Design patterns for learning are about articulating, testing and sharing the principles of problem solving in the educational context. In this way, multiple patterns are developed to solve common problems, described in various pattern language formats. Therefore, this work is about characterizing and establishing functional relationships between…

Most researchers receive formal training in frequentist statistics during their undergraduate studies. In particular, hypothesis testing is usually rooted on the null hypothesis significance testing paradigm and its p-value. Null hypothesis Bayesian testing and its so-called Bayes factor are now becoming increasingly popular. Although the Bayes…

As new technological developments continue to change the educational landscape, it is not an exception in the area of proof and proving. This classroom note introduces the use of one of the trending proofs assistants -- the Lean theorem prover. We first provide a technical account of Lean, then exemplify Lean proofs in propositional logic, number…

Educational curricula in data analysis are increasingly fundamental to statistics, data science, and a wide range of disciplines. The educational literature comparing coding syntaxes for instruction in data analysis recommends utilizing a simple syntax for introductory coursework. However, there is limited prior work to assess the pedagogical…

A staple of many spreadsheet-based management science courses is the use of Excel for activities such as model building, sensitivity analysis, goal seeking, and Monte-Carlo simulation. What might those things look like if carried out using Python? We describe a teaching module in which Python is used to do typical Excel-based modeling and…

When the new programming language Pascal was developed in the 1970's, Walter Gander did not like it because because many features which he appreciated in prior programming languages were missing in Pascal. For example the block structure was gone, there were no dynamical arrays, no functions or procedures were allowed as parameters of a procedure,…

Power analysis based on the analytical t-test is an important aspect of a research study to determine the sample size required to detect the effect for the comparison of two means. The current paper presents a reader-friendly procedure for carrying out the t-test power analysis using the various R add-on packages. While there is a growing of R…

Effect sizes are important because they are an accessible way to indicate the practical importance of observed associations or differences. Standardized mean difference (SMD) effect sizes, such as Cohen's d, are widely used in education and the social sciences -- in part because they are relatively easy to calculate. However, SMD effect sizes…

The process of diffusion is intimately related to random molecular displacement and is central to many problems in chemistry. Here, we provide an intuitive derivation of the diffusion equation based on the analysis of the random trajectories of particles generated and plotted by simple MATLAB and Python scripts. The codes are very simple and…

The COVID-19 pandemic, like past historical events such as the Vietnam War or 9/11, will shape a generation. Mathematics educators can seize this unprecedented opportunity to teach the principles of mathematical modeling in epidemiology. Compartmental epidemiological models, such as the SIR (susceptible-infected-recovered), are widely used by…

The procedures of carrying out factorial invariance to validate a construct were well developed to ensure the reliability of the construct that can be used across groups for comparison and analysis, yet mainly restricted to the frequentist approach. This motivates an update to incorporate the growing Bayesian approach for carrying out the Bayesian…

R is becoming the standard for teaching statistics due to its flexibility, and open-source nature, replacing software programs like Minitab and SPSS. The main driver for reform within Scottish statistical undergraduate programs is the creation of the Scottish Qualification Authority's Higher Applications of Mathematics course which has statistics…

In using software to write a scientific, technical, or other scholarly document, authors have essentially two options. They can either write it in a 'what you see is what you get' (WYSIWYG) editor such as a word processor, or write it in a text editor using a markup language such as HTML, LATEX, Markdown, or AsciiDoc. This paper gives an overview…

Ion channel sensors have several applications including DNA sequencing, biothreat detection, and medical applications. Ion channel sensors mimic the selective transport mechanism of cell membranes and can detect a wide range of analytes at the molecule level. Analytes are sensed through changes in signal patterns. Papers in the literature have…

Bibliometric mapping is widely used in educational technology research to visualize research field development (e.g. the current status and trend). However, there has been limited research examining the present state, challenges, and potential applications of bibliometric mapping techniques in the field of educational technology. In an effort to…