Rule-based Item Generation of Algebra Word Problems Based upon Linear Logistic Test Models für Item Cloning and Optimal Design

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Techniques from item response theory (IRT), hierarchical modelling, knowledge structures, cognitive diagnosis models, and optimal design theory are combined to develop procedures for automated item generation and test assembly for the testing of basic statistical competencies in upper secondary and higher education, as can be assessed with statistical word problems. It will also be investigated how the models and procedures should be optimized and generalized when they are applied in computerized adaptive testing, testing for diagnosis, and large-scale educational assessments. The final goal is the development of a software program which adaptively generates tailor-made items for statistical word problems based on optimal design, linear-logistic test models, and models for test item cloning. During the first phase of the project, cognitive rules for generating statistical world problems have been identified and field tested and models for rule-based item generation have been developed and made statistically tractable. The current grant application is for the next two years in which the research will focus on the improvement of the cognitive rules, development of statistical tests for the goodness of fit of the models, empirical studies to validate cognitive rules and test the models, and the application of optimal design principles to automate test assembly. In addition and beyond the first application period, knowledge structures and cognitive diagnosis models will be adapted to our models and empirical data.