We first review existing literature on cumulative logit models along with various ways to test the parallel lines assumption. Building on the traditional frequentist framework, we introduce a method of Bayesian assessment of null values to provide an alternative way to examine the parallel lines assumption using highest density intervals and…

It is well known that Newton's work on mechanics depended in a crucial way on the previous observations of Galileo. The key insight of Galileo was that one can analyze the motion of bodies using experiments and mathematical equations. One experimental observation that roughly emerges from this work in modern terms is that two objects of different…

In this article, we propose using the Bayes factors (BF) to evaluate person fit in item response theory models under the framework of Bayesian evaluation of an informative diagnostic hypothesis. We first discuss the theoretical foundation for this application and how to analyze person fit using BF. To demonstrate the feasibility of this approach,…

In 1881, Donald MacAlister posed a problem in the "Educational Times" that remains relevant today. The problem centers on the statistical evidence for the effectiveness of a treatment based on a comparison between two proportions. A brief historical sketch is followed by a discussion of two default Bayesian solutions, one based on a…

A central question in working memory research concerns the degree to which information in working memory is accessible to other cognitive processes (e.g., decision-making). Theories assuming that the focus of attention can only store a single object at a time require the focus to orient to a target representation before further processing can…

Assimilating multiple interactive elements simultaneously in working memory to allow understanding to occur, while solving an equation, would impose a high cognitive load. "Element interactivity" arises from the interaction between elements within and across operational and relational lines. Moreover, operating with special features…

Cluster randomized experiments are ubiquitous in modern education research. Although a variety of modeling approaches are used to analyze these data, perhaps the most common methodology is a normal mixed effects model where some effects, such as the treatment effect, are regarded as fixed, and others, such as the effect of group random assignment…

The aim of this study is to determine variance difference between maximum likelihood and expected A posteriori estimation methods viewed from number of test items of aptitude test. The variance presents an accuracy generated by both maximum likelihood and Bayes estimation methods. The test consists of three subtests, each with 40 multiple-choice…

The research field of intuitive physics focuses on discrepancies between theoretical and intuitive physical knowledge. Consideration of these discrepancies can help in the teaching of elementary physics. However, evidence shows that theoretical and intuitive physical knowledge may also be congruent. Physics teaching could further benefit from…

A multiple testing method for examining factorial invariance for latent constructs evaluated by multiple indicators in distinct populations is outlined. The procedure is based on the false discovery rate concept and multiple individual restriction tests and resolves general limitations of a popular factorial invariance testing approach. The…

We examined the use of balance and inverse methods in equation solving. The main difference between the balance and inverse methods lies in the operational line (e.g. +2 on both sides vs -2 becomes +2). Differential element interactivity favours the inverse method because the interaction between elements occurs on both sides of the equation for…

Developing expertise in physics problem solving requires the ability to use mathematics effectively in physical scenarios. Novices and experts often perceive the use of mathematics in physics differently. Students' perceptions and how they frame the use of mathematics in physics play an important role in their physics problem solving. In this…

This study develops a tool to identify errors in the presentation of natural laws based on the epistemology and ontology of the Scientific Realism of Mario Bunge. The tool is able to identify errors of different types: (1) epistemological, in which the law is incorrectly presented as data correlation instead of as a pattern of causality; (2)…

We find statistically significant relationships between changes in wages by occupation and subsequent changes in college majors completed in associated fields. College majors (defined at a detailed level) are most strongly related to wages observed three years earlier, when students were college freshmen. The responses to wages vary depending on…

Engaging learners in exploratory problem-solving activities prior to receiving instruction (i.e., explore-instruct approach) has been endorsed as an effective learning approach. However, it remains unclear whether this approach is feasible for elementary-school children in a classroom context. In two experiments, second-graders solved mathematical…