School district consolidation has continued at a rapid pace in the United States, with one in every nine districts consolidating between 2000 and 2015 (Collins forthcoming). The stated aim of consolidation efforts is usually improved efficiency -- growing larger to lower unit costs or improve student outcomes without spending more money (Callahan…

We identify a recent trend in school mathematics as well as in some of the research literature in mathematics education: an emphasis on the practical uses of mathematics and an increased emphasis on verbalizations as opposed to numerical and computational skills. With tools provided by John Dewey, an early advocate of contextual and practical…

We derive sample-allocation formulas that maximize the power of several mediation tests in two-level-group-randomized studies under a linear cost structure and fixed budget. The results suggest that the optimal individual sample size is typically smaller than that associated with the detection of a main effect and is frequently less than 10 under…

Multidimensional item response theory (MIRT) models use data from individual item responses to estimate multiple latent traits of interest, making them useful in educational and psychological measurement, among other areas. When MIRT models are applied in practice, it is not uncommon to see that some items are designed to measure all latent traits…

Considerable attention has been given to methods for knowledge estimation, a category of methods for automatic assessment of a student's degree of skill mastery or knowledge at a specific time. Knowledge estimation is frequently used to make decisions about when a student has reached mastery and is ready to advance to new material, but there has…

Manfred Hauben proposes an approach to teaching non-transitive relationships between 'paradoxical' dice using simple statistical graphics. This method usefully supplements traditional approaches of conditional probability calculations and trees, and students are thereby better able to see what is going on and the mechanism of these relationships.

Estimation skills are critical for students in the 21st century. The ability to estimate or approximate is widely accepted as fundamental to problem solving, and important for checking the reasonableness of results. (Dowker, 2003; Reys & Reys, 1989). Therefore, estimation should be an important aspect of problem solving in all year levels but…

This study explores classification consistency and accuracy for mixed-format tests using real and simulated data. In particular, the current study compares six methods of estimating classification consistency and accuracy for seven mixed-format tests. The relative performance of the estimation methods is evaluated using simulated data. Study…

Computation is a central aspect of 21st century physics practice; it is used to model complicated systems, to simulate impossible experiments, and to analyze mountains of data. Physics departments and their faculty are increasingly recognizing the importance of teaching computation to their students. We recently completed a national survey of…

M-fluctuation tests are a recently proposed method for detecting differential item functioning in Rasch models. This article discusses a generalization of this method to two additional item response theory models: the two-parametric logistic model and the three-parametric logistic model with a common guessing parameter. The Type I error rate and…

The high school grade point average (GPA) is often adjusted to account for nominal indicators of course rigor, such as "honors" or "advanced placement." Adjusted GPAs--also known as weighted GPAs--are frequently used for computing students' rank in class and in the college admission process. Despite the high stakes attached to…

In this study, how the length and characteristics of routing module in different panel designs affect measurement precision is examined. In the scope of the study, six different routing module length, nine different routing module characteristics, and two different panel design are handled. At the end of the study, the effects of conditions on…

In this study, we fitted a mixed-effects nonlinear continuous-time mutualism model of skill development proposed by van der Maas et al. (2006) to naturally collected irregularly spaced time series data from an online adaptive practice system for mathematics called Math Garden. Results showed that the mutualism model provided a better fit to the…

The increased presence of technology in all aspects of daily life makes computational thinking a necessary skill. Predictions say that the rising need for computational thinkers will be unmet by computer science graduates. An e-textile learning module, based on principles of constructionism, was designed as a method to develop computational…

Several factors seem important to understand the nature of mathematical learning. Byrnes and Miller combined these factors into the Opportunity-Propensity model. In this study the model was used to predict the number-processing factor and the arithmetic fluency in grade 4 (n = 195) and grade 5 (n = 213). Gender, intelligence and affect (positive…