Transition between the represantions of middle school students in term of fractions

The aim of this study is to reveal representations used by the middle school students in terms of fractional numbers and the transitions between the representations. The study was carried out with a total of 131 people consisting of 6th, 7th and 8th grade students in a public school in Kilimli District of Zonguldak. A 8-question application form, which was prepared by the researcher and students were expected to write the answers themselves, was used as the data collection tool. The study is a case study revealing representations used by the students in terms of fractional numbers and transitions between the representations in detail and the qualitative method was used in this study. The application form was applied to one each branch of all 6th, 7th and 8th grades randomly selected from 2 state schools in Kilimli and Kozlu districts of Zonguldak and the questions added to the form were seen to serve the purpose. While the data were being analyzed, descriptive analysis was made and the formed themes were analyzed in terms of linguistic, visual and symbolic representation. As a result of the analysis of the data obtained, it is seen that the visual representation is used more than the other types of representation by the students. In the use of visual representation, the region model is the most preferred model, whereas the line model is the model that is not preferred at all. The response rate is very low in applications related to the line model. The use of symbolic representation has been the type of representation in which students experience the most difficulties. As a result of the analyzes, another situation occurring is that the students know the representations separately, but they have difficulty in switching between the representations. The most common type of representation used by the students affects the transitions between representations. In addition, the vast majority of students see the representations as a goal rather than a means to reach the desired result. This causes the students to think that they have reached the desired answer when they use any representation.