Mathematical modelling emphasizes the connection between mathematics and reality -- still, tasks are often exclusively introduced inside the classroom. The paper examines the potential of different task settings for mathematical modelling with real objects: outdoors at the real object itself, with photographs and with a 3D model representation. It…

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 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…

Mathematical modelling and modelling activities are important for making sense of mathematical concepts in different extracurricular and daily life contexts. However, teachers may have difficulties in designing these activities in a way to establish meaningful relationships with real life, in accordance with the modeling process and the objectives…

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…

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…

This paper describes a teaching experiment in a Numerical Methods course for Master of Science students. The experiment uses scientific papers to develop modelling studies in the context of wine fermentation microbial interactions. The course involves theoretical and laboratory classes that focus on implementing numerical methods using Matlab for…

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…

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…

The purpose of this note is to describe a classroom activity that can be used in introductory Operations Research courses. It consists of modelling a one-dimensional puzzle using mathematical programming to produce glider models. The exercise is designed to motivate the students in solving a problem with the opportunity of producing by themselves…

Research into didactics of calculus has maintained a long-standing interest in students' grasp of the relations between definite integrals and areas. This study comes to contribute to this line of research by unpacking how students use the concept of area to find definite integrals. Specifically, we focus on mathematical situations where the…

The study of learning behaviors with multi features is of great significance for interactive cooperation. The data prediction and decision are to realize the comprehensive analysis and value mining. In this study, hierarchical learning behavior based on feature cluster is proposed. Based on the massive data in interactive learning environment, the…

The utilization of modeling tools has gained significant attention recently. These models typically involve a series of partial differential equations, which can be challenging for novice modelers. This paper presented an approach in practical teaching of modeling tools for ion-exchange chromatography with three parts: model introduction, model…

This study aimed to observe the competencies of pre-service mathematics teachers in designing mathematical modeling tasks. The participants were 45 pre-service mathematics teachers enrolled in a Mathematics Education Theory course at a university in Seoul, South Korea. Data were collected from surveys and task development reports. The participants…

Researchers continue to choose PCA in scale development and adaptation studies because it is the default setting and overestimates measurement quality. When PCA is utilized in investigations, the explained variance and factor loadings can be exaggerated. PCA, in contrast to the models given in the literature, should be investigated in…