Superitem test based on the SOLO model (Structure of the Observing Learning Outcome) has become a powerful alternative assessment tool for monitoring the growth of students' cognitive ability in solving mathematics problems. This article focused on developing a superitem test to assess students' algebraic solving ability through interview method.…

Capacity limitations in absolute judgment tasks are discussed in relation to information theory. Information theory can provide a quantitative way of resolving questions about limitations on the amount of information we can receive and the process of recoding. (SLD)

An item response model for multiple-choice items is described and illustrated in item analysis. The model provides parametric and graphical summaries of the performance of each alternative associated with a multiple-choice item. The illustrative application of the model involves a pilot test of mathematics achievement items. (TJH)

The partial credit model with a varying slope parameter is developed and called the generalized partial credit model (GPCM). Analysis results for simulated data by this and other polytomous item-response models demonstrate that the rating formulation of the GPCM is adaptable to the analysis of polytomous item responses. (SLD)

Presents logistic discriminant analysis as a means of detecting differential item functioning (DIF) in items that are polytomously scored. Provides examples of DIF detection using a 27-item mathematics test with 1,977 examinees. The proposed method is simpler and more practical than polytomous extensions of the logistic regression DIF procedure.…

This paper explores a logistic regression procedure for estimating item parameters in the Rasch model and testing the hypothesis of item parameter invariance across several groups/populations. Rather than using item responses directly, the procedure relies on "pseudo-paired comparisons" (PC) statistics defined over all possible pairs of…

The derivation of several item selection algorithms for use in fitting test items to target information functions is described. These algorithms circumvent iterative solutions by using the criteria of moving averages of the distance to a target information function and simultaneously considering an entire range of ability points used to condition…

Estimating item parameters from a two-parameter normal ogive model is considered using Gibbs sampling to simulate draws from the joint posterior distribution of ability and item parameters. The method gives marginal posterior density estimates for any parameter of interest, as illustrated using data from a 33-item mathematics placement…

This study investigated the dimensionality of mathematics subscale scores from the National Assessment of Educational Progress for the assessment's Technical Review Panel, specifically for the data from the 1990 and 1992 main assessment in relation to students' instructional and noninstructional background variables. Discriminant analysis was…

A two-level model for factor analysis is defined, and formulas for a scoring algorithm for this model are derived. A simple noniterative method based on decomposition of total sums of the squares and cross-products is discussed and illustrated with simulated data and data from the Second International Mathematics Study. (SLD)

Methods are proposed for the construction of weakly parallel tests, that is, tests with the same test information function. A mathematical programing model for constructing tests with a prespecified test information function and a heuristic for assigning items to tests such that their information functions are equal play an important role in the…

Data banks with items calibrated under an item response model can be used for the construction of tests. Mathematical programming models like the Maximin Model are formulated for computerized item selection from a bank. In this paper, mathematical programming models based on the Maximin Model are proposed for the construction of weakly parallel…

The need for scale linking in the National Assessment of Educational Progress (NAEP) is discussed, and the specific procedures used to carry out the linking in the context of the major analyses of the 1990 NAEP mathematics assessment are described. Issues remaining to be addressed are outlined. (SLD)

The conventional method of measuring ability--based on items with assumed true parameter values obtained from a pretest--is compared to a Bayesian method that deals with the uncertainties of such items. Data from a 1987 American College Testing Program mathematics test indicate that maximum likelihood/Bayesian techniques underestimate uncertainty.…

The adequacy of several approaches to estimation of proficiency distributions for the Trial State Assessment (TSA) in eighth grade mathematics of the National Assessment of Educational Progress was examined. These approaches are more restrictive than the estimation procedures originally used, with the same kind of plausible-values approach that…