A single discrete random variable is depicted by a stick diagram, a 2D picture. Naturally, to visualize a bivariate discrete distribution, one can use a bivariate stick diagram, a 3D picture. Unfortunately, many students have difficulty understanding and processing 3D pictures. Therefore, we construct an alternative 2D disc plot to depict the…

Baseball. Subway line. Maps. A flower. Each of these contexts involves some form of varying motion or constant change over time: the bi-directional motion of a fly ball, the speed of a subway car, or the growth of a flower until bloom. This article does not highlight students' calculus problem-solving abilities, but rather describes a set of…

"k[subscript cat]/K[subscript M]" is a fundamental kinetic parameter as important as "k[subscript cat]" in enzyme kinetics. Although the parameter provides critical information on how the enzyme lowers the energy barriers along the reaction pathway for catalysis, "k[subscript cat]/K[subscript M]" is frequently…

The article describes how to derive the equation of curves that are obtained from string art. Conversely, if the equation of a curve is given, one can find the relation between the intercepts either on a rectangular axes, skewed axis, or a circle to trace out these curves. Some of these curves can be easily traced out using the string art if they…

Fractions are an important concept used throughout advanced mathematical ideas and everyday life. Students need a solid understanding of fraction concepts, such as magnitude, equivalence, and operations. However, many students, including students with learning disabilities (LD) in mathematics, struggle with fractions. In this article, the use of…

The laser pointer has been widely used to demonstrate some simple optics phenomena, like reflection, refraction, total reflection, and diffraction. However, the rays of laser light cannot be seen in the air because the scattered light is too weak. Many physics teachers use milk or smoke to visualize rays of laser light in physics labs, but it is…

Information flow is one of the three main flows of supply chains. It is an abstract concept that can be challenging for students to grasp in its entirety. This article describes a role-playing game for teaching the topic of information flow in an undergraduate supply chain management course. The game allows students to simulate receiving and…

Financial literacy is crucial for making sound financial decisions and living a better life. However, the field of finance is full of abstract concepts, such as inflation, liquidity, asset allocation and credit. Abstract concepts may be harder to comprehend than concrete concepts due to their lack of tangible referents in the physical world. In…

In this reflection of teaching, we describe a series of activities that introduce the Taylor series through dynamic visual representations with explicit connections to students' prior learning. Over the past several decades, educators have noted that curricular materials tend to present the Taylor series in a way that students often interpret as…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

In at least two papers published in this "Journal," enzyme free energy diagrams were presented showing enzyme--substrate binding to be nonspontaneous. I present here several different approaches showing that enzyme--substrate binding is "always" spontaneous, and the y-axis of the reaction progress diagrams presented previously…

Science diagrams are an integral part of science because they are an important means of conveying and visualizing abstract science content. In recent years, researchers have demonstrated the educational benefits of encouraging students to draw their own conceptual diagrams, rather than focusing on interpreting diagrams given to them. To help…

After teaching last 10 years and analyzing student work, I realize that in developmental and Elementary Algebra courses there is a disconnection between the students conceptual understanding in context in contrast to their procedural fluency. In some cases, students can perform the procedure, but do not understand when the procedure is valid. In…

In place of a traditional Advanced Placement Chemistry class at the high school where I teach, I have recently developed and implemented a year-long, interdisciplinary curriculum that presents typical inorganic chemistry topics in the context of their relevant applications in archeology, art history, studio art, and the investigation,…

This paper proposes the design of an ontology of multiple programming languages and give three examples to show the methodology. Our ontology aims to summarize the core of computational thinking logic by elaborating the concepts of three object-oriented programming languages in the industry: Python, Java, and C#. Therefore, the construction of the…