Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

This study aims to examine the effect of multiple problem-solving skills on the problem-posing abilities of gifted and non-gifted students and to assess whether the possession of such skills can predict giftedness or affect problem-posing abilities. Participants' metaphorical images of problem posing were also explored. Participants were 20 gifted…

The Rasch model is an item analysis model with logistic item characteristic curves of equal slope, i.e. with constant item discriminating powers. The proposed goodness of fit test is based on a comparison between difficulties estimated from different scoregroups and over-all estimates. (Author)

A theory and a procedure are presented for estimating a domain parameter and item parameters for test items in a homogeneous domain, such that the combined domain and item parameters account for observed proportions right for each item in a test. (CTM)

The accuracy of trait estimates obtained from three vertical equating methods was examined. The procedures studied included two anchor test designs and a single-group design. Data from two content areas and two grade combinations were studied. A three-parameter logistic model was used to perform the equatings. The results obtained were used to…

Georg Rasch has developed a new one-parameter latent trait model to explain the performance of examinees on achievement tests. The model can be viewed as a special case of Birnbaum's two-parameter logistic model where all items are assumed to have equal discriminating power. Birnbaum's model permits items to vary in discriminating power. Both…

The mathematical models of this paper were developed as an outgrowth of working with the Comprehensive Achievement Monitoring project (Project CAM) which was conceived as a model and application of sampling procedures such as those used in industrial quality control techniques to educational measurement. This paper explores mathematical modeling…

A simplex model is presented for the analysis of longitudinal academic growth variables in which only one measure is obtained at each time. When this model fits the observed data, then reliabilities and unattenuated correlations can be estimated except for the first and last periods. (Author)

Goodman's logit analysis (the simplest form of log-linear models) was used with hypothetical school survey data to analyze and predict teachers' attitudes toward proficiency tests. Logit analysis can estimate the "main effects" and "interaction effects" of categorical explanatory variables on dichotomous-dependent variables in…

Two fundamental problems in mental test theory are to estimate true score and to estimate the amount of error when testing an examinee. In this report, three probability models which characterize a single test item in terms of a population of examinees are described. How these models may be modified to characterize a single examinee in terms of an…

Procedures are presented for equating simultaneously several tests which have been calibrated by the Rasch Model. Three multiple test equating designs are described. A Full Matrix Design equates each test to all others. A Chain Design links tests sequentially. A Vector Design equates one test to each of the other tests. For each design, the Rasch…

A procedure for obtaining maximum likelihood trait estimates from number-correct (NC) scores for the three-parameter logistic model is presented. It produces an NC score to trait estimate conversion table. Analyses in the estimated true score metric confirm the conclusions made in the trait metric. (Author/DWH)

Since all commonly used latent trait models assume a unidimensional test, the applicability of the procedure to obviously multidimensional tests is questionable. This paper presents the results of the application of latent trait, traditional, and factor analyses to a series of actual and hypothetical tests that vary in factoral complexity.…

During the past few years the problem of bias in testing has become an increasingly important issue. In most research, bias refers to the fair use of tests and has thus been defined in terms of an outside criterion measure of the performance being predicted by the test. Recently however, there has been growing interest in assessing bias when such…