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…

As new technological developments continue to change the educational landscape, it is not an exception in the area of proof and proving. This classroom note introduces the use of one of the trending proofs assistants -- the Lean theorem prover. We first provide a technical account of Lean, then exemplify Lean proofs in propositional logic, number…

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…

Many areas of mathematics naturally lend themselves to machine-based computing environments, which suggests that computational environments may serve as useful mediating tools for the teaching and learning of mathematical content. While some mathematics classes are leveraging the use of computational tools, the implementation of computer…

The aim of this paper is to review recently calculus curriculum reforms and research studies that document what types of understanding students develop in their precalculus courses. We argue that it is important to characterize what difficulties students experience to solve tasks that include the use of foundational calculus concepts and to look…

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.…

This work is the result of a master's investigation in Brazil, which discusses the teaching of the parabola in the initial training of mathematics teachers. Our theoretical framework addresses the relationship between intuition and the dialectics of the theory of didactic situations, which supports the analysis of the results of this study Its…

The purpose of this study is to examine the performances of university students' using dynamic mathematics software GeoGebra in argumentations and proving processes. A task related to the limit involving "sinx/x" was designed and 18 university students worked on the task during the collaborative learning, scientific debate, and…

We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in…

In this study, we examine students' mathematical reasoning within a technological environment designed to support understanding of relationships between quantities with adjustable measuring units. In particular, we provide a cross-sectional snapshot of how 30 elementary students (Grades 3-5) engaged in a series of fraction-as-measurement tasks…

The aim of this study is to explore how structural and process aspects of secondary school students' mathematical reasoning support each other in a collaborative learning environment through the integration of "GeoGebra" software and the ACODESA method. The study involved four eighth-grade secondary school students, who participated in…

Eye-tracking (ET) method provides a promising channel for educational researchers to connect learning outcomes to cognitive processes. The main principle of ET is that our gaze and our focus of attention are connected. Due to the advent of digital technologies, eye tracking studies are increasingly growing in different fields and in mathematics…

Traditional rote learning methods often fail to adequately develop reasoning skills in mathematics, particularly among pre-university students. This study addresses challenges in fostering mathematical reasoning abilities, as evidenced by declining TIMSS results and resistance to pedagogical innovations. My online teaching with GeoGebra (MyOT_G+)…

Educational institutions around the world have been integrating AI into their educational practices. Many studies and reports highlight both the advantages and disadvantages of this integration. This paper focuses on the positive aspects of AI in education, specifically through the lens of a high school geometry project at a technology-focused…