Automated test assembly (ATA) has been an area of prolific psychometric research. Although ATA methodology is well developed for unidimensional models, its application alongside cognitive diagnosis models (CDMs) is a burgeoning topic. Two suggested procedures for combining ATA and CDMs are to maximize the cognitive diagnostic index and to use a…

A Metropolis-Hastings Robbins-Monro (MH-RM) algorithm for high-dimensional maximum marginal likelihood exploratory item factor analysis is proposed. The sequence of estimates from the MH-RM algorithm converges with probability one to the maximum likelihood solution. Details on the computer implementation of this algorithm are provided. The…

We study the hydrogen atom confined to a spherical box with impenetrable walls but, unlike earlier pedagogical articles on the subject, we assume that the nucleus also moves. We obtain the ground-state energy approximately by means of first-order perturbation theory and show that it is greater than that for the case in which the nucleus is clamped…

Children's sense of numbers before formal education is thought to rely on an approximate number system based on logarithmically compressed analog magnitudes that increases in resolution throughout childhood. School-age children performing a numerical estimation task have been shown to increasingly rely on a formally appropriate, linear…

The granting of credit is a necessary risk of doing business. If companies only accepted cash, sales would be negatively impacted. In a perfect world, all consumers would pay their bills when they become due. However, the fact is that some consumers do default on debt. Companies are willing to accept default risk because the value of defaults does…

Hierarchical linear models (HLM) solve the problems associated with the unit of analysis problem such as misestimated standard errors, heterogeneity of regression and aggregation bias by modeling all levels of interest simultaneously. Hierarchical linear modeling resolves the problem of misestimated standard errors by incorporating a unique random…

The previous articles on class size and other productivity research paint a complex and confusing picture of the relationship between policy variables and student achievement. Missing is a conceptual scheme capable of combining the seemingly unrelated research and dissimilar estimates of effect size into a unified structure for policy analysis and…

Three undergraduate students functioned as teaching assistants in unit ops lab for their senior project, which included developing a purchased size exclusion chromatography experiment, supervising the running of this experiment, and assisting the junior students with their calculations. They also read the reports, graded them, and commented on…

Data from NCES indicate that it is two to three times more expensive to educate a student at a public four-year college than at a community college. These figures exaggerate the difference between the two when you calculate the costs of the first two years of education for students working on a bachelor's degree. Using modified Integrated…

To introduce students to an application of chemical engineering directly related to human health, we developed an experiment for the unit operations laboratory at Georgia Tech examining diffusion across cadaver skin in the context of transdermal drug delivery. In this laboratory module, students prepare mouse skin samples, set up diffusion cells…

This study investigated the effects of the TouchMath[C] program (Bullock, Pierce,&McClellan, 1989) to teach students with mild intellectual disabilities to subtract 3-digit money computational problems with regrouping. Three students with mild intellectual disabilities in high school received instruction in a special education mathematics…

Computation instruction continues to be one of the most important aspects of the mathematics curricula. Students who fail to understand and master the foundational components of addition, subtraction, multiplication, and division are likely to experience mathematics difficulties in both their school and post-school lives. A balanced instructional…

Student activities focused on discovering mathematics play an important role in the teaching and learning process. WebMathematics Interactive (WMI2) was developed to offer a fast and user-friendly on-line web interface to enhance the quality of both theoretical and applied mathematics courses. For the teacher, in the classroom, it provides…

Cognitive diagnostic models (CDMs) attempt to uncover latent skills or attributes that examinees must possess in order to answer test items correctly. The DINA (deterministic input, noisy "and") model is a popular CDM that has been widely used. It is shown here that a logistic version of the model can easily be fit with standard software for…

In models containing reciprocal effects, or longer causal loops, the usual effect estimates assume that any effect touching a loop initiates an infinite cycling of effects around that loop. The real world, in contrast, might permit only finite feedback cycles. I use a simple hypothetical model to demonstrate that if the world permits only a few…