Two objectives guided this research. First, this study examined how well teachers' tracking decisions contribute to the homogenization of their students' achievements. Second, the study explored whether teachers' tracking decisions would be outperformed in homogenizing the students' achievements by statistical models of tracking decisions. These…

This article examines the bodies of knowledge that influence and inform the teaching of mathematics methods courses for preservice early childhood teachers, focusing on the U.S. context. In particular, the article reports on an analysis of scholarship published over the last 20 years in four journals (two focused on early childhood education and…

A high-school third-year or undergraduate first-semester general chemistry laboratory experiment introducing simple-cubic, face-centered cubic, body-centered cubic, and hexagonal closest packing unit cells is presented. Latex balls and acrylic resin plates are employed to make each atomic arrangement. The volume of the vacant space in each cell is…

When children learn to count, they map newly acquired symbolic representations of number onto preexisting nonsymbolic representations. The nature and timing of this mapping is currently unclear. Some researchers have suggested this mapping process helps children understand the cardinal principle of counting, while other evidence suggests that this…

Test-retest studies for assessing stability and change are widely used in different domains and allow improved or additional individual estimates of interest to be obtained. However, if these estimates are to be validly interpreted the responses given at Time-2 must be free of retest effects, and the fulfilment of this assumption must be…

The Contextualised Assessment Tool for Risk and Protection Management (CAT-RPM) has been established as a valid and reliable tool for differentiating groups across age, sex and behaviour and assisting young people to find their strengths [Bower, J., A. Carroll, and A. Ashman. 2014. "The Development and Validation of the Contextualised…

The aim of this study was to explore Taiwanese college students' conceptions of and approaches to learning computer science and then explore the relationships between the two. Two surveys, Conceptions of Learning Computer Science (COLCS) and Approaches to Learning Computer Science (ALCS), were administered to 421 college students majoring in…

Item response theory (IRT) uses a family of statistical models for estimating stable characteristics of items and examinees and defining how these characteristics interact in describing item and test performance. With a focus on the three-parameter logistic IRT (Birnbaum, 1968; Lord, 1980) model, the current study examines the accuracy and…

The aim of this study was to investigate the specific numerical and calculation abilities of 28 children with ADHD without comorbid mathematical learning disabilities (LD), ranging from the 1st to the 5th grade of primary school, and to examine the stability or the development of the arithmetic profile. Our results showed that a high percentage of…

Although population modeling methods are well established, a paucity of literature appears to exist regarding the effect of missing background data on subpopulation achievement estimates. Using simulated data that follows typical large-scale assessment designs with known parameters and a number of missing conditions, this paper examines the extent…

Steinley (2007) provided a lower bound for the sum-of-squares error criterion function used in K-means clustering. In this article, on the basis of the lower bound, the authors propose a method to distinguish between 1 cluster (i.e., a single distribution) versus more than 1 cluster. Additionally, conditional on indicating there are multiple…

We describe a collaboration between mathematicians and ecologists studying the cyanobacterium "Gloeotrichia echinulata" and its possible role in eutrophication of New England lakes. The mathematics includes compartmental modeling, differential equations, difference equations, and testing models against high-frequency data. The ecology…

This author has had the privilege of knowing Professor Maydeu-Olivares for almost a decade and although their paths cross only occasionally, such instances were always enjoyable and enlightening. Edwards states that Maydeu-Olivares' target article for this issue, ("Goodness-of-Fit Assessment of Item Response Theory Models") provides…

A multiple baseline design was used across probe sets to evaluate the effect of detect, practice, and repair (DPR) on the math fact fluency rates of a third-grade class. DPR was applied with a large group (n = 11) selected from an intact class (n = 17) in a manner that allowed each student to work on specific problems from a specific basic fact…

This article presents a multiple-group latent class-profile analysis (LCPA) by taking a Bayesian approach in which a Markov chain Monte Carlo simulation is employed to achieve more robust estimates for latent growth patterns. This article describes and addresses a label-switching problem that involves the LCPA likelihood function, which has…