Partially automated assessment is implemented via the 'Printable worksheet' mode in the Numbas e-assessment system to create a mathematical modelling worksheet which is individualised with random parameters but completed and marked as if it were a non-automated piece of coursework, preserving validity while reducing the risk of academic misconduct…

The hanging rope problem is considered. The rope is subject to rotation with the rotation axis being parallel to the rope. Using a continuum model and the basic principles of dynamics, the differential equation governing the motion is derived. The dynamic equilibrium case without vibrational motion is assumed in deriving the equation. The equation…

The logistic differential equation is ubiquitous in calculus and differential equations textbooks. If the model is developed from first principles in these courses, it is usually done in an abstract mathematical way, rather than in one based in ecology. In this short note, we look at examples of how the model is derived in mathematical texts and…

A process is proposed to create the one-dimensional expected item characteristic curve (ICC) and test characteristic curve (TCC) for each trait in multidimensional forced-choice questionnaires based on the Rank-2PL (two-parameter logistic) item response theory models for forced-choice items with two or three statements. Some examples of ICC and…

"How do witnesses make identification decisions when viewing a lineup?" Understanding the witness decision-making process is essential for researchers to develop methods that can reduce mistaken identifications and improve lineup practices. Yet, the inclusion of fillers has posed a pivotal challenge to this task because the traditional…

Mathematics provides us with tools to capture and explain phenomena in everyday biology, even at the nanoscale. The most regularly applied technique to biology is differential equations. In this article, we seek to present how differential equation models of biological phenomena, particularly the flow through ion channels, can be used to motivate…

On 24 June 1994 at Fairchild Air Force Base, during practice for an air show, a low-flying B-52H aircraft banked its wings vertically and crashed. Emphasizing the activity of modeling drag and gravity, these notes examine the possibility of recovery with several models. First, with algebra, historical data lead to a model where in a free fall near…

Mathematical modelling has acquired relevance in different fields at an international level, both in education and research. This article states that, throughout the construction of the theoretical corpus of this mathematical process and competency -- among others -- two big issues have occurred: one of terminological nature since the definitions…

Should math educators care about what is happening in numeracy education research? Is the addition of a numeracy course something that mathematics departments should consider in their course offerings? Numeracy is often conflated with math-lite and dismissed as not useful to mathematicians and math educators. The term is used interchangeably with…

The notion of function is central in all of the secondary curriculum, and indeed functional models appear in almost all higher education that is based on mathematics. However, in secondary education, functions usually appear in restricted and somewhat sterile forms. In this (mostly theoretical) paper, we present a proposal -- exemplified by a…

Mathematical modeling tasks can engage students in ways in which they see themselves as mathematicians capable of using mathematics to solve real-world and complex problems. As mathematics teacher educators and researchers, the authors collaborated with two 5th-grade teachers, Liz and Anna (pseudonyms), focusing on equitable practices that foster…

A standard element of the undergraduate ordinary differential equations course is the topic of separable equations. For instructors of those courses, we present here a series of novel modeling scenarios that prove to be a compelling motivation for the utility of differential equations. Furthermore, the growing complexity of the models leads to the…

It has been over thirty years since the nuclear reactor meltdown at the Chernobyl nuclear power plant, but why there is still an officially designated exclusion zone? The Chernobyl Disaster Task combines the learning of exponential functions with properties of radioactive substances to help students understand the ongoing effects of the meltdown.…

Mathematics is most engaging when students see the relevance to their own lives and communities (Civil, 2002; National Council of Teachers of Mathematics [NCTM], 2000). The Temporary Skate-Safe Area task is an example of how mathematical modeling can be used to solve a real-world problem in a way that promotes mathematical belonging, social…

Mathematical modelling has great potential to motivate students towards studying mathematics. This article discusses several different approaches to integrating research work with a second-year undergraduate, mathematical modelling subject. I found sourcing papers from the areas of epidemiology and ecology to be a fruitful source area,…