A cluster-randomized trial (CRT) relies on random assignment of intact clusters to treatment conditions, such as classrooms or schools (Raudenbush & Bryk, 2002). One specific type of CRT, a multi-site CRT (MSCRT), is commonly employed in educational research and evaluation studies (Spybrook & Raudenbush, 2009; Spybrook, 2014; Bloom,…

Bayesian Knowledge Tracing is used very widely to model student learning. It comes in two different forms: The first form is the Bayesian Knowledge Tracing "hidden Markov model" which predicts the probability of correct application of a skill as a function of the number of previous opportunities to apply that skill and the model…

Numerous research articles and curricula standards maintain that learning is optimized when students are actively involved in the learning process by assimilating information and constructing their own meanings. The authors' experience with teaching probability concepts has shown that students struggle with concepts of counting. These…

The terms "concreteness fading" and "progressive formalization" have been used to describe instructional approaches to science and mathematics that use grounded representations to introduce concepts and later transition to more formal representations of the same concepts. There are both theoretical and empirical reasons to…

The use of boric acid in the Kjeldahl determination of nitrogen is a variant of the original method widely applied in many laboratories all over the world. Its use is recommended by control organizations such as ISO, IDF, and EPA because it yields reliable and accurate results. However, the chemical principles the method is based on are not…

The performance of the normal theory bootstrap (NTB), the percentile bootstrap (PB), and the bias-corrected and accelerated (BCa) bootstrap confidence intervals (CIs) for coefficient omega was assessed through a Monte Carlo simulation under conditions not previously investigated. Of particular interests were nonnormal Likert-type and binary items.…

Statistics anxiety is a problem for most graduate students. This study investigates the relationship between intolerance of uncertainty, worry, and statistics anxiety. Intolerance of uncertainty was significantly related to worry, and worry was significantly related to three types of statistics anxiety. Six types of statistics anxiety were…

This article describes a computational project designed for undergraduate students as an introduction to mathematical modeling. Students use an ordinary differential equation to describe fish weight and assume the instantaneous growth rate depends on the concentration of dissolved oxygen. Published laboratory experiments suggest that continuous…

As a result of the use of random assignment to treatment, randomized experiments typically have high internal validity. However, units are very rarely randomly selected from a well-defined population of interest into an experiment; this results in low external validity. Under nonrandom sampling, this means that the estimate of the sample average…

An undergraduate exercise in computational chemistry that investigates the energy barrier for pyramidal inversion of amines and phosphines is presented. Semiempirical calculations (PM3) of the ground-state and transition-state energies for NR[superscript 1]R[superscript 2]R[superscript 3] and PR[superscript 1]R[superscript 2]R[superscript 3] allow…

When evaluators plan site-randomized experiments, they must conduct the appropriate statistical power analyses. These analyses are most likely to be valid when they are based on data from the jurisdictions in which the studies are to be conducted. In this method note, we provide software code, in the form of a SAS macro, for producing statistical…

Mixtures of item response theory (IRT) models have been proposed as a technique to explore response patterns in test data related to cognitive strategies, instructional sensitivity, and differential item functioning (DIF). Estimation proves challenging due to difficulties in identification and questions of effect size needed to recover underlying…

We quantified the effect of first experience on behavior in operant learning and studied its underlying computational principles. To that goal, we analyzed more than 200,000 choices in a repeated-choice experiment. We found that the outcome of the first experience has a substantial and lasting effect on participants' subsequent behavior, which we…

The final step of the Kjeldahl method of nitrogen determination in biological and other samples faces a dilemma: which titrant, whether acid or base, should be used for the titration of ammonia? To solve this problem, a simple calculation procedure, illustrating the manner of ammonia determination in this method, enables one to resolve this…

In the last decades there have been several attempts to use computers in Music Education. New pedagogical trends encourage incorporating technology tools in the process of learning music. Between them, those systems based on Artificial Intelligence are the most promising ones, as they can derive new information from the inputs and visualize them…