Some diverse fields in which the effects of mental representations have been noticed are first discussed, largely through illustrations of differing problem-solving experiences. Then the LAKOS Project (Logical Analysis of Cognitive Organizational Structures) at the University of Osnabruck is described. A central concern is the specification of a model of the representation and organization of knowledge in memory. A primary goal is to describe the cognitive structures of individuals so precisely that a machine can be made to simulate aspects of their behavior. In the remainder of Part A of this paper, two cases of inconsistent student behavior in rational number learning are documented. Details from interviews are included, followed by comments. In Part B, a computer model of the mental organization of knowledge is presented which was conceptualized to understand in detail some crucial aspects of cognitive functioning and of the origins of suboptimal behavior. A tentative conclusion based on the interviews and model is then projected. (MNS)