We present an intriguing topic in a mathematical modelling course where Lanchester models are taught to our students. Lanchester models are some of the earliest and most important models used for combat modelling. We describe modelling activities and the use of technology that can be implemented in teaching this topic in this paper.

The training of non-specialists, particularly engineers, in mathematics requires designing specific didactic proposals that make the importance of mathematics evident. One approach to creating such proposals consists in analyzing the mathematics used in authentic contexts of engineering research and then effectuating a didactic transposition to…

An educational lattice model is proposed for the investigation of the influence of the density and indirectly of the pressure on the chemical equilibrium of the ideal gas phase reaction A [equilibrium] 2B. The model can be introduced by a board game simulating a stochastic process. This game can also be used to set up a corresponding computer…

Developing models and using mathematics are two key practices in internationally recognized science education standards such as the Next Generation Science Standards (NGSS, 2013). In this paper, we used a virtual performance-based formative assessment to capture students' competencies at both "developing" and "evaluating"…

A discrete model of invasion by subversive alien bodysnatchers is constructed and analysed numerically as a proposed undergraduate project. Several extensions of the model are demonstrated, including a spatial system of ten planets arranged on a one-dimensional lattice, and we discuss some of the practical considerations that arise when…

In this paper, we present the development of an investigation on the promotion of covariational reasoning in high school students (14-15 years old) in Mexico. The study consists of designing and applying a sequence of didactic activities that simulate a real situation virtually. The activities are organized through a Hypothetical Learning…

Excluded-volume interactions are ubiquitous to modeling the average size of polymers in solution. This paper shows how simulations can be used by students to explore the emergence of mathematical scaling relations from excluded-volume interactions. Simulations provide robust visual representations of the system, and can be used to investigate a…

This study explores how pre-service mathematics teachers build alternative model simulations of real-world scenarios. Inclusion in the formal structures for wealth generation and accumulation is a fervently debated issue in South Africa. Share owning in companies listed on the Johannesburg Stock Exchange (JSE) in South Africa is one of many…

The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave,…

This article describes a modeling project the author did with his algebra, geometry, and applications students in grades 9, 10, and 11 as an enrichment and exploration of an extremely relevant real-world phenomenon and introduction to the adult profession of epidemiologist. With discussion and exploration, this project consumed two periods of 88…

Developing models, using mathematics, and constructing explanations are three practices essential for science inquiry learning according to education reform efforts, such as the Next Generation Science Standards (NGSS Lead States, 2013). However, students struggle with these intersecting practices, especially when developing and interpreting…

The article proposes a new research object for a general physics course--the vapour Cartesian diver, designed to study the properties of saturated water vapour. Physics education puts great importance on the study of the saturated vapour state, as it is related to many fundamental laws and theories. For example, the temperature dependence of the…

Some researchers advocate a statistical modeling approach to inference that draws on students' intuitions about factors influencing phenomena and that requires students to build models. Such a modeling approach to inference became possible with the creation of "TinkerPlots" Sampler technology. However, little is known about what…

This report summarises the research activities and findings from the TLRI-funded project entitled "Visualising Chance: Learning Probability Through Modelling." This exploratory study was a 2-year collaboration among two researchers, two conceptual software developers/interactive graphics experts, three university lecturers/practitioners,…

Various approaches to the problem of computer modelling of assimilation and forgetting of the educational information are considered. With the help of the multi-component model the Ebbinghaus' curve of forgetting of poorly assimilating information to be remembered through recurrences is confirmed. It is taken into account, that while training…