We adapt the Lanchester combat model to represent conflict between vampires and humans. It is assumed that vampires attack humans during the hours of darkness whilst humans attack vampires during the hours of light. The right-hand side of the differential equation model therefore depends upon the hour of the day. A key insight is that to answer…

The hanging rope problem is considered. The rope is subject to rotation with the rotation axis being parallel to the rope. Using a continuum model and the basic principles of dynamics, the differential equation governing the motion is derived. The dynamic equilibrium case without vibrational motion is assumed in deriving the equation. The equation…

Problem posing engages students in generating new problems based on given situations (including mathematical expressions or diagrams) or changing (i.e., reformulating) existing problems. Problem posing has been at the forefront of discussion over the past few decades. One of the important topics studied is the process of problem posing as…

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…

The goal of this article is to propose a framework for understanding the nature of "how people construct problems" by interacting with situations and subsequently to offer implications for instructional design and future research. We propose that people must interactively frame the components of a situation in order to establish the…

Differential equations (DEs) are a powerful tool for modeling real-world contexts. Most research in this area has examined students' understanding and reasoning with pre-packaged DEs, with little attention being given to setting up sophisticated DEs to model complicated real-world situations. This study contributes through a collective case study…

The invention of problems is a fundamental competence that enhances the didactic-mathematical knowledge of mathematics teachers and therefore should be an objective in teacher training plans. In this paper, we revise different proposals for categorizing problem-creation activities and propose a theoretical model for problem posing that, based on…

The objective of this work was the theoretical modeling of a construct based on teaching practice about the perception that pupils have of difficulties in problem solving (PS) in experimental sciences, specifically physics, to predict pupil performance in PS. The research was carried out with an incidental sample of second year of secondary…

Successful computer-based assessments for learning greatly rely on an effective learner modeling approach to analyze learner data and evaluate learner behaviors. In addition to explicit learning performance (i.e., product data), the process data logged by computer-based assessments provide a treasure trove of information about how learners solve…

Mathematical modelling has acquired relevance in different fields at an international level, both in education and research. This article states that, throughout the construction of the theoretical corpus of this mathematical process and competency -- among others -- two big issues have occurred: one of terminological nature since the definitions…

The aims of this study were to synthesize and evaluate the learning model in gamification environment together with cartoon animation media to promote students' creative problem-solving skills. This study was divided into three phases, (i) synthesized and evaluated the appropriateness of learning model (ii) developed cartoon animation and (iii)…

In the contemporary world of digitalisation, comprehensive digital competence (DC) is and should be an integral part of students' repertoire to guarantee not only academic but also professional success. However, the level and requirements for DC may vary within specific educational contexts, especially in culturally oriented institutions. This…

Background/purpose: The application of learning models is expected to significantly promote the enhancement of students' problem-solving abilities through the development of interactive learning models. This study aims to (1) determine whether the Development of the Component Display Theory (CDT) Model is categorized as valid, practical, and…

Models-and-modeling perspective (MMP) is a problem-solving and learning perspective in mathematics education. Although modeling processes have been addressed widely in the international discussion on mathematical modeling, a homogeneous understanding has not been established yet. Hence, the field needs studies addressing the epistemological…

One of the popular creativity methods to solve technical problems is the Theory of Inventive Problem Solving, (TRIZ), however, requires a considerable investment of time. A teaching methodology for a simplified version of TRIZ (TRIZ10) has been developed for reducing learning time and improving the creative process in solving technical problems.…