Decision making through nano topology: A mathematics education study

Although many definitions related to the concept of the classical set have been proposed from the past to the present, the inadequacy of these definitions emerges in the present epoch where information and data processing are inevitable, and moreover, within the framework of these definitions, it is revealed that classical set theory cannot fulfill its function in real-life problems. Carrying the concept of the set to a deeper understanding and interpretation, Zadeh introduced the fuzzy set concept. A fuzzy set has the ability to interpret partial membership instead of the definite membership used in the classical definition of the set. The rough set theory introduced by Pawlak, on the other hand, has a structure that takes into account uncertain situations as well as fuzzy sets. Structures such as fuzzy and rough sets organize incomplete and uncertain information through information systems and decision tables, making the data suitable for processing. Nano topology is a method that enables the effective use of the rough set theory by using the tools of topology. In the light of the information above, in this thesis, classroom teachers were asked to evaluate the mathematics achievement of 5th-grade students from four different classes at the secondary school level for one semester, and then it was aimed to compare the results of the exams and other evaluations. Thus, it is discussed whether the nano-topology method will be an evaluation tool in education. For this purpose, the effectiveness of the nano-topology method was examined by analyzing whether the qualification of success of the students evaluated with the nano-topology method predicted their exam success or not. When this thesis is viewed from the aspect of educational studies, it brings some criticisms to the evaluation and assesment methodology in education. It should be noted that the evaluation process has an algorithmic nature that involves making decisions based on certain criteria. In today's education system, treating measurement and evaluation at the same level in general poses serious problems in terms of reaching more wholistic and realistic evaluations. Although it is generally recommended to make more holistic evaluations by employing more than one measurement tool in the literature, it is seen that there is not much scientific research on which algorithm and according to which logic these evaluations will be made. For this reason, it can be stated that this thesis contributes to the literature by presenting a mathematical model to the evaluation process in education.