathematical subjects is the most prominent one. This paper documents a qualitative case study undertaken at TVET College in Gauteng with the purpose of exploring the National Certificate Vocational (NC(V)) Level 4 students' errors…
Descriptors: Vocational Education, Student Reaction, Low Achievement, Mathematics Achievement
Shophika Vaithyanathasarma; France Caron; Geneviève Bistodeau-Gagnon; Jacques Bélair – International Journal of Mathematical Education in Science and Technology, 2024
The emergence of COVID-19 favoured the development at Université de Montréal of an educational initiative aimed at promoting modelling and simulation in teaching and learning postsecondary mathematics. In our learning activities, modelling is not reduced to curve fitting; software is used and questions are asked to get a deeper understanding of…
Descriptors: Foreign Countries, Mathematical Models, COVID-19, Pandemics