When a shock wave interacts with a contact discontinuity, there may appear a reflected rarefaction wave, a deflected contact discontinuity and a refracted supersonic shock. The numerical simulation of shock wave refraction at a plane contact discontinuity separating gases with different densities is performed. Euler equations describing inviscid…

Surface area and volume computations are the most common applications of integration in calculus books. When computing the surface area of a solid of revolution, students are usually told to use the frustum method instead of the disc method; however, a rigorous explanation is rarely provided. In this note, we provide one by using geometric…

Coefficient omega and alpha are both measures of the composite reliability for a set of items. Unlike coefficient alpha, coefficient omega remains unbiased with congeneric items with uncorrelated errors. Despite this ability, coefficient omega is not as widely used and cited in the literature as coefficient alpha. Reasons for coefficient omega's…

If educators presuppose that brain and mind are synonymous, perhaps it is out of necessity. Such an equivalency might be required in order for mind to be accessible, knowable and a "thing" like the brain is. Such a presupposition, that mind is a thing which we can understand nonetheless rests on an insecure foundation. As suggested by…

Using Cuisenaire Rods, metric measurement, and mapping, students worked collaboratively to calculate, keep records, build, and problem solve with use of decimal fractions as a key element.

The strategy underlying most computational models of word reading is to specify the organization of the reading system--its architecture and the processes and representations it employs--and to demonstrate that this organization would give rise to the behavior observed in word reading tasks. This approach fails to adequately address the variation…

An important concern when planning research studies is to obtain maximum precision of an estimate of a treatment effect given a budget constraint. When research designs have a "multilevel" or "hierarchical" structure changes in sample size at different levels of the design will impact precision differently. Furthermore, there…

Special ability in computing the day of week for given dates was observed in a 24 year-old male (FB) diagnosed with Asperger syndrome. FB performed almost flawlessly (98.2%) both with past and future dates, over a span of 40 years. Response latency was slower as temporal remoteness of future dates increased. Within the future timespan, FB's…

The problem of determining the angle ? at which a point mass launched from ground level with a given speed v[subscript 0] will reach a maximum distance is a standard exercise in mechanics. There are many possible ways of solving this problem, leading to the well-known answer of ? = p/4, producing a maximum range of D[subscript max] = v[superscript…

The Portland Timbers won their first Major League Soccer (MLS) Cup Championship in December 2015. However, if it had not been for a kind double goalpost miss during a penalty shootout a few weeks earlier, the Timbers would never have been in the finals. On Oct. 30th, after what has been called "the greatest penalty kick shootout in MLS…

Computational creativity, the generation of new, unimagined ideas or artifacts by a machine that are deemed creative by people, can be applied in the culinary domain to create novel and flavorful dishes. In fact, we have done so successfully using a combinatorial algorithm for recipe generation combined with statistical models for recipe ranking…

Equating methods make use of an appropriate transformation function to map the scores of one test form into the scale of another so that scores are comparable and can be used interchangeably. The equating literature shows that the ways of judging the success of an equating (i.e., the score transformation) might differ depending on the adopted…

When constructing multiple test forms, the number of items and the total test difficulty are often equivalent. Not all test developers match the number of items and/or average item difficulty within subcontent areas. In this simulation study, six test forms were constructed having an equal number of items and average item difficulty overall.…

The impact of response styles such as extreme response style (ERS) on trait estimation has long been a matter of concern to researchers and practitioners. This simulation study investigated three methods that have been proposed for the correction of trait estimates for ERS effects: (a) mixed Rasch models, (b) multidimensional item response models,…

Over the last decade, video games designed to teach academic content have multiplied. Students can learn about Newtonian physics from a game or prep for entry into the army. An emphasis on the instructionist approach to gaming, however, has overshadowed the constructionist approach, in which students learn by designing their own games themselves.…