This paper describes two examples of teaching situations in which the idea of infinity arises, and supports the conclusion that infinity is not a physical reality but a very powerful and useful mathematical device which facilitates modelling and the solution of problems in physics.

We discuss analysis of 5-grade Likert type data in the two-sample case. Analysis using two-sample "t" tests, nonparametric Wilcoxon tests, and ordinal regression methods, are compared using simulated data based on an ordinal regression paradigm. One thousand pairs of samples of size "n"=10 and "n"=30 were generated,…

Over the past ten years, propensity score methods have made an important contribution to improving generalizations from studies that do not select samples randomly from a population of inference. However, these methods require assumptions and recent work has considered the role of bounding approaches that provide a range of treatment impact…

Differential item functioning (DIF) of test items should be evaluated using practical methods that can produce accurate and useful results. Among a plethora of DIF detection techniques, we introduce the new "Residual DIF" (RDIF) framework, which stands out for its accessibility without sacrificing efficacy. This framework consists of…

Computational modeling and thinking skill sets were previously relegated to computer scientists and programmers. As a result, computational tools are largely unfamiliar to K-12 science teachers and students. Using Mathematical and Computational Thinking and Developing and Using Models were included in the "Next Generation Science…

Most of humanity's important and difficult problems such as pandemics, environmental health, and social unrest require recognizing and understanding complex systems. Students often have difficulty understanding complex systems concepts and previous research indicates that scaffolded computer simulations may facilitate learning. Few studies,…

Working collaboratively in groups can positively impact performance and student engagement. Intelligent social agents can provide a source of personalized support for students, and their benefits likely extend to collaborative settings, but it is difficult to determine how these agents should interact with students. Reinforcement learning (RL)…

The problem of an electrically charged pendulum above a grounded conducting surface is examined using traditional analyses, such as forces, energy, and torque. The system was numerically modelled using a finite difference method and analysed. A number of classroom activities have been suggested.

Inferential reasoning is an integral part of science and civic society, but research shows that it is a problematic domain for many people. One possibility for a more accessible approach to inferential reasoning is to use randomization tests via computer simulations. A case study was conducted with primary preservice teachers after they had passed…

The present simulation study examined the statistical properties (namely, Type I error and statistical power) of various novel randomized single-case multiple-baseline designs and associated randomized-test analyses for comparing the A- to B-phase immediate abrupt outcome changes in two independent intervention conditions. It was found that with…

This study compared three approaches for handling a fourth level of nesting when analyzing cluster-randomized trial (CRT) data. Although CRT data analyses may include repeated measures, individual, and cluster levels, there may be an additional fourth level that is typically ignored. This study examined the impact of ignoring this fourth level,…

Item Response Theory (IRT) models are a popular analytic method for self report data. We show how traditional IRT models can be vulnerable to specific kinds of asymmetric measurement error (AME) in self-report data, because the models spread the error to all estimates -- even those of items that do not contribute error. We quantify the impact of…

Hierarchical data is often observed in education data. Analyzing such data with Multilevel Modeling becomes crucial to understanding the relationship at the individual and group levels. However, one of the most significant problems with this kind of data is small sample sizes and very low Intraclass Correlations. The multivariate Latent Covariate…

Multistage adaptive testing (MST) has become popular in the testing industry because the research has shown that it combines the advantages of both linear tests and item-level computer adaptive testing (CAT). The previous research efforts primarily focused on MST design issues such as panel design, module length, test length, distribution of test…

Longitudinal randomized controlled trials generally assign individuals randomly to interventions at baseline and then evaluate how differential average treatment effects evolve over time. This study shows that longitudinal settings could benefit from "Recurrent Individual Treatment Assignment" ("RITA") instead, particularly in…