NEUTROSOPHIC ASSESSMENT OF STUDENT MATHEMATICAL SKILLS

Abstract

Formulation of the problem. Assessment is an important component of the teaching process, because it helps the instructor to determine the student mistakes and to improve their performance by adapting suitably his/her teaching methods. In this work we investigate the problem of evaluating the student overall performance, when the teacher is not sure about the accuracy of the grades assigned to them. This happens, either because the teacher had not enough time to assess properly the students’ mathematical skills, or because, in case of a written examination/test, some students did not present clearly or did not justified properly their answers.

Materials and methods. Fuzzy assessment methods using neutrosophic sets and grey numbers, as well as the calculation of the Grade Point Average (GPA) index are used in this work for the assessment of a student class mean performance, quality performance, and overall performance when the teacher has doubts about the grades assigned to some students.

Results. The paper focuses on a classroom application designed for the assessment, with qualitative (linguistic) grades, of mathematical skills of the engineering students of two Departments of the School of Engineering of the Graduate Technological Educational Institute (TEI) of Western Greece (University of Peloponnese) being at their first term of studies. The instructor was the same person for both Departments. The teaching methodology for the first Department (experimental group) involved a combined use of computers and classroom lectures, whereas for the second Department (control group) involved only lectures in the classical way on the board.

Conclusions. The use of neutrosophic sets provides a useful tool for evaluating the student overall performance when the teacher has doubts about the accuracy of the grades assigned to them. The outcomes of the classroom application demonstrated a superiority of the experimental group. This superiority, however, was significant with respect to its mean and overall performance (neutrosophic assessment), but rather negligible with respect to its quality performance. This gives a strong indication that the use of computers in the teaching process helps more the mediocre and weak students and not so much the good students.