This paper introduces the basic knowledge of integral factors of first-order ordinary differential equations and Lie symmetry analysis. It then discusses the principle of constructing an integral factor of the first-order ordinary differential equation by the Lie symmetric method. Finally, it presents some examples to show the process of…

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…

This study aims to clarify the role of generating questions in mathematical modeling and construct principles for teaching and learning mathematical modeling with an emphasis on generating questions. To achieve this purpose, the role of generating questions was determined by solving a sprinkler problem and considering the investigation process.…

In this paper, we introduce novel instructional approaches to engage students in using modelling with data to motivate and teach differential equations. Specifically, we introduce a pedagogical framework that will execute instructional modules to teach different solution techniques for differential equations through repositories and notebook…

Operations Research (OR) is a branch of applied mathematics that deals with optimization problems arising from different real contexts. The solving process of its problems is based on the construction and resolution of mathematical models, showing the possible connections between mathematics and the real world. Nevertheless, OR is not typically…

This study aimed to examine the collective mathematical creativity of gifted middle school students within a group through model-eliciting activities. The current study employed the case study design. The participating four gifted students were selected through the purposive sampling technique. To examine the collective creativity of the students…

The purpose of this literature review is to explicate the facets of mathematical problem solving taxonomies in relation to mathematical modeling. Subsequently, components and learning benefits of mathematical modeling are discussed. Examples of mathematical problems are embedded in the discussion and pragmatic applications to mathematical…

Task enrichment is an important teacher competency that can be considered as a special case of problem posing. For that reason, the theoretical framework of this article includes an overview of this topic, complemented with the analysis of inverse problems. The field work of this research was carried out in master courses in the University of…

Engagement in complex, challenging and multifaceted model-eliciting activities is considered helpful for preparing learners for everyday life. The current study seeks to trace the evolution of modelling routines during two model-eliciting activities. To identify how these routines emerged and evolved, we video-recorded a group of five prospective…

This study investigated the role of the bar model method, a significant aspect of the Singapore mathematics curriculum, in the remediation of seventh-grade students' errors on algebra word problems. To accomplish this purpose, we first assessed students' errors on a written test involving algebra problems and identified ten students based on the…

This study investigates prospective elementary and secondary school mathematics teachers' ways of reasoning about differentiability at a point and corner points while working on a mathematical modelling activity. Adopting a multiple-case study design, the participants of the study were 68 prospective elementary school mathematics teachers enrolled…

These notes discuss several related problems in geometry that can be explored in a dynamic geometry environment. The problems involve an interesting property of hexagons.

Socio-cultural theories in mathematics education field recently emphasize the importance of the collective argumentation within small-group work. Since mathematical modelling tasks require a process in which students search for a solution for real life problems through small-group work, the arguments in this process become an issue of concern.…

This paper uses a post-qualitative philosophical perspective to find new ways of understanding teaching and learning. The paper presents a series of examples that were used in a longitudinal study, with the aim of creating variation patterns that would make it possible for students to discern the use of the four basic arithmetic operations in…

This study investigated pre-service secondary mathematics teachers' (PSMTs') anticipation and identification of students' thinking as they engaged in examining and analyzing student work on four modelling problems. The study comprised four two-week-long cycles. The data were collected through individual reflection papers and written group reports…