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…

The visual method in this paper solves linear inequalities in one variable by considering them initially as two competing linear expressions, each of which is then expressed as a linear equation. When the solution of these two linear equations exist, it is viewed as a highlighted area or a line. These linear equations convey the intended visual…

In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the "philosophy of mathematical practice." In this paper we offer a survey of this movement aimed at mathematics educators. We first describe the core questions philosophers of mathematical practice…

With the help of augmented reality apps objects and text can be added virtually to the physical world (e.g. physical experiments) in real time. The augmented reality (AR) app 'PUMA: "Spannungslabor"' enhances simple electric circuits experiments for students with virtual representations based on the electron gas analogy including…

As students learn physics, they are often required to reason about the behavior of macroscopic and microscopic phenomena, and to synthesize prior knowledge from several different areas of physics to construct understanding of new ideas. This can be a tremendously difficult cognitive task for novice students, especially when the unfamiliar…

This article shares two activities geared toward students in middle school that engage students in analyzing measures of center, specifically the arithmetic mean, and using transnumerative thinking with the ultimate goal of improving students' statistical literacy. Both activities support the Common Core standard, 6.SP.B.5 "Summarize and…

Visualization can be a motivating way to teach students about molecules. Nowadays, the available experimental data and accurate computational results allow students to build realistic and accurate molecular models. These models include the representation of complex systems such as proteins, membranes, or nanotubes. However, the visualization of…

Visualizations are useful tools for helping students to understand chemistry concepts at the particulate level. A classroom activity was developed based on learning theory and evidence-based practices, combining protein visualization with thermodynamic parameters from differential scanning fluorimetry (DSF) data analysis. Coding of student…

Spatial ability was defined by Lohman (1996) as the ability to create, maintain, retrieve, and change visual pictures. Linn and Peterson (1985) distinguished among spatial perception, mental rotation, and spatial visualization. Spatial perception is the determination of spatial connections with respect to the orientation of the learners' body;…

We present an accessible implementation of augmented reality projections for the depiction of complex structures and motifs, including atomic orbitals and elemental allotropes. The utilization of a free, cross-platform-compatible, online database of these structures provides the access route for closer examination, either via augmented reality or…

The "Yet Another extended Hu¨ckel Molecular Orbital Package" (YAeHMOP) has been merged with the Avogadro open-source molecular editor and visualizer. It is now possible to perform YAeHMOP calculations directly from the Avogadro graphical user interface for materials that are periodic in one, two, or three dimensions, and to visualize…

Unlike the large number of laboratory experiments on phase-transfer catalysis (PTC) that focus on a catalyzed chemical process, the present laboratory emphasizes the mechanism of phase transfer catalysis itself. Students can follow visually the actual transfer of the reagent by the catalyst, and its consumption in the organic phase, in a…

Increasingly students, particularly those in the social sciences, work with survey data collected through a more complex sampling method than a simple random sample. Failing to understand how to properly approach survey data can lead to inaccurate results. In this article, we describe a series of online data visualization applications and…

Public art installations are part of university campuses across the United States, and these installations can be useful in teaching important geographic concepts, skills, and geovisualization techniques. Using public on-campus art resources in geography classes can both enhance student learning of important geography content, themes, and…

Literature on the use of design tools in educational settings notes an uneasy relationship between student use of traditional hand sketching and digital modelling tools (CAD) during the industrial design process. This is often manifested in the transition from sketching to CAD and exacerbated by a preference of current students to use CAD. In this…