This paper explores the theoretical and research contributions of many authors concerning group status and intergroup relations. Highlighted are: (1) Coleman's insights on the classroom reward structure; (2) Pettigrew's principles for successful ethnic contact; (3) Sherif's experimental work on the reduction of intergroup hostility through the pursuit of superordinate goals; and (4) Samuels' observations on the distribution of rewards within competitive and cooperative groups. It is suggested that in order to facilitate intergroup relations in a classroom situation, students be allowed to compete for grades in racially mixed work teams with rewards dispensed on the basis of the accomplishments of the group rather than the individual. These changes in classroom grouping procedures and classroom reward structures, it is argued, should create in-group feelings in the members of the various work teams which cut across ethnic identities. (Author/APM)