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…

Nowadays, it is essential to promote an interdisciplinary approach in classrooms, integrating disciplines such as biology and mathematics. This necessitates familiarity with specific problem-solving practices employed by the expert community, such as mathematical modelling. This perspective piece explores a mathematical modelling practice to…

Humans can learn complex functional relationships between variables from small amounts of data. In doing so, they draw on prior expectations about the form of these relationships. In three experiments, we show that people learn to adjust these expectations through experience, learning about the likely forms of the functions they will encounter.…

Imaginary latent variables are variables with negative variances and have been used to implement constraints in measurement models. This article aimed to advance this practice and rationalize the imaginary latent variables as a method to detect possible latent deficiencies in measurement models. This rationale is based on the theory of complex…

Research has shown that multiple-indicator multiple-cause (MIMIC) models can result in inflated Type I error rates in detecting differential item functioning (DIF) when the assumption of equal latent variance is violated. This study explains how the violation of the equal variance assumption adversely impacts the detection of nonuniform DIF and…

Predictive modeling is a core technique used in tackling various tasks in learning analytics research, e.g., classifying educational forum posts, predicting learning performance, and identifying at-risk students. When applying a predictive model, it is often treated as the first priority to improve its prediction accuracy as much as possible.…

Process data from educational assessments enhance the understanding of how students answer cognitive items. However, effectively making use of these data is challenging. We propose an approach to identify solution patterns from operation sequences and response times by generating networks from process data and defining network features that…

The current meta-analysis investigates the longitudinal association between prior and subsequent mathematics performance, involving mathematics measured at three time points, and to identify potential factors that could moderate this association, including age, time lag, and types of mathematics. Our analysis included 105 studies, comprising 111…

Problem solving in chemical kinetics poses substantial challenges for university students since it often involves significant use of mathematics as a tool and language, with challenging translations and transitions between chemical phenomena and mathematical representations. In this paper, we present key findings from a study investigating…

This study aimed to explore preservice elementary teachers' use of a bar model as a heuristic for conceptualising relationships between quantities in situations involving ratio and percentages. As a part of a larger project, we focused on two preservice teachers, Maia and Jane, and investigated their solution paths in ratio and percentage problems…

We demonstrate how developmental theories may be instantiated as statistical models, using hierarchical continuous-time dynamic systems. This approach offers a flexible specification and an often more direct link between theory and model parameters than common modeling frameworks. We address developmental theories of the relation between the…

This study proposes transformation functions and matrices between coefficients in the original and reparameterized parameter spaces for an existing linear-linear piecewise model to derive the interpretable coefficients directly related to the underlying change pattern. Additionally, the study extends the existing model to allow individual…

This article considers starting with an existing SIMIODE modeling scenario [Winkel, B. (2015). 1-031-CoolIt-ModelingScenario. SIMIODE (Version 2.0). "QUBES Educational Resources." https://doi.org/10.25334/3WG8-EC31] that develops Newton's law of cooling by considering data on the cooling of a beaker of water in a room, and expanding upon…

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…

Based on expectancy-value theory, this study adopted a person-centred approach to explore the heterogeneous profiles of secondary German and Taiwanese students' mathematical modelling task values, and examined the differences in their mathematical modelling performance, controlling for the variable of intra-mathematical knowledge among the…