When the item response theory (IRT) model uses the marginal maximum likelihood estimation, person parameters are usually treated as random parameters following a certain distribution as a prior distribution to estimate the structural parameters in the model. For example, both PARSCALE (Muraki & Bock, 1999) and BILOG 3 (Mislevy & Bock,…

Students can learn great lessons when placed in decision-making roles. Simulating a Senate confirmation hearing can give students a glimpse of how government works and a chance to evaluate historical figures and issues. Any simulation, however, is an imperfect imitation of a real event. Having to make a decision based on incomplete information…

During periods of high unemployment, many workers exhaust their unemployment insurance (UI) benefits before regaining employment. To help alleviate this problem, Congress created the extended benefits (EB) program, expanding the number of weeks of benefits available to UI recipients in high unemployment states. The EB program operates by…

Facts, or skills? Content, or process? Teachers of history and social studies teachers often lock horns over these questions, trying to define the nature of their field and its role in secondary education. Teachers of history often focus on content, presenting the past as a series of important people and events, an accumulated cultural lore that…

This article describes a project in which certain key concepts in probability were explored using graphics calculators with year 10 students. The lessons were conducted in the regular classroom where students were provided with a Casio CFX 9850 GB PLUS graphics calculator with which they were familiar from year 9. The participants in the…

Ignoring a level can have a substantial impact on the conclusions of a multilevel analysis. For intercept-only models and for balanced data, we derive these effects analytically. For more complex random intercept models or for unbalanced data, a simulation study is performed. Most important effects concern estimates and corresponding standard…

The likelihood ratio test statistic G[squared](dif) is widely used for comparing the fit of nested models in categorical data analysis. In large samples, this statistic is distributed as a chi-square with degrees of freedom equal to the difference in degrees of freedom between the tested models, but only if the least restrictive model is correctly…

Using evidence from eye-tracking studies, Van Gompel, Pickering, Pearson, and Liversedge (2005) have argued against currently implemented constraint-based models of syntactic ambiguity resolution. The case against these competition models is based on a mismatch between reported patterns of reading data and the putative predictions of the models.…

The effect of item parameters (discrimination, difficulty, and level of guessing) on the item-fit statistic was investigated using simulated dichotomous data. Nine tests were simulated using 1,000 persons, 50 items, three levels of item discrimination, three levels of item difficulty, and three levels of guessing. The item fit was estimated using…

If one rolls a coin across a chessboard and it comes to rest on the board, what is the probability that it covers some corner of one of the grid squares? The online magazine "Plus" (2004) posed this problem for students to solve. It is a useful problem for several reasons: it introduces the idea of probability in a continuous sample space, it has…

P. A. Frazier, A. P. Tix, and K. E. Barron (2004) highlighted a normal theory method popularized by R. M. Baron and D. A. Kenny (1986) for testing the statistical significance of indirect effects (i.e., mediator variables) in multiple regression contexts. However, simulation studies suggest that this method lacks statistical power relative to some…

This article analyzes collaboration in a computer-supported learning environment based on the professional practices of mediation and dispute resolution. In so doing, it explores the nature of collaborative learning in a setting marked by competition as much as cooperation. Interviews with students suggest that the processes of collaborative…

A real-life analytical assignment is presented to students, who had to examine an air conditioning coolant solution for metal contamination using an atomic absorption spectroscopy (AAS). This hands-on access to a real problem exposed the undergraduate students to the mechanism of AAS, and promoted participation in a simulated industrial activity.

In this study we investigated the effects of the average signed area (ASA) between the item characteristic curves of the reference and focal groups and three test purification procedures on the uniform differential item functioning (DIF) detection via the Mantel-Haenszel (M-H) method through Monte Carlo simulations. The results showed that ASA,…

This paper describes an interactive modelling, simulation, animation, and real-time control (MoSART) environment for a class of 'cart-pendulum' electromechanical systems that may be used to enhance learning within differential equations and linear algebra classes. The environment is useful for conveying fundamental mathematical/systems concepts…