A fascinating and catchy method for proving that a number of special lines concur is using the concept of locus. This is now the classical method for proving the concurrency of the internal angle bisectors and perpendicular side bisectors of a triangle. In this paper, we prove the concurrency of the altitudes and the medians by showing that they…

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.

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…

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.

Problem solving and proofs have always played a major role in mathematics. They are, in fact, the heart and soul of the discipline. The using of a number of different proof techniques for one specific problem can display the beauty, and elegance of mathematics. In this paper, we present one specific, interesting geometry problem, and present four…

This work is devoted to exploring proof abilities in Graph Theory of undergraduate students of the Degree in Computer Engineering and Technology of the University of Seville. To do this, we have designed a questionnaire consisting of five open-ended items that serve as instrument to collect data concerning their proof skills when dealing with…

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…

Education currently only prioritizes mastery of scientific aspects and students' intelligence. Math problems are still related to fictitious general knowledge. For this reason, local wisdom-based learning is needed whose learning is packaged using objects, events, and various things that are close to students' lives to raise the local potential of…

GeoGebra is a dynamic software that is frequently used and of increasing importance in mathematics teaching processes in our digital age. Accordingly, in this study a new perspective has been brought to the proofs of the "two square difference identity" expressed for the square, which is a flat polygon, made with different approaches.…

While there are many documented approaches to using technological tools to support collaboration in remote environments, studies related to proof-based courses are overwhelmingly situated in the context of geometry. This study uses instrumental genesis theory to study how students in an introduction to proofs course operationalize the…

PWW style are presented. The difference of evidence is based on various additional auxiliary constructions, which in itself is a "mathematical art" that the student can master as a result of much practice. The PWW are accompanied by GeoGebra applets containing HINT buttons that allow the student to get step-by-step help in completing the…

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.…

Using a Dynamic Geometry System (DGS) students can engage in a dynamic learning process that allows them to experiment, create strategies, make conjectures, argue, and deduce mathematical properties. A DGS enables the introduction of proofs, by providing visual aids. The proof of the conjectures made emerges as the next step towards formalising…

This study aims to examine how being involved in an argumentation process relates to the formal proof process in geometry. Prospective mathematics teachers were involved in an argumentation process while producing conjectures before engaging in formal proof of the recently produced conjectures. To collect data, four geometry-proof tasks that…

This is a preliminary study of design research that investigates preservice mathematics teachers' proof level and the possible task of scaffolding-based interventions in proving the triangle theorem. The research subjects consisted of 58 second-semester mathematics education students at Universitas Negeri Surabaya, Indonesia. This research is…