This discussion of how the multilevel character of data should influence analyses of the determinants of educational achievement is grounded in the context of planning explanatory analyses for the longitudinal Second International Mathematics Study (SIMS). The intention is to describe how a multilevel perspective in the specification of substantive questions and, as a consequence, in the analysis strategies employed, can potentially clarify the ways in which instructional practices affect student performance. One multilevel analysis approach examines the interrelations and antecedents of a variety of indices of group-level outcomes. A second approach analyzes multilevel data more formally by modeling the decomposition of data into components suggested by the kinds of educational processes at work. This second approach incorporates all the features of the previously described analysis within a larger analytical model. In the two-level (classroom, pupil) analysis, multilevel decomposition of the factors influencing cognitive outcomes between and within classrooms addresses four questions, including the relationship between the class composition at pretest and class-level performance at posttest; adjusted between-class effects; pooled within-class analysis; and specific within-class relationships. The function of the specificity of the achievement measures and the general path model for multilevel analysis are examined. (CM)