A widely recognized concern in elementary school mathematics education is that teachers' understanding of the mathematical curricular content generally appears quite fragmented, sparsely connected, and procedurally oriented. This pilot study applies methods of educational neuroscience to investigate and improve preservice teachers' learning and…

As a group, children from disadvantaged, low-income families perform substantially worse in mathematics than their counterparts from higher-income families. Minority children are disproportionately represented in low-income populations, resulting in significant racial and social-class disparities in mathematics learning linked to diminished…

Recognizing the need to implement standards-based instructional materials with school-wide coherence led some Philadelphia schools to adopt whole-school reform (WSR) models during the late 1990s. The authors report on the relation between mathematics achievement growth for middle-grade students on the Pennsylvania System of School Assessments and…

This article demonstrates an active learning technique for teaching the Central Limit Theorem (CLT) in an introductory undergraduate business statistics class. Groups of students carry out one of two experiments in the lab, tossing a die in sets of 5 rolls or tossing a die in sets of 10 rolls. They are asked to calculate the sample average of each…

Children's understanding of the cardinal significance of counting is often assessed by the "give x" task, in which they are categorized as "counters" or "grabbers". Previous research indicates a sudden stage-like shift, implying insight into a principle. Employing a microgenetic approach, the present study was…

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…