Interesting conservation properties that exist in parallelograms are well known, such as: diagonal intersection, pairs of interior triangles that overlap each other, and other properties. This article presents a dynamic study of choosing any point inside and outside the parallelogram and connecting it with two of the vertices of the parallelogram.…

In this paper we deal with a geometric machine that has gone somewhat unnoticed in mathematics education: the Perfect Compass. It allows conics to be drawn using a special two aperture compass, based on Apollonius' conic sections. Proposed in the 10th century, it seems that it was never built in medieval times--at least no archaeological remains…

Throughout the years of the history of the development of mathematics, starting with the ancient mathematicians, new things were discovered from time to time, which made it a central component of the computerized world, which serves us in many fields, with the young "swimming" in it, and the adults asking: how could we live without it!…

In high school geometry, students are expected to deepen their understanding of geometric shapes and their properties, as well as construct formal mathematical proofs of theorems and geometric relationships. The process of helping students learn to construct a geometric proof can be challenging given the multiple competencies involved (Cirillo…

Transitioning from material to theoretical geometry is often considered a significant challenge in compulsory education. Over the last twenty years, research rooted in the Theory of Didactical Situations (TDS) has explored how material geometry can support the teaching and learning of theoretical geometry, promoting continuity in teaching. These…

An interesting geometric conservation problem is presented. Here proof is presented in a 'proof without words' style, with the aim of developing the reader's visual proof ability. The study of the task and its expansion is accompanied by a dynamic sketch to highlight the conservation property.

This article presents a theoretical-didactic perspective on the formation and development of concepts concerning mathematical objects as a result of research on didactic difficulties in dealing with concepts in school. The theoretical foundation that supports the research is based on the contributions of the materialist approach to the theory of…

Comprehending and formulating strategies for geometry problems that require higher-order thinking skills (HOTS) is crucial in enhancing mathematics education. This study implements a qualitative case study approach to comprehend how prospective mathematics teachers with varying Adversity Quotients (AQ) solve geometry Higher-Order Thinking Skill…

Visualization and argumentation are central processes in the learning of geometry, giving rise to specific lines of research in mathematics education. However, it is worth asking whether they should be developed independently or if it is possible and in what way an articulation between them can be promoted. The objective of this paper is to search…

In this study, the effect of the Mathematics Bag Early Education Program (MAÇEP) on the mathematics skills (number/counting, geometry, measurement) of 57-69-month-old preschool children was investigated. A quasi-experimental design with a pretest, posttest, follow-up test, and control group were used in the study. The study group consisted of 22…

In this article, the author shares two investigations that relate the variables of height and volume using different contexts. Each of the investigations surfaced unfinished learning for students, regardless of their starting place, and facilitated growth in understanding of measurement and algebra. The Functions and Volume of Vases task…

Teacher gestures support mathematics learning and promote student collaboration. Aligned with speech, gestures can help students to notice the important visual information of geometry tasks. However, students' visual attention to the teacher's gestural cues during collaborative problem solving remains a largely unexplored field in mathematics…

This study aims to examine postgraduate theses focusing on technology integration in the field of mathematics education in Turkey between 2015-2023, taking into account the didactic focus classification. In this research, systematic literature review was used to address research questions. This systematic literature review followed the Preferred…

This paper focuses on the difficulties encountered by Italian students in performing geometry tasks. A quantitative analysis, aimed at understanding the extent of the phenomenon, is carried out using the results of district competitions from the year 2018 to 2020, comparing the scores obtained in geometry questions with those in other areas of…

When justifying a mathematical statement, textbooks often interweave several instances of justification, creating, what we term, "paths of justification." This study aims to characterize the paths of justification of mathematical statements that are offered in eight 7th grade Israeli mathematics textbooks. The study attended to context…