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.

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…

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.…

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…

Geometric constructions present an opportunity to help students develop geometric proofs and justifications while actively creating mathematical representations (Mariotti, 2001). Though traditionally carried out with paper and pencil, dynamic geometry software allows students to produce more precise constructions with greater certainty…

In this study, we explore automated reasoning tools (ART) in geometry education and we argue that these tools are part of a wider, nascent ecosystem for computer-supported geometric reasoning. To provide some context, we set out to summarize the capabilities of ART in GeoGebra (GGb), and we discuss the first research proposals of its use in the…

Windmill images and shapes have a long history in geometry and can be found in problems in different mathematical contexts. In this paper, we share and discuss various problems involving windmill shapes and solutions from geometry, algebra, to elementary number theory. These problems can be used, separately or together, for students to explore…

The paper argues that there is a need for new approaches to teaching proof with newly-available technology. It contributes to filling this need by opening a discussion on digital proof assistants, programs that allow one to do mathematics with the aid of a computer, construct proofs, and check their correctness. The paper starts by exploring such…

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…

The present paper describes beautiful conservation relations between areas formed by different geometrical shapes and area relations formed by algebraic functions. The conservation properties were investigated by students at an academic college of education using a computerized technological tool and were subsequently accompanied by justified…

The capability of computer programming language logic is one of the basics of technical education. How to improve students "interest in program logic design and help overcome students" fears of coding has become vital for educators. Cultivating practical talents with information technology application and basic programming development…

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+)…

In this paper, we investigate how a research mathematician conjectures and proves when conducting her research. To be precise, the aim of this study is to achieve a comprehensive understanding of the way this research mathematician develops these mathematical practices and thus gain insight to improve the teaching and learning of these two…

The current study, aimed to examine the development of flexibility and strategy use through instructional sequence encouraging the preservice middle school mathematics teachers' geometric thinking and problem-solving performance on dynamic geometry environment. Mixed-method research design was used in the study. The study was conducted with 46…