The effective teaching and learning of mathematics through mathematical modeling and connecting mathematics to the real world has gained rapid growth at various educational levels all over the world. The growth in modeling practices in the United States of America (US) and the international community is the result of the development and…

General diagnostic models (GDMs) and Bayesian networks are mathematical frameworks that cover a wide variety of psychometric models. Both extend latent class models, and while GDMs also extend item response theory (IRT) models, Bayesian networks can be parameterized using discretized IRT. The purpose of this study is to examine similarities and…

This paper discusses new psychometric analyses that improve capabilities for relating performance on achievement test items to instruction received by examinees. The modeling discussion is closely tied to data for eighth graders in the United States provided by the Second International Mathematics Study (SIMS), comprising not only responses to a…