Modellierung von Fehlkonzepten in einer algebraischen Wissensstruktur

An extension of the theory of knowledge spaces by Doignon &; Falmagne (1985) is presented that tries to account for subjects’ typical errors and wrong answers. This extension concerns two major points: The usual dichotomous item format (right/wrong) is generalized to polytomous response categories, and the theoretical structure (knowledge, skills, misconceptions) is clearly separated from the empirical structure (observable solution behavior, subject’s responses). Using examples from a set of questions about properties of simple electric circuits the general method is demonstrated. Axioms of an algebraic structure known as “information system” (Scott, 1982) are shown to provide an appropriate characterization of the theoretical domain. The structural properties of the data, on the other hand, can be derived from assumptions about the influence of knowledge and misconceptions on specific answers for a set of questions.