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…

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…

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…

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…

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…

This study examined seventh-grade students' emergent and progressive financial literacy in the context of risk and reward while working on two mathematical modelling tasks. The participants were six seventh-grade students identified as 'good at mathematics' by their teachers. The data sources comprised videotaped group discussions, group…

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…

The limitation of conventional visual acuity assessment, which primarily focuses on individual eye performance (monocular visual acuity tests). This study addresses this limitation by emphasizing the importance of binocular vision, where both eyes work together. Binocular vision provides numerous advantages, such as improved depth perception, a…

In this paper, we draw on recent research on so-called Fermi problems and situate the fundamental principles underlying this type of tasks and their use from a task design perspective. We use the models and modelling perspective on teaching and learning to elaborate on aspects related to the design of single-use, as well as sequences of, Fermi…

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…

Developing students' competence in algorithmic thinking is emerging as an objective of mathematics education, but despite its inclusion in mathematics curricula around the world, research into students' algorithmic thinking seems to be falling behind in this curriculum reform. The aim of this study was to investigate how the mathematical modelling…

Critical thinking is a key transversal competency of the 21st century, but some students have difficulty, especially during the transition to online learning due to the COVID-19 pandemic. This study aims to identify epistemological obstacles in critical thinking related to proof, generalization, alternative answers, and problem-solving. This…

The relevance of metacognition and mathematical modeling competencies to the development of good mathematics achievement throughout schooling is well-documented. However, few studies have explored the longitudinal relationship among metacognition, mathematical modeling competencies, and mathematics achievement. More importantly, the existing…