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…

We report on a group theory activity in which learners explored dihedral symmetries through a tangible geometric model. This approach has historical roots in the work of Felix Klein's Erlangen Program and his "Elementary Mathematics from an Advanced Standpoint." We situate our study with respect to this history as well as current…

This article outlines a series of lessons the author led to help students understand gerrymandering, which is the practice of drawing district boundaries to favor a particular group or party and which undermines the fairness of a representative democracy. These lessons were developed to capture student interest and engagement by linking…

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…

Our study aims to determine how Habermas' construct of rationality can serve to identify and interpret the difficulties experienced by university students in the mathematical problem-solving process. To this end, a problem which required modelling and solving a differential equation was used. The problem-solving processes of university students…

The need to develop consistent theoretical frameworks for the teaching and learning of discrete mathematics, specifically of graph theory, has attracted the attention of the researchers in mathematics education. Responding to this demand, the scope of the Van Hiele model has been extended to the field of graphs through a proposal of four levels of…

This study takes a closer look at Form Four students' initial mathematical modelling process when solving mathematical problems using GeoGebra. The modelling process was observed from cognitive perspective to learn the difficulties students faced during the process and the result would give ideas for intervention. Qualitative approach by using…

In this article, the authors describe their experiences with planning, implementing, and revising a lesson for which the goal is for students to consider the mathematical and pragmatic issues that are related to a task of maximizing the area for a fixed perimeter. The authors also wanted students to engage in the Standards for Mathematical…

Ethnomathematics can empirically improve the cognitive abilities of students in elementary and secondary schools. However, in undergraduate study, there are still limited studies on integrating ethnomathematics in learning resources. This study aims to apply interpolation in modelling polynomial functions and integral volume on the shape of…

We investigated how students' strategic knowledge about situational (pictorial) drawings and mathematical (schematic) drawings affects drawing accuracy and modeling competencies in the domain of geometry. We conducted a pre-posttest experimental study with 473 students in grade 9. Students were randomly assigned to one of three treatment…

When examining students' participation in these mathematics discussions, the focus is on their verbal contributions. However, students' nonverbal contributions--such as pointing, drawings, and models-- can be crucial resources for advancing the mathematical thinking and the collective activity of a classroom community (Johnson et al., 2023; Webb…

This paper reports on a teaching experiment on mathematical modelling in an upper secondary school class that investigates how the constructs of "model eliciting" and "emergent modelling" may be brought together to inform teaching and learning. A prominent role is covered by the process of task design, seen as a complex process…

This study presents a bibliometric analysis of research on mathematics education from 1980 through 2020. The purpose of the study is to provide scientific data on the distribution pattern of mathematics education journals, the most prolific authors, countries, institutions, current research topics, potential international collaboration, and…

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.

This study examined the influence of mathematical modeling in GeoGebra environment on students' learning of the concept of the derivative and its application. The study included an experimental and a control group with 204 first-year undergraduate students of applied sciences. The students in the experimental group (102 students) conducted the…