The methodological implications of using instructional information combined with the usual test item responses are discussed as they affect the linkage of achievement measurement and instruction. Models that expand those of standard Item Response Theory (IRT) are illustrated using achievement data from the United States sample of the Second International Mathematics Study (SIMS) (4,129 eighth-grade students). In the SIMS, opportunity-to-learn (OTL) responses were obtained from teachers and students corresponding to each item. The subjects' responses concerned whether or not the required mathematics curriculum was covered during the present school year and, if not, whether it had been covered in previous years. Focus was on the means by which modeling captures the fact that the measurement relationship between the items and the latent trait may vary across student groups. This question is formulated as a problem of assessing item bias or instructional sensitivity in the items when item-specific OTL information is available. Approaches using traditional IRT methodology, the weakness of the item bias approach, a new method of assessing item bias that generalizes IRT modeling to allow for item specific variation in measurement relations across student groups with varying instructional background, and application of traditional and new methods to the SIMS data were addressed. (TJH)