This conference paper suggests a promising model, based on a study of elementary school teachers in California, to investigate the relationship between the cognitive characteristics of teachers, their teaching behavior, and the academic success of their pupils. In the research model, two major components which affect student achievement were measured: (1) Teacher Knowledge (knowledge of subject being taught and knowledge of teaching); and (2) Teacher Aptitude (verbal, numerical, reasoning, memory, and kinds of divergent production aptitude). It is hypothesized that certain matches between teacher and pupil knowledge, skill, aptitude, and cognitive style tend to facilitate pupil learning. A preliminary factor analysis of the above components indicates that the Teacher Test Battery developed in conjunction with this research model was actually able to measure these structures. (CS)