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…

In this work, we delve into geometric analysis, particularly examining the interplay between lower bounds on Ricci curvature and specific functionals. Our exploration begins with an investigation into the implications of Yamabe invariants for asymptotically Poincare-Einstein manifolds and their conformal boundaries under conditions of…

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…

From my home on the west bank of the Columbia River in Richland, Washington (46.3°N latitude), I have an unobstructed view of the sunrise along the east bank during an entire year. As a retirement project after a career of teaching and research in physics, I decided to take photographs of the sunrise for a year and, and at the same time, carry out…

One of our favorite face-to-face teaching frameworks is "Launch, Explore, Summarize" (LES). However, transitioning LES activities to online settings challenged us to reimagine how learning and its interactions could be supported in this new environment. We explore our experience transitioning an LES lesson on the quadrilateral hierarchy…

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.

In this paper, a simple proof of the Morley's Trisector Theorem is presented which involves basic plane geometry only. The use of backward geometric approach, trigonometry or advanced mathematical techniques is not required. It is suitable for introducing to secondary or undergraduate students, as well as teachers or instructors for learning or…

Creativity is often characterized by the capacity to generate novel ideas, explore unconventional approaches, and solve problems through intuition, curiosity, and innovative thinking. Assessing this multifaceted skill is both essential and challenging, especially in educational and game-based environments where creativity drives engagement and…

Several studies on student's understanding of the concept of the tangent line agree that the difficulties students have when dealing with lines tangent to curves at inflection points or tangent lines that have more than one point in common with the curve are due to a misconception of tangency that is limited to the geometric relationship between…

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…

Geometry processing holds a foundational position within the realm of computer graphics, with advancements in this field regularly published at SIGGRAPH annually. The journey from writing the paper to implementing the algorithms is a meticulous and error-prone process, demanding significant dedication and attention to detail. Authors frequently…

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…

This report details a set of three tasks used in an exploratory study of pre-service teachers' (PSTs) experiences of task design for the mathematics classroom. The three tasks, which I call the "Orange Dot Tasks," were constructed in Desmos, a dynamic geometry environment (DGE), and participants engaged each task through manipulating…

This study provides a framework for explaining the way individuals might construct the final result of infinite iterative processes in a geometrical context. To this end, 30 undergraduate students were interviewed. The analysis of the data collected yielded two different views: first, there were those who believed that the presented infinite…