Realistic mathematics education approach and its reflectionsin teaching the subject of sets in the 6th grade mathematics class

It is possible to talk about Mathematics and Mathematics Education in almost every area of our lives. Unfortunately, despite this fact; Mathematics is at the beginning of the most frightened and unsuccessful lessons. Realistic Mathematics Education, a mathematics teaching approach proposed by the Mathematician and educator Hans Freudenthal in 1971 at the Freudental Institute of the University of Utrecht in the Netherlands, is a special education theory for the field. According to this approach, Mathematics should be related to children's interests and their daily life situations. Learning process should start with real life problems, matematical concepts and formulas should be reached at the latest. According to Freudenthal, mathematics is a human activity, and is invented but not explored. The concept of set, which is abstract in nature, forms the basis of many subject in mathematics. It is very difficult for students to understand abstract concepts. Therefore, the concept of "Set" can become meaningful for students through a process in which they encounter real life situations. The general purpose of this study is to demonstrate how the teaching of "Sets" in the sixth grade mathematics course is carried out with the Realistic Mathematics Education model. In the study, which was designed as a descriptive case study based on unstructured observation from a qualitative research model, integrated single case study pattern design was adopted. The participants of the study consisted of 33 sixth grade students from a public school on the European side of Istanbul. In determining the sample of the study, purposive sampling method, one of the random sampling methods, which is specific for qualitative researches was used. Data collection tools used in the research; Tasks developed in accordance with the Realistic Mathematics Education model, working and task papers of the student groups and Semi-Structured Interview Form. Tasks and application process were subjected to descriptive analysis according to Realistic Mathematics Education learning principles and students' mathematical processes. Interview records obtained from the semi-structured interview form for evaluating instruction were analyzed first using descriptive analysis and then content analysis for more in-depth analysis. According to the results of the research, although there are some individual differences between the groups, almost all of the groups experienced the expected mathematical process as horizontal and vertical mathematization in the worksheets during the implementation process of the activities. In general, from the learning principles based on the Realistic Mathematics Education model, "creation and concretization", "social context and interaction", "structuring and co-processing" learning were more experienced then "levels and models" and in-depth thinking and special assignments". When the opinions of the students were taken to evaluate the teaching based on the Realistic Mathematics Education model, the students interviewed were satisfied with the education model applied by expressing a positive opinion and even expressed their opinion that they wanted it to be applied in other courses.