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…

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…

Cybersex is the use of the Internet and its services to achieve sexual arousal and pleasure. This use, however, can become excessive and uncontrolled. Common consequences of a problematic engagement in online sexual activities are the deterioration of real-life romantic relationships and the occurrence of sexual dysfunctions, even in young…

Mathematical modelling and modelling activities are important for making sense of mathematical concepts in different extracurricular and daily life contexts. However, teachers may have difficulties in designing these activities in a way to establish meaningful relationships with real life, in accordance with the modeling process and the objectives…

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…

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…

The study of learning behaviors with multi features is of great significance for interactive cooperation. The data prediction and decision are to realize the comprehensive analysis and value mining. In this study, hierarchical learning behavior based on feature cluster is proposed. Based on the massive data in interactive learning environment, the…

The utilization of modeling tools has gained significant attention recently. These models typically involve a series of partial differential equations, which can be challenging for novice modelers. This paper presented an approach in practical teaching of modeling tools for ion-exchange chromatography with three parts: model introduction, model…

This study aimed to observe the competencies of pre-service mathematics teachers in designing mathematical modeling tasks. The participants were 45 pre-service mathematics teachers enrolled in a Mathematics Education Theory course at a university in Seoul, South Korea. Data were collected from surveys and task development reports. The participants…

Researchers continue to choose PCA in scale development and adaptation studies because it is the default setting and overestimates measurement quality. When PCA is utilized in investigations, the explained variance and factor loadings can be exaggerated. PCA, in contrast to the models given in the literature, should be investigated in…

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…

This paper reports a study of 10 post-secondary STEM (Science, Technology, Engineering, Mathematics) instructors' beliefs about mathematical modelling and the role of mathematics in STEM coursework. The participants were selected from STEM disciplines that are atypical to the literature base (e.g. anthropology and geography), in order to extend…

The aim of this study is to investigate the production and dissemination of mathematical modeling-based projects by gifted students, intended to solve real-life problems, over the four-year Project Production and Management Program (PPMP). The longitudinal research methodology was utilized to examine the project production process among…

In this paper, we discuss how a professor could have students, using rational and exponential functions, develop models for several different density-dependent populations based on characteristics of the species. Students would then need to choose an appropriate method from among three different analytic methods (find a solution, phase-line…

Differential equations (DEs) are a powerful tool for modeling real-world contexts. Most research in this area has examined students' understanding and reasoning with pre-packaged DEs, with little attention being given to setting up sophisticated DEs to model complicated real-world situations. This study contributes through a collective case study…