A theoretical framework Is presented that distinguishes among three knowledge sources that form the basis for generative performance. The three knowledge sources, termed conceptual, procedural, and utilizational competence, were implemented as a computational model that derives plans for counting procedures. In a previous analysis, Greeno, Riley, and Gelman (1984) developed a characterization of the conceptual competence (implicit understanding of general concepts and principles) associated with the skill of counting and related conceptual competence to various models of performance. In the current (...) work all three knowledge sources are formalized in a computer program (COUNTPLAN) that generates planning nets of counting procedures. The sufficiency of COUNTPLAN's knowledge components is demonstrated through its capacity to generate new plans for counting in novel settings from a core of conceptual competence. The utility of COUNTPLAN to facilitate the distinction between hypotheses of competence and hypotheses of performance is discussed. (shrink)