This article is about knowledge spaces in mathematical psychology. For the concept studied by philosopher Pierre Lévy, see Knowledge space (philosophy).
In mathematical psychology and education theory, a knowledge space is a combinatorial structure used to formulate mathematical models describing the progression of a human learner.[1] Knowledge spaces were introduced in 1985 by Jean-Paul Doignon and Jean-Claude Falmagne,[2] and remain in extensive use in the education theory.[3][4] Modern applications include two computerized tutoring systems, ALEKS[5] and the defunct RATH.[6]
Formally, a knowledge space assumes that a domain of knowledge is a collection of concepts or skills, each of which must be eventually mastered. Not all concepts are interchangeable; some require other concepts as prerequisites. Conversely, competency at one skill may ease the acquisition of another through similarity. A knowledge space marks out which collections of skills are feasible: they can be learned without mastering any other skills. Under reasonable assumptions, the collection of feasible competencies forms the mathematical structure known as an antimatroid.
Researchers and educators usually explore the structure of a discipline's knowledge space as a latent class model.[7]
^Doignon, J.-P.; Falmagne, J.-Cl. (1999), Knowledge Spaces, Springer-Verlag, ISBN 978-3-540-64501-6.
^Doignon, J.-P.; Falmagne, J.-Cl. (1985), "Spaces for the assessment of knowledge", International Journal of Man-Machine Studies, 23 (2): 175–196, doi:10.1016/S0020-7373(85)80031-6.
^A bibliography on knowledge spaces maintained by Cord Hockemeyer contains over 400 publications on the subject.
^Introduction to Knowledge Spaces: Theory and Applications, Christof Körner, Gudrun Wesiak, and Cord Hockemeyer, 1999 and 2001.
^"Homepage of RATH". Archived from the original on 2007-06-30.
^Schrepp, M. (2005), "About the connection between knowledge structures and latent class models", Methodology, 1 (3): 93–103, doi:10.1027/1614-2241.1.3.93.
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