Computer algebra systems are being used more and more frequently in mathematics courses of all levels. For instructors to use these systems effectively, they need to have an idea of how the systems work. To illuminate the mechanics, the implementation of a simple computer algebra system will be described. Further, if instructors understand the…

In a previous paper, we showed the importance of using low-level commands of a CAS in order to enhance the students' conceptual insight into mathematics. In this paper, we wish to emphasise a different use of a CAS, which makes possible the exploration of new topics, when the necessary theoretical results have still not been acquired, and avoids…

We investigated how size and depth are perceived in a plane or convex mirror. In Experiment 1, using a plane or convex mirror, 20 observers viewed a separation between two objects that were presented at a constant distance and reproduced it by a separation between other two objects in a natural viewing situation. The mean matches generally…

It is argued that studies of early adolescent peer victimization and bullying should be longitudinal because of the dynamism of this developmental period. Traditional methods for analyzing longitudinal data are inadequate because of the strict data requirements and inflexibility of models. A better alternative is linear mixed models (LMMs) for…

One important and promising application of item response theory (IRT) is computerized adaptive testing (CAT). The implementation of a nominal response model-based CAT (NRCAT) was studied. Item pool characteristics for the NRCAT as well as the comparative performance of the NRCAT and a CAT based on the three-parameter logistic (3PL) model were…

Several goodness of fit (GOF) criteria have been developed to assist the researcher in interpreting structural equation models. However, the determination of GOF for structural equation models is not as straightforward as that for other statistical approaches in multivariate procedures. The four GOF criteria used across the commonly used…

The relationship between levels of reliability and the power of two bias and differential item functioning (DIF) detection methods is examined. Both methods, the Mantel-Haenszel (MH) procedure of P. W. Holland and D. T. Thayer (1988) and the Simultaneous Item Bias (SIB) procedure of R. Shealy and W. Stout (1991), use examinees' raw scores as a…

The following seven statistical procedures are compared in terms of the ability to recover a unidimensional latent trait from Likert-type data: (1) factor analysis based on Pearson correlations (FA-PR); (2) factor analysis based on polychoric correlations (FA-PL); (3) the graded response model in item response theory (IRT-GRM); (4) internal…

Detection of differential item functioning (DIF) is most often done between two groups of examinees under item response theory. It is sometimes important, however, to determine whether DIF is present in more than two groups. A method is presented for the detection of DIF in multiple groups. The method, the Q(sub j) statistic, is closely related to…

The use of multiple representations with or without technology is one of the major topics in mathematics education that has gained importance in recent decades. The use of multiple representations is advocated by many mathematics educators and supported by the National Council of Teachers of Mathematics (NCTM) Standards. In this paper, multiple…

A new approach to the development of the item characteristic curve (ICC), which expresses the functional relationship between the level of performance on a given task and an independent variable that is relevant to the task, is presented. The approach focuses on knowledge states, decision processes, and other circumstances underlying responses to…

Hierarchical Bayes procedures were compared for estimating item and ability parameters in item response theory. Simulated data sets from the two-parameter logistic model were analyzed using three different hierarchical Bayes procedures: (1) the joint Bayesian with known hyperparameters (JB1); (2) the joint Bayesian with information hyperpriors…

Three methods of estimating test score distributions that may improve on using the observed frequencies (OBFs) as estimates of a population test score distribution are considered: the kernel method (KM); the polynomial method (PM); and the four-parameter beta binomial method (FPBBM). The assumption each method makes about the smoothness of the…

The robustness of a partial credit (PC) model-based computerized adaptive test's (CAT's) ability estimation to items that did not fit the PC model was investigated. A CAT program was written based on the PC model. The program used maximum likelihood estimation of ability. Item selection was on the basis of information. The simulation terminated…

Two modification formulas are presented for the test information function in order to provide better measures of local accuracies of the estimation of "theta" when maximum likelihood estimation is used to provide the estimate of ability "theta." A minimum bound of any estimator, biased or unbiased, is considered; and Formula 1…