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.

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…

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…

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…

Building activities can be used any time in the school year in mathematics classes to promote problem solving, perseverance, and to develop students' spatial thinking. Spatial visualization skills are the "ability to mentally manipulate, rotate, twist, or invert a pictorially presented stimulus object." The authors were guided by the…

Simulations can provide opportunities for engaged exploration in physics teaching and learning. Beyond the two-dimensional world of screen-based simulations, abstract concepts like vectors (for example, of electric fields) can frequently be visualized better in a three-dimensional virtual reality (VR) environment. These visualizations can be…

Optimization is introduced to teaching in secondary school, focussing on functions of one variable with the first derivative criterion for critical points and monotonicity of functions. The second derivative criterion is also used to determine the nature of the critical points. Similarly, in university-level teaching, algebraic work using criteria…

Biological interactions and associations underlie life's processes at every level of organization. Here, we present a classroom activity that allows students to visualize and understand the connections within almost any biological system, from cell functions to ecological relationships. We recommend that instructors implement this activity to…

Network meta-analysis (NMA) is an established method for assessing the comparative efficacy and safety of competing interventions. It is often the case that we deal with interventions that consist of multiple, possibly interacting, components. Examples of interventions' components include characteristics of the intervention, mode (face-to-face,…

This short paper presents an educational approach to teaching three popular methods for encoding DNA sequences: one-hot encoding, binary encoding, and integer encoding. Aimed at bioinformatics and computational biology students, our learning intervention focuses on developing practical skills in implementing these essential techniques for…

The Grand Challenges for Assessment in Higher Education project is a collaborative effort of 10 endorsing organizations and over 400 volunteers to increase the extent to which assessment (1) supports equity; (2) is visible, actionable, and drives innovation; and (3) guides rapid improvements in pedagogy (Singer-Freeman and Robinson 2020). Several…

How do learners make sense of what they are learning? In this article, I present a new framework of sense-making based on research investigating the benefits and boundaries of generative learning activities (GLAs). The generative sense-making framework distinguishes among three primary sense-making modes--explaining, visualizing, and…

This contribution deals with effect measures for covariates in ordinal data models to address the interpretation of the results on the extreme categories of the scales, evaluate possible response styles, and motivate collapsing of extreme categories. It provides a simpler interpretation of the influence of the covariates on the probability of the…

This article presents an original puzzle that supports students' development of visual thinking and geometry ideas based on the Van Hiele levels of geometric thought. The "Triangle Puzzle" is one of many tools teachers can use to guide students' learning of geometry. The Van Hiele's theory provides a way to assess and support this…