APPLICATION OF SOFT SETS TO ASSESSMENT OF MATHEMATICAL MODELLING SKILLS - Voskoglou , Michael Gr. (Physical and Mathematical Education, 2022)
Formulation of the problem. Formulation of the problem. Mathematical modelling is a very important component of mathematics education, because by applying the mathematical theories to practical needs of our everyday life increases the student interest for mathematics. The main steps of the mathematical modelling process include analysis of the given real world problem, formulation of the problem and construction of the mathematical model (mathematization), solution and control of the model and implementation of the final mathematical results to the real situation. Mathematization possesses the greatest difficulty among the steps of the MM process, because it involves a deep abstracting process, which is not always easy to be achieved by a non-expert.  It is sometimes, however, the transition from the solution of the model to the real world (control and/or implementation of the model) that presents difficulties for students too. An example is given to illustrate this remark.Materials and methods. In this paper soft sets are used as tools for developing a model for assessing human activities in a parametric manner and an example is presented (assessment of football players performance) to illustrate its applicability under real situations.  A soft set, being a parametrized family of subsets of the universal set of the discourse, is a generalization of the concept of fuzzy set designed on the purpose of dealing with the existing uncertainty in a parametric manner. The theory of soft sets has found many and important applications to several sectors of the human activity like decision making, parameter reduction, data clustering and data dealing with incompleteness, etc. Results. The soft set assessment model is applied for evaluating student mathematical modelling skills with respect to the parameters excellent, very good, good, mediocre, and failed. It serves both for assessing the general performance of a student class and the individual performance of each student with respect to the steps of the mathematical modelling process. Conclusions. The constructed in this paper model is very useful in cases where the assessment has qualitative rather than quantitative characteristics and could also be applied to a variety of other cases for assessing human and/or machine (e.g. computer programs) activities.
Keywords: mathematical modelling; assessment methods; soft sets; fuzzy logic