COMPETENCE AND PERFORMANCE IN SOLVING GEO METRY PROBLEMS

Within the last ten years Doignon and Falmagne's knowledge structures theory has become well-known in knowledge psychology. With the aim of modeling a certain domain of knowledge in the area of elementary geome try, this paper discusses critically the theory of knowledge structure s. An extension of this theoretical approach is proposed, in which ''k nowledge'' is modeled as competence and performance. Performance refer s to the observable behavior in solving the given problems, whereas co mpetence is conceived as a not directly observable theoretical constru ct (interpreted as ''ability'', ''skill'' or ''knowledge'') for the de scription, explanation, and prognosis of the observable solution behav ior. The connection between competence and performance is formally spe cified on the basis of deterministic test-theoretical assumptions. The competence-performance conception is illustrated by modeling a knowle dge domain within the area of the geometry of right triangles. Results from an empirical validation study are reported and analyzed. Finally , the advantages and disadvantages of the proposed competence-performa nce conception of the knowledge structures theory are discussed.