Item response theoretic methods are applied to the measurement of achievement of students from various instructional backgrounds. This extended item response theory (IRT) approach serves as a tool for studying instructional bias, or instructional sensitivity. The model maintains the form of an IRT model, but has parameters that quantify the extent of the effect attributed to opportunity to learn (OTL). The technique is applied to detect instructional sensitivity using the Second International Mathematics Study (SIMS) set of 40 core items for eighth-graders in the United States. The SIMS data came from about 280 schools and about 7,000 students measured at the end of spring 1982. The achievement test used contained 180 items in the areas of arithmetic, algebra, geometry, and measurement distributed among four test forms. In the SIMS data, there was considerable heterogeneity in the mathematics instruction experiences of students. The model features parameters estimating the influence of student background and OTL content pertinent to each specific test item on a single latent mathematics ability trait, and the effects of the mathematics ability trait and the item-specific OTL on the difficulties of test items. The analysis indicates that certain test items representing early stages of learning about selected mathematical topics were particularly sensitive to specific instruction. An 18-item list of references is included. (SLD)