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…

The current study is part of a comprehensive research on linking visualization, students' construction of geometrical concepts and their definitions, and students' ability to prove. The aim of the current study is to investigate the effect of learners' understanding of definitions of geometrical concepts on their understanding of the essence of…

Mathematical justifications offer an approach to which students deepen and extend their mathematical thinking. This process has the potential to enhance students' conceptual understanding. Mathematical practices and process standards ask students to use critical thinking skills to justify their reasoning, but this is usually seen as proofs in high…

Constructing mathematical proofs is a fundamental yet challenging skill in secondary school geometry. While technology has been used to scaffold different aspects of the proving process, existing approaches often separate inquiry and conjecturing from formal proof or focus on structural and technical assistance without addressing students' initial…

With the ever-evolving implementation of technology in the teaching and learning of geometry, the task of designing and/or finding suitable questions or problems that can facilitate and promote mathematical reasoning and accurately assess students' understanding of the subject matter can be a challenge. It is the aim of this article to share the…

It's often useful extending students beyond the limiting geometry of triangles and quadrilaterals to regularly consider generalizations of results for triangles and quadrilaterals to higher order polygons. A brief heuristic description is given here of the author applying this strategy, and which led to an interesting result related to the…

Proof, as a central and integral part of mathematics, is an essential component of mathematical education and is considered as the basic procedure for revealing the truth of mathematical propositions and for teaching productive reasoning as part of human civilization. Is there therefore room for conjectures in mathematics? In this paper after…

We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16-17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the…

This study investigated the effect of situated learning environment in enhancing mathematical reasoning and proof among tenth grade students. To achieve the aim of the study, a pre-posttest of mathematical reasoning and proof was used, and its validity and reliability were verified. The sample of the study consisted of 50 female students who were…

Mathematics in its nature is exploratory, giving learners a chance to view it from different perspectives. However, during most of their schooling, South African learners are rarely exposed to mathematical explorations, either because of the lack of resources or the nature of the curriculum in use. Perhaps, this is due to teachers' inability to…

This paper highlights the pedagogical importance of gaps in mathematical proofs to foster students' learning of proofs. We use the notion of 'gap-filling' (Perry & Sternberg, 1986) from literary theory to analyze a task based on a Proof Without Words, which epitomizes the notion of gaps. We demonstrate how students fill in gaps in this…

Constructing formal geometry proofs in is an important topic in the mathematics curriculum. But students' difficulties with proof are well documented. This article focuses on proofs that use triangle congruence postulates in US high school geometry. Examining students' proof reasoning in one-on-one task-based interviews, we analyzed students' oral…

This study was conducted to examine whether newly enrolled 9th grade students were ready to directly engage in the theoretical discursive process from the perspective of Duval's Cognitive Model. The sample of the study was comprised of 51 newly enrolled 9th grade students between the ages of 14 and 15, who had not received any prior geometry…

This paper discusses strategies that two high school geometry teachers employed to solve a challenging geometry problem with the aid of dynamic geometry software (The Geometer's Sketchpad (GSP). The teachers were part of a group of teachers who participated in a summer professional institute funded by the National Science Foundation. The paper…

Materialist design is presented as an embodied perspective on educational design that can be applied to redesign of classroom-based learning environments. Materialist design is informed by a framework of materialist epistemology, which positions material innovation on equal placement with symbol-based formal theory. Historical examples of…