This study tested whether 10- and 12-year-olds who can correctly compare the magnitudes of fractions with common components access the magnitudes of the whole fractions rather than only compare the magnitudes of their components. Time for comparing two fractions was predicted by the numerical distance between the whole fractions, suggesting an…

The "credit card effect" describes a finding where greater value is given to consumer items if credit card logos are present. One explanation for the effect is that credit cards elicit spending behavior through associative learning. If this is true, social, economic and historical contexts should alter this effect. In Experiment 1, Year…

Recently, Vul and Pashler (2008) demonstrated that the average of 2 responses from a single subject to general knowledge questions was more accurate than either single estimate. Importantly, this reveals that each guess contributes unique evidence relevant to the decision, contrary to views that eschew probabilistic representations of the…

Mathematics teachers are often asked, "What is the most difficult topic for you to teach?" Their answer is teaching students to count. The concepts can be challenging and slippery to apply in problems. Many times, no rigid procedures or formulas can be used to solve the problems directly, and students simply do not know where or how to approach…

A latent variable modeling approach for examining population similarities and differences in observed variable relationship and mean indexes in incomplete data sets is discussed. The method is based on the full information maximum likelihood procedure of model fitting and parameter estimation. The procedure can be employed to test group identities…

Common source bias has been the focus of much attention. To minimize the problem, researchers have sometimes been advised to take measurements of predictors from one observer and measurements of outcomes from another observer or to use separate occasions of measurement. We propose that these efforts to eliminate biases due to common source…

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…