This paper presents a derivation of all five Lagrange points by methods accessible to sixth-form students, and provides a further opportunity to match Newtonian gravity with centripetal force. The predictive powers of good scientific theories are also discussed with regard to the philosophy of science. Methods for calculating the positions of the…

A plausible factorial structure for many types of psychological and educational tests exhibits a general factor and one or more group or method factors. This structure can be represented by a bifactor model. The bifactor structure results from the constraint that each item has a nonzero loading on the primary dimension and, at most, one of the…

Public rates of return on higher education expenditures are calculated by state. Benefits accruing to states from their investments in higher education are measured by differential tax revenues collected from college-educated citizens versus high-school-educated citizens. For most states we find an adequate rate of return on such investments.…

A key question in early number development is how 4- and 5-year-olds learn the roles that counting and cardinal numbers play when comparing quantities. Children who wrongly used length to identify numerosity were assigned to five experimental groups and trained to judge whether a puppet--who sometimes miscounted--created equivalent sets. Over…

Patients with corticobasal degeneration (CBD) have calculation impairments. This study examined whether impaired number knowledge depends on verbal mediation. We focused particularly on knowledge of very small numbers, where there is a precise relationship between a cardinality and its number concept, but little hypothesized role for verbal…

This article describes a general item response theory model for personality items that allows the information provided by the item response times to be used to estimate the individual trait levels. The submodel describing the item response times is a modification of Thissen's log-linear model and is based on the distance-difficulty hypothesis in…

The adverse effect of increasing age and/or body weight on distance run performance has been well documented. Accordingly, nearly all five kilometer (5K) road races employ age categories and, sometimes, a heavier body weight classification. Problems with such conventions include small numbers of runners within older age categories and the…

Often one needs to calculate the evolution time of a state under a Hamiltonian with no explicit time dependence when only numerical methods are available. In cases such as this, the usual application of Fermi's golden rule and first-order perturbation theory is inadequate as well as being computationally inconvenient. Instead, what one needs are…

Advances in the biological sciences necessitate the training of chemical engineers to translate these fundamental discoveries into applications that will benefit society. Accordingly, Tulane University revised its core chemical engineering curriculum in 2005 to include a new introductory course in bioengineering and biotechnology for sophomores.…

Large-scale testing programs involving classification decisions typically have multiple forms available and conduct equating to ensure cut-score comparability across forms. A test developer might be interested in the extent to which an examinee who happens to take a particular form would have a consistent classification decision if he or she had…

This article describes one teacher's journey to improve her teaching of mathematics by conducting classroom-based inquiry to meet the specific mathematical needs in her second grade classroom. Her process to develop and improve computational fluency through research-based methods is detailed. (Contains 9 figures.)

Practical meta-analysis of correlation matrices generally ignores covariances (and hence correlations) between correlation estimates. The authors consider various methods for allowing for covariances, including generalized least squares, maximum marginal likelihood, and Bayesian approaches, illustrated using a 6-dimensional response in a series of…

The standard error of the maximum likelihood ability estimator is commonly estimated by evaluating the test information function at an examinee's current maximum likelihood estimate (a point estimate) of ability. Because the test information function evaluated at the point estimate may differ from the test information function evaluated at an…

Various modern electronic structure methods are now days used to teach computational chemistry to undergraduate students. Such quantum calculations can now be easily used even for large size molecules.

Mental computation helps children understand how numbers work, how to make decisions about procedures, and how to create different strategies to solve math problems. Although researchers agree on the importance of mental computation skills, they debate how to help students develop these skills. The present study explored the existing literature in…