Subjects with initially extreme observations upon remeasurement are found closer to the population mean. This tendency of observations toward the mean is called regression to the mean (RTM) and can make natural variation in repeated data look like real change. Studies, where subjects are selected on a baseline criterion, should be guarded against…

There are two schools of thought in statistical analysis, frequentist, and Bayesian. Though the two approaches produce similar estimations and predictions in large-sample studies, their interpretations are different. Bland Altman analysis is a statistical method that is widely used for comparing two methods of measurement. It was originally…

Longitudinal data structures are frequently encountered in a variety of disciplines in the social and behavioral sciences. Growth curve modeling offers a highly extensible framework that allows for the exploration of rich hypotheses. However, owing to the presence of interrelated sources of potential data-model misfit at multiple levels, the…

In this literature review, we survey student naïve ideas (frequently referred to as 'misconceptions') that plausibly relate, at least in part, to difficulty in understanding probability. We collected diverse naïve ideas from a range of topics in physics: Non-linear Dynamics; Cosmology; Thermal Physics; Atomic, Nuclear, and Particle Physics;…

In educational and psychological research, we are often interested in discrete latent states of individuals responding to an assessment (e.g., proficiency or non-proficiency on educational standards, the presence or absence of a psychological disorder). Diagnostic classification models (DCMs; also called cognitive diagnostic models [CDMs]) are a…

The purpose of this study was to analyze the problem-solving techniques that students in a fifth-grade classroom applied while solving mathematical word problems. Fifth-grade students in a private school with Ministry of Education curricula in Al Ain, Abu Dhabi, were given a set of 15-word problems to solve with detailed justifications. The…

The Forty Fifth Annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education was held PME-NA 45 in Reno, Nevada, October 1-4, 2023. The conference theme is "Engaging All Learners." Math learning should be a joyful experience for all students. When students are engaged and inspired,…

These proceedings are a written record of the research presented at the 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in Nashville, Tennessee, and virtually. This year's conference theme is "Critical Dissonance and Resonant Harmony." The aim of this…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

Many important high-stakes decisions--college admission, academic performance evaluation, and even job promotion--depend on accurate and reliable scores from valid large-scale assessments. However, examinees sometimes cheat by copying answers from other test-takers or practicing with test items ahead of time, which can undermine the effectiveness…

Randomized experiments are considered the gold standard for causal inference because they can provide unbiased estimates of treatment effects for the experimental participants. However, researchers and policymakers are often interested in using a specific experiment to inform decisions about other target populations. In education research,…

Modeling the distribution of site level effects is an important problem, but it is also an incredibly difficult one. Current methods rely on distributional assumptions in multilevel models for estimation. There it is hoped that the partial pooling of site level estimates with overall estimates, designed to take into account individual variation as…

These proceedings are a written record of the research presented at the 41st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in St. Louis, Missouri, November 14-17, 2019. This year's conference theme is "...against a new horizon." The papers comprise 67…

"Mathematical Thinking: From Assessment Items to Challenging Tasks" is a compilation of 36 problem-based lessons that encourage students to engage in productive struggle and deep thinking. Its 36 full-length lessons for grades 2-8 are each inspired by an actual test item from the National Assessment of Educational Progress (NAEP).…

We propose a new limited-information goodness of fit test statistic C[subscript 2] for ordinal IRT models. The construction of the new statistic lies formally between the M[subscript 2] statistic of Maydeu-Olivares and Joe (2006), which utilizes first and second order marginal probabilities, and the M*[subscript 2] statistic of Cai and Hansen…