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.

Eye gaze tracking has recently become indispensable for domains like virtual reality, augmented reality, human-computer interaction and advertisement. The commercial eye gaze tracking equipment is too expensive to be used by the masses. In this manuscript, a non-invasive, low-resolution ordinary camera-based system has been proposed for tracking…

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…

This study demonstrates the use of two web-based programs, one to identify video preferences and the other to assess their reinforcing effects. We used the Multiple-Stimulus-Without-Replacement Preference Assessment Tool (MSWO PAT) to identify the video preference hierarchies of seven participants, ages 4-11 years old. We then used a customized…

This technical report provides an authoritative bibliographic resource of all the studies conducted on "easyCBM"® and published on the main website for Behavioral Research and Teaching under Publications (https://brtprojects.org). The "easyCBM"© software is a direct descendent of "Curriculum-based Measurement" (CBM)…

Courses: This activity can be used in writing-based (communication) courses across various disciplines including, but not limited to, introduction to writing and rhetoric, business communication, and communication research methods. Objectives: On completion of this activity, students will develop critical reading, thinking, and writing skills as…

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.…

The remarkable strides in artificial intelligence (AI), exemplified by ChatGPT, have unveiled a wealth of opportunities and challenges in assessment. Applying cutting-edge large language models (LLMs) and generative AI to assessment holds great promise in boosting efficiency, mitigating bias, and facilitating customized evaluations. Conversely,…

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…

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…

It is of critical importance to be aware of the historical discrimination embedded in the data and to consider a fairness measure to reduce bias throughout the predictive modeling pipeline. Given various notions of fairness defined in the literature, investigating the correlation and interaction among metrics is vital for addressing unfairness.…

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,…

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…

The procedures of carrying out factorial invariance to validate a construct were well developed to ensure the reliability of the construct that can be used across groups for comparison and analysis, yet mainly restricted to the frequentist approach. This motivates an update to incorporate the growing Bayesian approach for carrying out the Bayesian…