The Assessment Of Learning Competence Based On Disjunctive Skill Functions

In the competence based-knowledge space theory,the objective of an assessment is to infer students’skills from their responses to a set of problems.A major issue of this method is that there is no one-to-one correspondence between the competence states and performance states.Changes caused at the competence level may not be represented by changes at the performance level,so we cannot determine whether learning takes place.Based on the disjunctive skill functions,this impasse can be solved by describing the coverage structure of effective skills in any competence states.Based on the disjunctive skill functions,this paper covers the competence sets in the forward-graded knowledge structures,the backward-graded knowledge structures and the knowledge structures respectively,and describes the coverage structures of effective skills of individual competence states concretely by using the coverage approximation operator in rough set theory.In the forward-graded knowledge structure,the intersection of the upper approximation of an effective skill and the competence state is an empty set;In the backward-graded knowledge structures,from the perspective of learning forgetting,the intersection between the upper approximation of an effective skill and the competence state is the effective skill itself.Finally,it is generalized to the knowledge structures,that is,effective skills exist in the lower approximation of the complement of the competence states.Moreover,in these three types of knowledge structures,any effective skill exists in only one coverage.For each kind of knowledge structure,the expression form in pedagogical example is given.At the same time,the algorithm analysis of three types of coverage structures are described,and the program is designed for data experiment to illustrate the validity of the corresponding conclusions.