Fuzzy Concepts—A New Approach in the Description of Boundaries as Creative Knowledge Environments in Educational Sciences

Abstract

Since the implementation of educational sciences as a discipline in universities, the society observes a permanent area of conflict between theory and application in pedagogics ("Pedagogics is always too late"). The history of this discipline shows that in the context of the general development of the society, this conflict creates boundaries. These boundaries are characterized by remarkable disruptions (fractality) of pedagogical academic contents of teaching and its implementation in contexts of application in daily routines. The crucial question is always the same: where does theory end and where do practical rules begin. The period of use of successful pedagogic concepts is also limited. This temporal limitation also indicates a creative area of conflict in the context of educational sciences. Because of these conditions, a diversity of creative knowledge environments are constituted. The problem of membership and the problem of assignment of pedagogic contents to theory or to application, and accordingly to disciplines dealing with similar contents is well known. We find the same problem already described in a more abstract mathematical way in the so-called "Fuzzy Sets": what are the degrees of membership of a single element x to a set A and to a set B at the same time? In the context of educational sciences,the same question is expressed as: what are the degrees of membership of a certain pedagogic content to theory which is taught in different departments on universities and to concrete pedagogic situations at school in the daily routines. It will be shown that by means of "Fuzzy Concepts"—a fuzzy set application in the context of humanities—it is possible to cope with these problems in an adequate way. This article focuses on the question how to design a fuzzy concept which is adapted to contexts already described. This fuzzy concept should fulfill the requirements of an adequate description of temporarily changing and evolving (fractal) boundaries of theory and application in pedagogical contexts as well as the identification of scopes and limits of integration of artistic and playful elements besides hardcore scientific facts in such concepts. In the first place, the objective of this article is to identify the potentialities and contexts in which fuzzy concepts represent an improvement in the daily pedagogic work and secondly to identify concrete creative knowledge environments in these evolving boundaries in the context of educational science.