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Kognitionswissenschaft

, Volume 6, Issue 4, pp 196–204 | Cite as

Modellierung von Fehlkonzepten in einer algebraischen Wissensstruktur

  • Josef Lukas
Article

Zusammenfassung

Die Theorie der Wissensstrukturen nach Doignon & Falmagne (1985) wird so erweitert, daß sich damit auch typische Fehler von Probanden modellieren lassen. Die Erweiterung betrifft vor allem zwei Punkte: (a) die Verallgemeinerung der dichotomen Antwortkategorien (richtig/falsch) auf mehrere Antwortalternativen und (b) die explizite Trennung von theoretischer Struktur (Wissen, skills, Lösungsheuristiken, Fehlkonzepte etc.) und empirischer Struktur (Aufgabenbeantwortung, Lösungsvektoren, beobachtbares Antwortverhalten). Für die theoretische Struktur liefert die Axiomatik der sogenannten Informationssysteme (Scott, 1982) eine geeignete algebraische Charakterisierung. Die empirische Struktur läßt sich aus Annahmen über den Zusammenhang von Wissen und Antwortverhalten ableiten. Anhand von Aufgaben aus dem Wissensbereich „Elementarphysik einfacher elektrischer Stromkreise“ wird die Vorgehensweise exemplarisch dargestellt

Modeling misconceptions in an algebraic knowledge structure

Abstract

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.

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Copyright information

© Springer Verlag 1997

Authors and Affiliations

  1. 1.Institut für PsychologieMartin-Luther-Universität Halle-WittenbergHalle (Saale)Deutschland

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