Nomographs (or nomograms, or alignment charts) are graphical representations of mathematical relationships (extending to empirical relationships of data) which are used by simply applying a straightedge across the plot through points on scales representing independent variables, which then crosses the corresponding datum point for the dependent…

We derive formulas for the differential item functioning (DIF) measures that two routinely used DIF statistics are designed to estimate. The DIF measures that match on observed scores are compared to DIF measures based on an unobserved ability (theta or true score) for items that are described by either the one-parameter logistic (1PL) or…

From his first attempts to explain attachment phenomena in the 1940s through his "Attachment and Loss" trilogy (Bowlby, 1969/1982, 1973, 1980), John Bowlby reformulated the theoretical underpinnings of attachment theory several times. He initially attempted to explain attachment phenomena in psychoanalytic terms. Then he invoked…

Regression mixture models are a statistical approach used for estimating heterogeneity in effects. This study investigates the impact of sample size on regression mixture's ability to produce "stable" results. Monte Carlo simulations and analysis of resamples from an application data set were used to illustrate the types of problems that…

Parameter linking in item response theory is generally necessary to adjust for differences between the true values for the same item and ability parameters due to the use of different identifiability restrictions in different calibrations. The research reported in this article explores a precision-weighted (PW) approach to the problem of…

There have been a few methods described in this journal and elsewhere for measuring the wavelength of the standing electromagnetic waves in a microwave oven. Typically, these involve melting chocolate, cheese, or some other substance on a plate that is prevented from rotating. In this article I describe a more dynamic and colorful technique that…

The idea of using fingers as a key component in arithmetic development has received a great deal of support, much of which is based on neuroscientific evidence. However, this body of work pays limited attention to how fingers are used and possible different outcomes in arithmetic problem solving. The aim of our paper, based on an analysis of 126…

We proposed an extended form of the Govindarajulu and Barnett margin of error (MOE) equation and used it with an analysis of variance experimental design to examine the effects of aggregating student evaluations of teaching (SET) ratings on the MOE statistic. The interpretative validity of SET ratings can be questioned when the number of students…

Counting is an important functional skill that is embedded throughout people's daily lives, which can result in numerous meaningful opportunities through which students can learn. Counting, especially early counting, provides a foundation for the development of later mathematics understanding and is highly predictive of later mathematics…

The commenter's proposal may be a reasonable method for addressing uncertainty in predictive modeling, where the goal is to predict "y." In a treatment effects framework, where the goal is causal inference by conditioning-on-observables, the commenter's proposal is deeply flawed. The proposal (1) ignores the definition of…

Recently, Robin claimed to introduce clever innovations ('wrinkles') into the mathematics education literature concerning the solutions, and methods of solution, to differential equations. In particular, Robin formulated an iterative scheme in the form of a single integral representation. These ideas were applied to a range of examples involving…

Item response theory is a widely used framework for the design, scoring, and scaling of measurement instruments. Item response models are typically used for dichotomously scored questions that have only two score points (e.g., multiple-choice items). However, given the increasing use of instruments that include questions with multiple response…

Artificial intelligence (AI) and computational sciences have aroused a growing interest in education. Despite its relatively recent history, AI is increasingly being introduced into the classroom through different modalities, with the aim of improving student achievement. Thus, the purpose of the research is to analyse, quantitatively and…

In recent years, the integration of STEM disciplines has been increasingly advocated. It is crucial to prepare and support teachers for integrated STEM education. However, few studies in the literature explore collaborating with teachers from different disciplines. This study investigates the effect of the professional development (PD) program…

There is strong evidence from research conducted in the United States that fraction magnitude understanding supports mathematics achievement. Unfortunately, there has been little research that examines if this relation is present across educational contexts with different approaches to teaching fractions. The current study compared fourth and…