Title: Skill Set Analysis in Knowledge Structures
Author: Günther Gediga , Institut für Evaluation und Marktanalysen , Jeggen, Germany
Ivo Düntsch , Dept of Computer Science , Brock University , St Catherines, Ontario, L2S 3A1, Canada
(Equal authorship implied)
Status: To appear in British Journal of Mathematical and Statstical Psychology
Abstract: This paper continues our earlier work on the connections between the skills a student has and the observed set of problems (s)he is able to solve. In the first part of the paper we exhibit some structural properties of the skill-problem relationship and consequences for the interpretation of concurrent theories in terms of the skill theory. The second part of the paper offers a test theory based on skill functions: We present measurements for the data consistency of the skill-problem relationship, and estimate abilities in terms of lower and/or upper boundaries of problem states and skills, given a special instance of the skill-problem relationship. Some practical considerations are discussed, which enable the user of a skill based system to optimise a partial theory about the skill based behaviour of subjects based on empirical results.

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