I provide a visual proof for the "Convergence of a Hyper power sequence," which generalises a beautiful result; also proved visually by Azarpanah in 2004.

This article presents a visualization tool adapted from rehabilitation exercise therapy as a means for coaches to organize and select activities to progress or regress the skill difficulty to match the needs and abilities of their athletes.

In contexts where people lack prior knowledge and risk awareness--such as the COVID-19 pandemic--even truthful visualizations of data can seem surprising. This can lead people to mistrust the veracity of the data and to discount it, leading to poor risk decisions. In this work, we illustrate how narrative visualizations can achieve a balance…

The leaders of Networks for School Improvement (NSIs) have complex, challenging jobs which require constant learning and adaptation. To support these leaders, the contributors to this volume have developed a survey-based data visualization system--the Improvement Network Health Development (INHD) Information System--designed to generate insight…

The Uncertainty Principle is usually discussed twice in a Quantum Chemistry course. The first discussion is a "pre-wave function" explanation that occurs before students know about wave functions, but "do" know the de Broglie hypothesis. The second description of the Uncertainty Principle is "post-wave function",…

The trace plot is seldom used in meta-analysis, yet it is a very informative plot. In this article, we define and illustrate what the trace plot is, and discuss why it is important. The Bayesian version of the plot combines the posterior density of [tau], the between-study standard deviation, and the shrunken estimates of the study effects as a…

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…

This study investigates the cognitive strategies employed during a mental rotation task through the integration of interview data and eye-tracking heat map analysis. A total of 20 interviews between 4 participants were analyzed independently by two coders to identify holistic and piecemeal rotation strategies and eye-tracking heat maps were…

The function of proteins is governed by their three-dimensional structure. This structure is determined by the chemical characteristics and atomic interactions of amino acids. Students of biochemistry, with a particular focus on protein chemistry, benefit from looking at protein structures and understanding how proteins are built and fold. Due to…

Large-scale data and data visualizations are ubiquitous now in the stories that shape our society. In particular, these stories influence youth and families' communication and understanding of scientific, social, and personal issues. Consequently, we need to better understand how youth and families can engage and learn with the tools that generate…

Background: Visual representations are pervasive in electrical engineering instruction in various instructional settings. Further, electrical engineering instruction often requires students to extend simple visual representations to learn about more complex visualization in subsequent instruction. Yet, students often struggle to understand…

The success of online learning relies on college students' self-regulated learning. The common visualizations (e.g., presentation learning behaviors' frequency and duration) are widely used to enhance online self-regulated learning. But most college students still have difficulty in accurately understanding their learning patterns and…

Principal Component Analysis (PCA) is a powerful statistical technique for reducing the complexity of data and making patterns and relationships within the data more easily understandable. By using PCA, students can learn to identify the most important features of a data set, visualize relationships between variables, and make informed decisions…

As visual cultures scholars have argued, visual expression and aesthetic artifacts largely comprise the modern world. This includes the production of the school as an institution. A critical approach to education therefore must reinscribe students with the ability to see what educational processes attempt to hide and to construct an understanding…

This study aimed to identify science teacher candidates' mental structures about the concept of the atom. This study included 120 science teacher candidates who were chosen using the convenience sampling method. This research is a phenomenological study. The data on students' mental models of the atom was collected using a metaphor form and an…