Models are at the core of scientific reasoning and science education. They are especially crucial in scientific and educational contexts where the primary objects of study are unobservables. While empirical science education researchers apply philosophical arguments in their discussions of models and modeling, we in turn look at exemplary…

Contribution: Two general rules for calculating, in the time domain, step discontinuities of voltages and currents in electric circuits, combining physical principles and basic mathematical treatment. The two general rules, resulting from a formal method of analysis, provide a straightforward way to update the states of a circuit, immediately…

We consider the following hypothesis: whereas, the institutions in charge of the teaching of mathematics for future professional mathematicians (IPM, in short) share a "didactic paradigm" (strongly based on logical arguments), there does not seem to be such a thing in secondary mathematics education. In this work, we analyse the notion…

Our planet is facing a biodiversity crisis and mathematics is involved. In this article, I focus on reports of a wolf hunt to examine different ways in which mathematics contributes to this crisis, shapes our understanding of the ecosystem and guides future actions. My examination contributes to understanding the ethical dimension of mathematics…

Linear functional relationships are intended to be symmetric and therefore cannot generally be accurately estimated using ordinary least squares regression equations. Orthogonal regression (OR) models allow for errors in both "Y" and "X" and therefore can provide symmetric estimates of these relationships. The most…

A chemical engineering analysis course was modified to include analytics with advanced numerical methods. The course uses the MATLAB computational environment to develop student programming, modeling, analytics, and optimization skills. Case studies reinforce MATLAB, numerical methods, and advanced optimization skills. Students reported confidence…

Item response theory (IRT) refers to a family of mathematical models which describe the relationship between latent continuous variables (attributes or characteristics) and their manifestations (dichotomous/polytomous observed outcomes or responses) with regard to a set of item characteristics. Researchers typically use parametric IRT (PIRT)…

This article presents a mathematical modeling activity for students related to the process of memorization in which students collect their own data to drive their model development, parameterization, and validation. Engaging in the data collection gives them insight to critique and evaluate various models. This task is a low-floor high ceiling…

One can identify at least three different types of relationships between mathematics and crises. First, "mathematics can picture a crisis." This is in accordance with the classic interpretation of mathematical modelling, which highlights that a mathematical model provides a representation of a piece of reality, a reality that could be a…

In the article 'How Long Is My Toilet Roll--A Simple Exercise in Mathematical Modelling' several models of increasing complexity are introduced and solved to calculate indirectly the length of paper on a toilet-roll. All these results are presented without errors. The authors of this comment believe the error analysis of measurements made in a…

Though there is an extensive research literature on understanding and assessing individual modeling competencies, less attention has been given to characterizing the social context of the classroom in which modeling occurs. Yet a classroom's culture of modeling--its negotiated system of beliefs and values about the nature of modeling and what…

This article presents a synthesis of existing literature on ethnomodeling and the ways in which it extends mathematical modeling research in mathematics teacher education. We also call on the field to consider ways to connect and value culture and content in teaching mathematics. There have been increasing calls for integration of a culturally…

This paper addresses two aspects of integrating mathematics education with engineering education that may address persistence of engineering majors (and STEM majors more broadly): an emphasis on modeling as a vehicle for more authentic learning activity (Niss et al. 2007), and the need for measures that can support academic units' efforts to…

A phenomenon from the natural world, cricket chirping behavior in relation to ambient temperature, is used as the springboard for engaging the curiosity of gifted students in an interdisciplinary classroom curriculum. Mathematics and science standards and disciplinary practices are prominent in the investigation, while other disciplines deepen the…

This article argues the importance of teaching students about the philosophical and mathematical underpinnings of Australia's superannuation system as an example of a real-world problem context. It also provides a rationale for teaching financial modelling and decision-making in ways that respect the diverse financial realities represented in…