Issues related to between-class and within-class decomposition of achievement variance and the change of this decomposition over the course of the eighth-grade were examined using the Second International Mathematics Study (SIMS, 1985), a study in which there was a nested or hierarchical data structure of students within classes, within schools, in school districts. The usefulness of multilevel factor analysis (MFA) was explored with a subset of data containing 3,724 eighth graders in the United States from about 200 classes in about 100 schools. The core test for analysis consisted of 39 items in arithmetic, algebra, geometry, and measurement given as a pretest and posttest in fall 1982 and spring 1983. It was found that the strong elements of tracking in eighth-grade mathematics classes make for between-class variation that is about as large as the within-class student variation. Within-class variability increases much more substantially than between-class variation over the course of the eighth-grade. MFA is considered to give better results than analysis of variance or conventional factor analysis. However, MFA calls for data with a sizable number of groups, preferably at least 100. Extensions of the MFA model are briefly discussed. Seven tables of study data, 2 figures, and a list of 27 references are included. (SLD)