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…

As technology advances, virtual museums have gained popularity as a new form of learning resources. However, persuading audiences to absorb and comprehend a tremendous volume of information in an unregulated online environment is the challenge. Considering the use of an online application in educational practice, collaborative teamwork can be…

Nowadays, SPOCs (Small Private Online Courses) have been used as complementary methods to support classroom teaching. SPOCs are courses that apply the usage of MOOCs (Massive Open Online Courses), combining classroom with online education, making them an exciting alternative for contexts such as emergency remote teaching. Although SPOCs have been…

Calculating analytical uncertainties as a part of method validation is a relevant aspect of field and laboratory practices in instrumental analytical chemistry subjects, which usually require complex algorithms. This work describes the development and didactic use of an automatic and straightforward informatics tool, implemented in an Excel macro,…

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…

This research aims to design immersive virtual reality with cognitive conflict to support practical learning of quantum physics. This type of research is design research through the stages of needs analysis, product design, validity test, and practicality test. The needs analysis used questionnaire sheets distributed with Google Forms and obtained…

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…

Through design and development research (DDR), we aimed to create a validated automatic question generation (AQG) system using large language models (LLMs) like ChatGPT, enhanced by prompting engineering techniques. While AQG has become increasingly integral to online learning for its efficiency in generating questions, issues such as inconsistent…

Purpose: This study investigates the impact of AI-assisted pair programming on undergraduate students' intrinsic motivation, programming anxiety, and performance, relative to both human-human pair programming and individual programming approaches. Methods: A quasi-experimental design was conducted over two academic years (2023-2024) with 234…

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 first of the two postulates of relativity states that the laws of physics are the same in all inertial reference frames. Often it is assumed that the postulates are mainly concerned with objects moving at a significant fraction of the speed of light. However, the postulates are applicable at all speeds from a snail to a photon. To practically…

As generative artificial intelligence tools like ChatGPT become increasingly integrated into educational environments, understanding their impact on critical thinking is crucial. Despite growing concerns about AI's potential to diminish students' independent reasoning, there is a lack of research tools specifically designed to evaluate students'…