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.

As a person obsessed, perhaps overly so, with preventing water damage, an ailing dishwasher led to a system whereby who did the dishes in our household became a matter of chance. What happened next, however, was besmirchment of my character from hockey teammates, close friends, and especially from a room full of future elementary school…

The introduction of large language models (LLMs) may change future pedagogical practices. Current research mainly focuses on the use of LLMs to tutor students, while the exploration of LLMs' potential to assist teachers is limited. Taking high school mathematics as an example, we propose a method that utilizes LLMs to enhance the quality of…

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…

In this article, we describe the theoretical and pragmatic considerations behind our development of a set of nine protocols and training materials for engaging prospective secondary mathematics teachers in live, interactive clinical simulations. Our designs are grounded in theoretical principles from situated cognition and variation theory and…

The development of mathematical reasoning skills has increasingly been of focus for the teaching and learning of mathematics. This research utilizes a teaching simulation using the methodology of scriptwriting, in which prospective teachers are asked to complete a script of a dialogue from a classroom simulation involving fraction multiplication…

Rehearsals have become an increasingly popular pedagogy to support preservice teachers in developing competency in enacting challenging instructional practices and communicating associated pedagogical commitments. To understand how best to support learners participating in rehearsals, researchers have begun to analyse the facilitation of teacher…

This study contributes to the call for influencing practice by increasing attention to how learning environments can be designed to support learning in statistical inference. We report on a design experiment in secondary school (students 14-16 years old), that resulted in a set of lessons with the learning goal of teaching students how to apply…

Background: Many studies have shown that ambitious, "student centered" approaches to STEM instruction benefit K-12 student learning. However, relatively little research has systematically investigated the learning processes that support teachers to skillfully enact these challenging pedagogies. In this study, we used a mixed-methods,…

This study aims to understand a middle school mathematics teacher's instruction and reflections on her experiences with supplementary curricular materials enriched with interactive simulations--PhET interactive simulations (sims) and sim-based materials--over two years. We conceptualize Linda's (pseudonym) teaching in terms of both thinking and…

This article asks the question: is the "Last Banana" game fair? Engaging in this exploration provides students with the mathematical power to answer the question and the mathematical opportunity to explore important statistical ideas. Students engage in simulations to calculate experimental probabilities and confirm those results by…

The investigation at scale of the tensions that teachers need to manage when deciding to follow recommendations for practice has been hampered by the problem of occurrence: The conditions in which those decisions could be made need to occur during an observation in order for observers to document how teachers handle them. Simulations have been…

This article shows results on the simulation of partial differential equations such as the heat equation, the Laplace equation and the wave equation in a course called mathematical methods at a university in Bogotá Colombia. In this course, the concept of partial differential equations and different solution methods were explained to them, both in…

In regression analysis courses, there are many settings in which the response variable under study is continuous, strictly positive, and right skew. This type of response variable does not adhere to the normality assumptions underlying the traditional linear regression model, and accordingly may be analyzed using a generalized linear model…

Too often, statistical inference and probability are treated in schools like they are unrelated. In this paper, we describe how we supported students to learn about the role of probability in making inferences with variable data by building models of real world events and using them to simulate repeated samples.