In this contribution, we address the gap that has appeared in mathematics education research and practice with the emergence of dynamic geometry environments and build on the opportunities these environments offer to school geometry. In our qualitative empirical study, we investigate how to elaborate on the general model of conceptual knowledge to…

We introduce, motivate, and exemplify a proposed theoretical construct guiding the design and facilitation of collaborative geometry activities, conceptually generative perspectival complementarity (CGPC). Participants in CGPC activities learn content by negotiating their respective perceptions of situated features they manipulate to accomplish…

Choosing an unsuitable method of delivering material is one of the factors that gives students difficulties in applying concepts in solving mathematical problems. Strong mathematical concepts will help students develop their mathematical thinking skills, including geometric thinking skill. The use of ethnomathematics combined with worked example…

In response to the challenge of geometry's abstract and less engaging nature for students, this study explored the potential of connecting geometry to cultural elements, specifically geometric ornaments found in various cultures worldwide. Geometric ornaments, laden with cultural and spiritual significance, serve as a bridge between mathematics…

This study aims to determine the effectiveness of ethnomathematics-based learning on students' mathematical literacy through a meta-analysis study. Primary studies were collected from Google Scholar and ERIC databases based on the inclusion criteria. The results of the literature review obtained 16 studies, either from theses, proceedings, or…

In the disciplines of dance and mathematics, binary identities commonly split individuals into either (non)dance and/or (non)math people. However, these shorthand assessments become dangerous because they constrain disciplinary knowledge, and limiting one's identity and capabilities remains antithetical to broad education goals. Capitalizing on…

This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become "thinkable" the…

To prevent difficulties in learning mathematics, effective and innovative teaching methodologies should be used. The present study presents the results of a relational and comparative study between the application of the open number-based algorithm (ABN) and the closed number-based algorithm (CNB) method. The research was of a descriptive…

We discuss how mathematics and secondary mathematics education majors developed an understanding of Fermat points for the triangle as well as Steiner points for the square and regular pentagon, and also of soap film configurations between parallel plates where forces are in equilibrium. The activities included the use of soap films and the…

In line with the latest positions of Gottlob Frege, this article puts forward the hypothesis that the cognitive bases of mathematics are geometric in nature. Starting from the geometry axioms of the "Elements" of Euclid, we introduce a geometric theory of proportions along the lines of the one introduced by Grassmann in…

This study explored the effect of PowerPoint integration on students' motivation and achievement in less endowed Senior High Schools (SHSs). The study employed the embedded mixed method approach involving quasi-experimental design in which 80 students were randomly selected from two government-assisted Senior High Schools and assigned to control…

The solution of problems and the provision of proofs have always played a crucial part in mathematics. In fact, they are the heart and soul of this discipline. Moreover, the use of different techniques and methods of proof in the same mathematical field, or by combining fields, for the same specific problem, can show the interrelations between the…

Given two vectors u and v, their cross product u × v is a vector perpendicular to u and v. The motivation for this property, however, is never addressed. Here we show that the existence of the cross and dot products and the perpendicularity property follow from the concept of linear combination, which does not involve products of vectors. For our…

Students are faced with many transitions in their middle school mathematics classes. To build knowledge, skills, and confidence in the key areas of algebra and geometry, students often need to practice using numbers and polygons in a variety of contexts. Teachers also want students to explore ideas from probability and statistics. Teachers know…

In this work, we study the mathematical practice of defining by mathematics researchers. Since research is an important part of many professional mathematicians, understanding how they do research is a necessary step before thinking about future researchers' undergraduate and postgraduate education. We focus on the defining process associated with…