This article considers the problem of estimating dynamic linear regression models when the data are generated from finite mixture probability density function where the mixture components are characterized by different dynamic regression model parameters. Specifically, conventional linear models assume that the data are generated by a single…

In group-allocation studies for comparing behavioral, social, or educational interventions, subjects in the same group necessarily receive the same treatment, whereby a group and/or group-dynamic effect can confound the treatment effect. General counterfactual outcomes that depend on group characteristics, group membership, and treatment are…

The study of federal education initiatives that takes place over multiple years in multiple settings often calls for aggregating and comparing data-in particular, student achievement data-across a broad set of schools, districts, and states. The need to track the trends over time is complicated by the fact that the data from the different schools,…

The purpose of this exploratory study was to investigate the impact of writing during mathematical problem solving. The study involved an analysis of ninth grade algebra students' written and verbal descriptions of their mathematical problem solving processes. Through this comparison, a better understanding of the connection between problem…

Object perception requires interpolation processes that connect visible regions despite spatial gaps. Some research has suggested that interpolation may be a 3-D process, but objective performance data and evidence about the conditions leading to interpolation are needed. The authors developed an objective performance paradigm for testing 3-D…

The primary purpose of this research is to examine the impact of estimation methods, actual latent trait distributions, and item pool characteristics on the performance of a simulated computerized adaptive testing (CAT) system. In this study, three estimation procedures are compared for accuracy of estimation: maximum likelihood estimation (MLE),…

This study investigates children's ability to use language to guide their choice of individuation criterion in the domains of objects and events. Previous work (Shipley, E. F., & Shepperson, B. (1990). Countable entities: developmental changes. "Cognition," 34, 109-136.) has shown that children have a strong bias to use a spatio-temporal…

Measuring transfer is as varied as it is controversial, particularly in an era of increased accountability and in the case of Ontario Colleges, in a time of flux and change. American Community Colleges have been grappling with the definition of a transfer rate, continuing to fail on reaching a consensus. The importance of an acceptable transfer…

This study assessed agreement between participants' rating (PMET) and compendium coding (CMET) of estimating physical activity intensity in a population of older minority women. As part of the Women on the Move study, 224 women completed a 7-day activity diary and wore an accelerometer for 7 days. All activities recorded were coded using PMET and…

Simple examples are really encouraging in the understanding of rearrangements of infinite series, since many texts and teachers provide only existence theorems. In the absence of examples, an existence theorem is just a statement and lends little confidence to understanding. Iterated sums of double series seem to have a similar spirit of…

This paper compliments two recent articles by the author in this journal concerning solving the forced harmonic oscillator equation when the forcing is periodic. The idea is to replace the forcing function by its Fourier series and solve the differential equation term-by-term. Herein the convergence of such series solutions is investigated when…

Time delays are an important aspect of mathematical modelling, but often result in highly complicated equations which are difficult to treat analytically. In this paper it is shown how careful application of certain undergraduate tools such as the Method of Steps and the Principle of the Argument can yield significant results. Certain delay…

The method for geometric transforms (probability generating functions) is used to study the expected number of observations until the pattern 123123 . . . 123 is obtained. These results provide a first generalization of similar problems considered by other authors. (Contains 1 figure.)

For those instructors lacking artistic skills, teaching 3-dimensional calculus can be a challenge. Although some instructors spend a great deal of time working on their illustrations, trying to get them just right, students nevertheless often have a difficult time understanding some of them. To address this problem, the author has written a series…

The Law of Sines and The Law of Cosines are of paramount importance in the field of trigonometry because these two theorems establish relationships satisfied by the three sides and the three angles of any triangle. In this article, the authors use these two laws to discover a host of other trigonometric relationships that exist within any…