Student evaluation through membership functions in CAT systems

Abstract

Generally speaking, the process of student evaluation is based on a procedure where we assume that the student belongs just to one set in a completely specified way, for example the set of excellent students, or the set of regular students. In this paper we use fuzzy sets concepts just to propose a different procedure which can be useful to manage the student's performance in a variation of a computerized adaptive testing administration process. This can be made by assuming that, for a given student, a membership function $\mu_{A}$ is assigned. This membership function gives the membership degree of the student to the fuzzy set $A$, which can be the set of excellent students, or the set of regular students, or the set of poor performance students. Furthermore, we assume that the item bank contains items belonging, with certain degree, to fuzzy sets describing the complexity of the given items. For example, we can talk about the fuzzy set of difficult questions or the fuzzy set of easy questions. By considering the evaluation process as a problem in the field of control theory, we establish a proper metaphor with a very simple, and very well studied, physical system with behavior described by variables such as the position, velocity and acceleration. Based in this model, we propose fuzzy rules just to control the item administration process as a function of the ability of the student and the item complexity.