Cognitive complexity level is important for measuring both aptitude and achievement in large-scale testing. Tests for standards-based assessment of mathematics, for example, often include cognitive complexity level in the test blueprint. However, little research exists on how mathematics items can be designed to vary in cognitive complexity level.…

The ordered partition model is described as an extension of the partial credit model, its relationship to other models is discussed, and two examples are presented. The model is designed for a measurement context in which categories of response to an item cannot be completely ordered. (SLD)

Describes three open-ended response types that could broaden the conception of mathematical problem solving used in computerized admissions tests: (1) mathematical expression (ME); (2) generating examples (GE); and (3) and graphical modeling (GM). Illustrates how combining ME, GE, and GM can form extended constructed response problems. (SLD)

A model for solving very large item selection problems is presented. The model builds on binary programming applied to test construction. A heuristic for selecting items that satisfy the constraints in the model is also presented, and various problems are solved using the model and heuristic. (SLD)

Mixed Rasch models add latent classes to conventional Rasch models, assuming that the Rasch model applies within each class and that relative difficulties of items are different in two or more latent classes. This article considers a family of stochastically ordered mixed Rasch models, with ordinal latent classes characterized by increasing total…

Presents componential item response theory as a model-oriented approach to studying processes and strategies underlying the incorrect/correct responses to cognitive test tasks. Results from 417 elementary school students show that combining knowledge of solution strategies with Item Response Theory modeling produced a useful unidimensional scale…