This ethnographic study of two kindergarten classes in a racially-mixed "magnet" school investigates three issues: (1) the extent to which teachers' definitions of appropriate behavior in an instructional context are shared by children in free play context, (2) whether or not classroom social structure differs when teachers have contrasting beliefs about their teaching role, and (3) how differences within and between classrooms are related to race. Over a period of 8 months, each classroom was visited weekly for 2 to 3 hours. Detailed notes and videotapes were made of classroom behaviors in instructional, cleanup and free play contexts, and videotapes were used in interviews with teachers and with two child informants from each class. It was found that the separation of children in Class A into two labeled instructional groups based on academic performance was reproduced in the structure of children's play activities. Children came to know one another as "smart" or "dumb" and became very competitive. Black children sank low in the class hierarchy. Instructional grouping in Class B was based on three unlabeled degrees of ability to work independently and two degrees of academic ability. Class B children did not classify classmates by ability. In Class B, cooperation in lessons carried over into interaction in play groups and black children enjoyed a high degree of prestige. In general, results indicate that teachers' organization of instruction affected children's peer interaction. (Author/RH)