Examination of middle school students' mathematization processes through mathematical modeling problems

The aim of this study is to investigate the horizontal and vertical mathematization skills of 8th grade students, which are the two dimensions of mathematization, while solving problems through mathematical modeling activities. In this study, case study, one of the qualitative research methods, was used. This study was carried out in the spring semester of the 2020-2021 academic year. The participants of the study were six students studying in the eighth grade of a public secondary school located in a district of Yozgat province. Six students were selected from a total of 7 students who took the 8th grade mathematics course. The mathematization process of the students was examined based on the theoretical framework of Realistic Mathematics Education (RME). The data obtained from this study were analyzed using the descriptive analysis approach. The findings of the study revealed that students' horizontal and vertical mathematization processes differ according to the mathematical modeling problems. In the Gas Station (Akaryakıt İstasyonu) problem and Apple Pie (Elmalı Turta) problems, the students accepted the real-life problem situation as a starting point for each modeling problem they solved,and developed their concepts according to the content of the problem in the horizontal mathematization process. It was also seen that the students were more successful in procedural operations in the vertical mathematization process of the Gas Station and Apple-Pie problems; however, they could not reach generalizations because they had difficulty in establishing the associations between concepts and operations. They were limited in both horizontal and vertical mathematization processes by not establishing a new strategy while developing their distance skills while transitioning to new concepts by using their own schemes such as drawing perpendicularity in Hay Bale (Saman Balyası) and Ancient Theater (Antik Tiyatro) problems.