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…

Vectors have important applications both within and outside mathematics, but the concept of vectors is often taught to students in a less-than-engaging way, leading to students feeling inadequate and frustrated. This article describes the use of a mathematical microworld, "Driving with Vectors," to explore vectors using equitable…

Today math teachers can best reach their students and show them how math surrounds us by using manipulatives, children's literature, and GeoGebra while teaching mathematics. These are some of the best pedagogical practices for teaching mathematics today. In our high-tech world, students need to be proficient in science, technology, engineering,…

CRISPR-Cas9 is revolutionizing how we conduct scientific research, treat disease, and develop new crops. The widespread impact of this genome-editing technology makes it critical for undergraduate students to understand and engage with this new tool. In this article, we describe a multi-week lab module that teaches undergraduates how to design…

In this article, the authors share activities designed to help students make a connection between the complex roots of X[superscript 2] - 2x + 5 = 0 and the graph of y = X[superscript 2] - 2x + 5. We piloted these activities in three precalculus classes. The activities involved both concrete and technological representations of the mathematical…

The use of symmetry is widespread in chemistry, as it is used for predictions of the number of allowed and forbidden absorptions in electronic, vibrational, and rotational spectroscopies; for predictions of the combination of atomic orbitals to produce molecular orbitals; and in many other chemical applications. One critical step in these…

A bachelor's degree program in chemistry typically starts with basic concepts in mathematics, physics, and chemistry. Those principles are very important because they pave the ground for future advanced studies and, therefore, one needs to present them in a clear but rigorous way. One example is provided by the mathematical notion of an iterative…

Informal Digital Learning of English (IDLE) refers to individual's learning endeavor occurring in out-of-class environments in a naturalistic way independent from the requirements of a formal education program including assessment. Learners' IDLE experiences in English as a Foreign Language (EFL) contexts are quite important to understand their…

Facile visualization of biomolecules is an essential component of the undergraduate biochemistry curriculum. In the past, a number of tools have been used to display biomolecules. More recently, the advent of greater accessibility to virtual reality (VR) and augmented reality (AR) programs has created a new mechanism to visualize biomolecules.…

This research endeavors to assess the efficacy of Mobile Assisted Language Learning (MALL) in elevating students' English proficiency to the Common European Framework of Reference (CEFR) B1 level. The study involves identifying the most suitable mobile application for formative assessment, implementing it to enhance students' English competency,…

Principal component analysis (PCA) is one of the most important and powerful methods in chemometrics as well as in a wealth of other areas. Running a PCA results in two main elements, the score plot and the loading plot; the score plot provides the location of the samples, and the loading plot indicates correlations among variables, the trends in…

When the author first started teaching twenty years ago, he thought that as long as he was using dynamic geometry software (DGS) for students to "discover" conjectures instead of them learning the conjectures from a lecture or the textbook, he was maximizing their learning potential because they were using technology. Over the years, he…

Context is what makes mathematical modeling tasks different from more traditional textbook word problems. Math problems are sometimes stripped of context as they are worked on. For modeling problems, however, context is important for making sense of the mathematics. The task should be brought back to its real-world context as often as possible. In…

As solar energy becomes increasingly affordable, many schools are considering installing new solar power systems. In this article, the authors present Solarize Your School, an engineering project that gives students the opportunity to design and evaluate solar power solutions for their own schools. This STEM project requires students to learn and…

This article aims to provide teachers with a practical introduction to the capabilities of augmented and virtual reality (AR/VR) in foreign language education. We first provide an overview of recent developments in this field and review some of the affordances of the technologies. This is followed by detailed outlines of a number of activities…