Results are reported from a survey of 6,185 students in 23 elementary schools, 10 middle schools, and 6 high schools of a Maryland suburban district where schools vary significantly in the authority systems of the classrooms at each grade level. Analyses of the relationship between the 'openness' of a school's instructional program and student achievement failed to show a consistent pattern across four elementary and secondary grades. Family background variables were then statistically controlled for. In no case was more than 3 percent of the total variation uniquely accounted for by school openness. However, in every case there was a large interaction effect between school openness and student family background on achievement. The pattern was always the same: students from the higher social class categories showed a more positive relationship between school openness and achievement than students from the lower social classes. In grades where the overall relationship was positive, the more advantaged students were most strongly positive; where the overall relationships were negative, the higher social class group was least negative; where the overall relationship was not significant, the higher social class group tended toward a positive relationship, while the lower social class group tended toward a negative one. (Author/JM)