The teaching quality evaluation of college teachers is an important indicator of school evaluation, performance assessment and teacher promotion. However, the existing evaluation methods are only limited to the formal evaluation of teaching behavior, and have not achieved objective, reasonable and scientific evaluation results. The purpose of this…

Simple mathematical models can serve to reveal the essence of experimental phenomena and scientific concepts. The particle in a box (PIB), for example, is widely used in undergraduate programs to teach the quantum mechanical principles behind the UV--vis spectra of conjugated polyenes and polyynes. In this work, the particle on a ring (POR) and…

This paper explores use of a set of diagrammatic tools for representation and analysis of the moves a teacher makes implementing a mathematical modelling task. The focus here is on identifying what the teacher did so we can subsequently interrogate this, as to the why. Data include pre and post lesson teacher interviews and transcripts of a video…

According to expectancy-value models, two important motivational constructs are task value and self-efficacy expectations. As students work intensively on mathematical problems in the classroom, teachers need the competence to judge whether students value solving the problem and how confident they are that they will succeed. However, not much is…

How might fourth graders address the problem of measuring the size of a leaf? And why might their classroom teachers choose such a shape to measure? One group of fourth-grade students in an urban Australian school were interested in knowing the sizes of leaves on a passionfruit vine growing at their school. The children were excited after a visit…

This study focuses on the potential of university mathematics courses to advance teachers' knowledge regarding an important component of knowledge about the nature of mathematics as a scientific discipline, namely the mutual contribution between mathematics and various fields: mathematics contributes to solving problems in different fields, and…

Minimal guidance or maximal independence? How can teachers achieve that complex balance when teaching mathematics? In this pre-and post-test quasi-experimental research study, the authors explored the above broad questions in Grade 10 Financial Mathematics following guided discovery and mathematical modelling principles. Fifty-four (54) Grade 10…

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)…

The purpose of the work described in this paper is to emphasize the importance of using mathematical models and mathematical modelling in order to be able to understand and to learn possible behaviours in epidemic situations such as that of the COVID-19 pandemic, besides suggesting modelling techniques with which to evaluate certain sanitary…

The main aim of this paper is to present results of an experimental test focused on the validity and effectiveness of composed methodology aimed at increasing the student's attention in Virtual Learning Environment. Areas of presented methodology which were subject of our research is students behavior during learning. The behavioral part of…

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…

Possessing mathematical competence is a pre requisite for independently comprehending, understanding and applying all features of mathematical modelling in a particular setting. This research study thus explores the mathematical modelling competencies that Grade 10 learners exhibit while solving contextual problems in a mathematics learning and…

This curated collection covers a selection of PRIMUS articles published over a roughly 12-year period that focus on modeling and applications. The collection includes sections on individual projects, courses with a significant modeling component, and modeling and applications in extracurricular settings and throughout the curriculum.

Differential equations are widely used tools for modelling the world around us, making a course in differential equations a natural place for students to connect concrete mathematical applications to abstract concepts. Since students grasp the concepts better by applying them, introducing differential equations through modelling becomes essential.…

While existing studies acknowledge the importance of using technology in the mathematical modelling process, questions about how to integrate digital tools into mathematical modelling are not still answered. This study aims to examine pre-service mathematics teachers' designing and solving mathematical modelling problems by using different digital…