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…

A method is presented which can be used to obtain analytical solutions for boundary value problems (BVPs) using the matrix exponential and Maple. Systems of second order, linear differential equations are expressed as two or more first order equations in matrix form, and their solutions are obtained using the matrix exponential, matrix…

Physical experiments in classrooms have many benefits for student learning, including increased student interest, participation and knowledge retention. While experiments are common in engineering and physics classes, they are seldom used in first-year calculus, where the focus is on solving problems analytically and, occasionally, numerically. In…

In this article, we consider certain minimization problems. If d[subscript 1], d[subscript 2] and d[subscript 3] are the distances of a boundary or inner point to the sides of a given triangle, find the point which minimizes d[subscript 1][superscript n] + d[subscript 2][superscript n] + d[subscript 3][superscript n] for positive integer n. These…

It is crucial nowadays to predict in a fast and simple manner physical-chemical behaviors like, the size-dependent optical properties of gold nanospheres (Au NSs). The idea behind this experiment is trying to replace (as much as possible) robust and expensive microscopy techniques with UV-vis spectrophotometry and friendly simulations. Students…

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…

This paper shows how the freely downloadable software package called "SMath Studio" can be used to solve the time-independent Schrödinger equation using a simple step-wise approximation. The solution is illustrated with reference to the hydrogen atom for which trial eigenvalues are supplied by the energy level formula of the Bohr atom.

This paper reviews algorithmic or artificial intelligence (AI) bias in education technology, especially through the lenses of speculative fiction, speculative and liberatory design. It discusses the causes of the bias and reviews literature on various ways that algorithmic/AI bias manifests in education and in communities that are underrepresented…

This is the first of four columns by Tim Erikson which introduces us to the Common Online Data Analysis Platform (CODAP). CODAP is a free, web-based software tool that your students can use for many types of tasks. This first column shows how CODAP can be used for mathematical modelling and where it might fit with the "Australian Curriculum:…

These educators share the "how" and "why" behind their use of open middle tasks in the classroom. In this article, the authors share a type of mathematics task, called Open Middle, that exhibits the characteristics outlined above. The authors frequently use Open Middle tasks in their classrooms because they teach students that…

As the importance of non-technical skills in the software engineering industry increases, the skill sets of graduates match less and less with industry expectations. A growing body of research exists that attempts to identify this skill gap. However, only few so far explicitly compare opinions of the industry with what is currently being taught in…

For a century and a half, the scene of mathematics competitions underwent a remarkable transformation from isolated and geographically scattered events to a full-scale and a full-featured vibrant global ecosystem comprising an impressive variety of competitions, school students, university students, teachers, mentors, scientists, schools,…

The COVID-19 crisis has demonstrated the importance of being able to understand complex computational models for everyday life. To make sense of the evolving predictive models of the COVID-19 pandemic, global citizens need to have a firm grasp of both systems thinking (ST) and computational thinking (CT). ST is the ability to understand a problem…

For years, researchers have recognized the expectation within the business community that business school graduates possess a working knowledge of spreadsheet applications. Academics continue to seek effective ways to teach these skills in an academic setting. This exercise uses Wordle, a five-letter word guessing game, to teach students…

It is often necessary to enrich the teaching environment in order for students to learn optics in depth and to interpret the real optical situations with the information they have learned. In this study, a virtual teaching environment was developed using by Algodoo, a 2D simulation software. An eye model was created in order to explain the…