This paper outlines the potential gains for Constructionist research and praxis in modelling that might be obtained by recognising the power of the Patch--a humble computational being in the NetLogo modelling environment that has been overshadowed by its more popular fellow agent, the Turtle. To contextualise this opportunity, I describe how…

The article shows that even a small number of iterations give a very large length of the Koch Curve. The overall purpose of this work is to show that even a small number of iterations can give a very complex fractal structure. In this case it is the very big length of Koch's curve. As examples, the distance from the Earth to the Moon and from the…

Cohen's kappa coefficient was originally proposed for two raters only, and it later extended to an arbitrarily large number of raters to become what is known as Fleiss' generalized kappa. Fleiss' generalized kappa and its large-sample variance are still widely used by researchers and were implemented in several software packages, including, among…

In a typical first physics class, homework consists of problems in which numerical values for physical quantities are given and the desired answer is a number with appropriate units. In contrast, most calculations in upper-division undergraduate physics are entirely symbolic. Despite the need to learn symbolic manipulation, students are often…

In this article we show that the electrostatic field intensity of a uniformly charged straight line equals that of the corresponding arc of a circle charged with the same linear density. This new method greatly simplifies the calculation of the electrostatic field of a system consisting of uniformly charged straight lines.

In this article, we show a "very" simple algorithm for the evaluation of the character tables applicable to all finite point groups. The method uses linear combinations of the symmetry operators associated with the point group's classes as the basis set. Eigenvectors of the resulting matrix of such representations are related to the…

The analysis, calculations and graphical charts presented here in this paper are based directly on a recently published paper by the first two of the above-named authors. In the present paper, it is clearly demonstrated that all of the following nine (or eleven including the centripetal acceleration and total mechanical energy) principal physical…

This article aims to clarify the fundamental aspects of aggregating fuzzy scores of conditions with multiple attributes in fuzzy set qualitative comparative analysis (fsQCA). Fuzzy multiple attribute conditions (FMACs) are conditions that are built using different types of concepts. FMACs are flexible conditions that express the ontological nature…

Network meta-analysis has been an essential methodology of systematic reviews for comparative effectiveness research. The restricted maximum likelihood (REML) method is one of the current standard inference methods for multivariate, contrast-based meta-analysis models, but recent studies have revealed the resultant confidence intervals of average…

Before embarking on an individual participant data meta-analysis (IPDMA) project, researchers should consider the power of their planned IPDMA conditional on the studies promising their IPD and their characteristics. Such power estimates help inform whether the IPDMA project is worth the time and funding investment, before IPD are collected. Here,…

Theoretical and practical foundations of basic electrochemical concepts of heterogeneous charge transfer reactions that underline electrochemical processes are presented for their detailed study by undergraduate and postgraduate students. Several simple methods for calculating key variables, such as the half-wave potential, limiting current, and…

Visuospatial representations of numbers and their relationships are widely used in mathematics education. These include drawn images, models constructed with concrete manipulatives, enactive/embodied forms, computer graphics, and more. This paper addresses the analytical limitations and ethical implications of methodologies that use broad…

Computer programming has become an essential part of K12 education, promoted as a way for students to engage in computational thinking that helps develop students' ability to analyze and solve problems and prepare them for future careers. Tabletop board games are seen as an effective means to help students learn computer programming. Several board…

While computational thinking arises as an essential skill worldwide, formal primary and secondary education in Latin America rarely incorporates mechanisms to develop it in their curricula. The extent to which students in the region acquire computational thinking skills remains largely unknown. To start addressing this void, this article presents…

Analyzing qualitative data from learning processes is considered "messy" and time consuming (Chi in J Learn Sci 6(3):271-315, 1997). It is often challenging to summarize and synthesize such data in a manner that conveys the richness and complexity of learning processes in a clear and concise manner. Moreover, qualitative data often…