Numerous researchers have suggested that there are multiple mathematical knowledge and skill areas needed by teachers in order for them to be effective teachers of mathematics: knowledge of the mathematics that are the goals of instruction, advanced mathematics beyond the instructional material, and mathematical knowledge that is specific to what…

A conceptual framework is proposed for a psychometric theory of standard setting. The framework suggests that participants in a standard setting process (panelists) develop an internal, intended standard as a result of training and the participant's background. The goal of a standard setting process is to convert panelists' intended standards to…

A class of multidimensional latent trait models is described. The properties of the model parameters, and initial results on the accuracy of a maximum likelihood procedure for estimating the model parameters are discussed. The model presented is a special case of the general model described by Rasch (1961), with close similarities to the models…

This paper reviews the existing multidimensional item response theory (IRT) models and demonstrates how one of the models can be applied to estimation of abilities from a test measuring more than one dimension. The purposes of this paper were threefold. First, the fundamental concepts required when considering multidimensional models for the…

Several special cases of the general Rasch model, varying in complexity, were investigated to determine whether they could successfully model realistic multidimensional item response data. Whether the parameters of the model could be readily interpreted was also investigated. The models investigated included: (1) the vector model; (2) the product…

Work on item response theory was extended to two areas not extensively researched previously, including models for: (1) test items that require more than one ability for a correct response (MIRT); and (2) interaction between modules of instruction that have a hierarchical relationship (HST). In order to develop the MIRT and HST models, the author…

This paper demonstrates the relationship between the concept of unidimensionality and direction of an item in a multidimensional space. The basic premise is that if items that measure in the same direction are combined to form a test, that test will meet the item response theory requirements of unidimensionality. This will be true even if the…