The controversy about ability grouping in education boils down to a conflict between the educational goals of excellence and of equity. There is considerable evidence that ability grouping is effective in producing learning, but not for all students. This study addresses substantive issues raised in previous research, exploring whether ability grouping works, and for whom it works. The focus of the study is the use of one type of ability grouping, within class ability grouping, in eighth-grade mathematics instruction. Data from the Second International Mathematics Study were used, with a sample of 3,991 U.S. eighth graders from 127 schools. Student- and class-level data files were created, and Rasch measures were developed. The statistical model used was hierarchical linear modeling. Results show that the use of within-class ability grouping and instructional tailoring has no effect on average eighth-grade mathematics achievement. In addition, the use of within-class grouping has no effect on the link between previous and subsequent eighth-grade mathematics achievement and the extent to which it varies across classes. It appears that instructional tailoring allows high achievers to perform to their maximum but does not have negative effects on low achievers. (Contains 2 tables, 6 figures, and 15 references.) (SLD)