In this brief we shift the current academic integrity conversation from "detecting and preventing plagiarism" to "examining how plagiarized contents can be corrected with an objective knowledge of the number of words to modify and properly acknowledged". We proposed a simple, yet useful and powerful mathematical model that is…

Adjusting the Calculus I curriculum by putting modelling and differential equations literally at its centre leads to a better-organised and better-motivated course. The biggest change is including a section on "qualitative" and "numerical" solutions to ordinary differential equations between the customary sections on…

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.

Calculus education research on integration is coalescing around the theme that teaching integration based on quantitative reasoning is crucial for robust understanding of and usage of integrals. This paper contributes to this International Journal for Research in Undergraduate Education special issue on the teaching and learning of definite…

Previous research explicates ordinal and disordinal interactions through the concept of the "crossover point." This point is determined via simple regression models of a focal predictor at specific moderator values and signifies the intersection of these models. An interaction effect is labeled as disordinal (or ordinal) when the…

The theoretical reflection on the nature of school algebra and the development of algebraic thinking from the first educational levels is a relevant topic in mathematics education. In this paper, we first summarize and clarify the positions held on this topic by two theoretical frameworks: the Theory of Objectification and the Onto-semiotic…

Modelling roles of mathematics in physics has proved to be a difficult task, with previous models of the interplay between the two disciplines mainly focusing on mathematical modelling and problem solving. However, to convey a realistic view of physics as a field of science to our students, we need to do more than train them to become fluent in…

In application-oriented mathematics, particularly in the context of nonlinear system analysis, phase plane analysis through SageMath offers a visual display of the qualitative behaviour of solutions to differential equations without inundating students with cumbersome calculations of the plane-phase. A variety of examples is usually given to…

Mathematical modeling describes how events, concepts, and systems of interest behave in the world using mathematical concepts. This research approach can be applied to theory construction and testing by using empirical data to evaluate whether the specific theory can explain the empirical data or whether the theory fits the data available.…

Although reasoning is a central concept in mathematics education research, the discipline is still in need of a coherent theoretical framework of mathematical reasoning. With respect to epistemological problems in the dominant discourses on proof, mathematical modelling, and post-truth politics in the discipline, and in accordance with trends in…

One of the most vexing challenges facing developmental researchers today is the statistical modeling of two or more behaviors as they unfold jointly over time. Although quantitative methodologists have studied these issues for more than half a century, no widely agreed-upon principled strategy exists to empirically analyze codevelopmental…

The extent of competition in the market affects the balance of bargaining power of market participants. When price discrimination is low, it increases consumer welfare - that is, if the price does not correspond to the evaluation of each product by the consumer, then discrimination allows for additional consumers to buy the product at a price,…

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…