This study attempted to broaden the perspective of homogeneous classroom grouping strategies through an examination of a grouping plan which matched both students and their teachers on the basis of compatible levels of specific personality characteristics. The focus of the study was to examine empirically the degree of relationship that existed between a series of noncognitive grouping criteria, defined as personality characteristics, and the cognitive outcomes of classroom instruction in mathematics. It was found, in general, that personality grouping was feasible on the basis of certain specific personality characteristics, but more research is needed to study different groups, other content areas, and other personality grouping criteria. (Author)