This study shows that residual variation can cause problems related to scaling in exponential random graph models (ERGM). Residual variation is likely to exist when there are unmeasured variables in a model--even those uncorrelated with other predictors--or when the logistic form of the model is inappropriate. As a consequence, coefficients cannot…

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,…

One of the most prevalent features of digital mathematics textbooks, compared to traditional ones, is the provision of automated feedback on students' solutions. Since feedback is regarded as an important factor that influences learning, this is often seen as an affordance of digital mathematics textbooks. While there is a large body of mainly…

This research is aimed to describe a learning trajectory for probability through game-based learning. The research employed design research consisting of three stages: preparing for the experiment, design experiment, and retrospective analysis. A hypothetical learning trajectory (HLT) using Sudoku and Snake-and-ladder games was developed by…

The present study compares the fit of two- and three-parameter logistic (2PL and 3PL) models of item response theory in the performance of preschool children on the Raven's Colored Progressive Matrices. The test of Raven is widely used for evaluating nonverbal intelligence of factor g. Studies comparing models with real data are scarce on the…

This study investigates whether infants are sensitive to backward and forward transitional probabilities within temporal and spatial visual streams. Two groups of 8-month-old infants were familiarized with an artificial grammar of shapes, comprising backward and forward base pairs (i.e. two shapes linked by strong backward or forward transitional…

"p" values are commonly reported in quantitative research, but are often misunderstood and misinterpreted by research consumers. Our aim in this article is to provide special educators with guidance for appropriately interpreting "p" values, with the broader goal of improving research consumers' understanding and interpretation…

Although students' understanding of frequency information presented in two-way tables was first explored in the 1990s, there is a surprising lack of research in this area. Furthermore, researchers and practitioners continue to highlight students' difficulties in comprehending probability including concepts related to conditioning. Using an…

Extreme Learning Machine (ELM) is a training algorithm for Single-Layer Feed-forward Neural Network (SLFN). The difference in theory of ELM from other training algorithms is in the existence of explicitly-given solution due to the immutability of initialed weights. In practice, ELMs achieve performance similar to that of other state-of-the-art…

Many existing student persistence and retention studies overlooked the different types of departure (e.g., dropout, transfer) and aggregate them into a single departure variable, as a result, the estimates from these studies are spurious when one is interested in what student characteristics prompt dropout but not transfer. This can be especially…

Background: It is of grave concern that kindergartners are missing more school than students in any other year of elementary school; therefore, documenting which students are absent and for how long is of upmost importance. Yet, doing so for students with disabilities (SWDs) has received little attention. This study addresses this gap by examining…

Identifying students at risk of failing a course has potential benefits, such as recommending the At-Risk students to various interventions that could improve pass rates. The challenges however, are firstly in measuring how effective these interventions are, i.e. measuring treatment effects, and secondly, to not only predict overall (average)…

Emphasis in teaching and learning statistics has shifted from memorizing formulas and procedures to investigating situations, creating models, and using data to understand problems. The Common Core State Standards for Mathematics (CCSSM) (NGA Center and CCSSO 2010) Grade 8 Statistics and Probability content standards drive this point home.…

Previous work has ostensibly shown that readers rapidly adapt to less predictable ambiguity resolutions after repeated exposure to unbalanced statistical input (e.g., a high number of reduced relative-clause garden-path sentences), and that these readers grow to disfavor the a priori more frequent (e.g. main verb) resolution after exposure (Fine,…

Most likely a large number of students have heard of the Northern Lights (Aurora Borealis), and know that they are a phenomenon in the sky. Although they may not have seen the Northern Lights, most have probably seen other phenomena in the sky, such as a rainbow, shooting star, or super moon. These experiences provide an opportunity for students…