In this article, we state an interesting geometric conservation property between the three angle bisectors of three similar right triangles and provide a proof without words for its justification. A GeoGebra applet is also presented to help with the understanding of the progression of the proof from inductive to deductive stage.

Hands-on experiments with overturning some prisms (partially filled with water) lead students to a conjecture which can be confirmed by using a 3D geometry programme and reinterpreting the process of "overturning of a prism" in an appropriate way. But such confirmations are not a proof and particularly cannot answer the question…

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…

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…

This contribution focuses on reasoning about quadrilaterals provided by lower secondary school students when working with pre-prepared dynamic constructions. On this topic, we present an exploratory empirical qualitative study carried out within a GeoGebra Classroom environment, and our diagnostic instrument consists of a set of dynamic…

Students' difficulties with proofs are well documented. To remedy this, it is often recommended that reasoning and proving be focused on in all grades and content areas of school mathematics. However, proofs continue to have a marginal place in many classrooms, or are only given explicit attention in courses in Euclidean geometry. Geometry is also…

This study aims at elaborating a well-established theoretical framework that distinguishes three modes of thinking in linear algebra: the analytic-arithmetic, the synthetic-geometric, and the analytic-structural mode. It describes and analyzes the bundle of signs produced by an engineering student during an interview, where she was asked to recall…

This article presents a curricular reasoning model developed based on research conducted with middle grades teachers as they planned, taught, and reflected on a geometric transformations unit. Teachers can use the model to become aware of their own curricular reasoning to make key mathematical decisions as they plan and teach their lessons. While…

In this paper, we explore how the typical second year undergraduate topic of matrix diagonalisation can be applied to solve a geometric problem which arises frequently in Vector Calculus: to find the curve of intersection of a plane and a surface. We use GeoGebra, which offers a cost-free and dynamic interface, to explore a specific variant of…

Although research highlights the importance of analyzing the geometric work of teachers, there are few validated instruments in this line. This study presents the processes of design and validation of a forced-choice questionnaire that allows the characterization, from a theoretical basis, of how geometry teachers organize their teaching practice.…

As an interdisciplinary and multicultural educational framework takes the centrality of the delivery of 21st-century education across all levels, this study attempts to address the competencies that prospective and neophyte teachers need to possess to effectively design contextualized education. Through stepwise multiple regression analysis,…

This study aims to explain the Metaverse application development process for teaching geometry in a virtual reality environment. The application was developed based on the instructional design model including analysis, design, development, implementation and evaluation phases. The target group was secondary school students. During the analysis…

I explore some facts about the area, position, etc. of the Steiner ellipse using GeoGebra and numerical analysis. Students can use these for mathematical inquiry.

Textbook is one of the most tangible resources for teaching and learning mathematics, offering valuable opportunities for both teachers and students. This study compared the mathematical tasks in 6th-grade textbooks from the United States and Turkey, focusing on three dimensions of the tasks: representation, contextual features, and cognitive…

Teaching diverse student populations effectively requires implementing thoughtfully planned and flexible rich tasks and understanding a community's strengths so students can make meaningful connections to mathematics. Using a culturally relevant teaching approach can develop appropriate geometry vocabulary to support students in articulating their…