Transition Across Levels In The Process Of Learning: A Fuzzy Model

Michael Gr. Voskoglou

Abstract


The fuzzy sets theory was created in response to have a mathematical representation of situations of everyday life in which definitions have not clear boundaries. Such a situation is the process of learning, since the knowledge that students have about various concepts is usually imperfect and therefore from the teacher's point of view there exists a vagueness about the degree of acquisition of the new knowledge by them. In the present paper we introduce a fuzzy model to describe the process of learning a subject-matter by a group of students in the classroom. Namely we present the main stages of learning as fuzzy sets in the universal set of the linguistic labels of negligible, low, intermediate, high and complete acquisition of each stage and we use the total possibilistic uncertainty as a measurement tool for the degree of acquisition of the new knowledge by students. A classroom experiment is also presented on teaching / learning mathematics, illustrating the use of our fuzzy model in practice.


Keywords


Learning and Transfer, Cognition, Mathematical modelling, Fuzzy sets, Uncertainty

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