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…

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 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…

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,…

One of the challenges of discussing validity arguments for machine scoring of essays centers on the absence of a commonly held definition and theory of good writing. At best, the algorithms attempt to measure select attributes of writing and calibrate them against human ratings with the goal of accurate prediction of scores for new essays.…

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…

Students in an upper-level physical chemistry course utilized an open-sourced statistical software package to construct models fitted to experimental pressure-volume data. In the first part of the experiment, students familiarize themselves with model fitting. In the second part of the experiment, students determine which truncated version of 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…

Proof, as a central and integral part of mathematics, is an essential component of mathematical education and is considered as the basic procedure for revealing the truth of mathematical propositions and for teaching productive reasoning as part of human civilization. Is there therefore room for conjectures in mathematics? In this paper after…

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 cutting-edge technology, namely Cloud of Things (CoT) has shaped the existing business process into a new orientation in terms of performance, usability, and reliability. Among different business processes, online education is one of the prime areas where CoT can be used to make it more agile in the context of performance and usability. In…