Determining the levels of association of middle school students' fraction knowledge and geometric measurement knowledge

In this study, it was aimed to determine the level of associating the fraction knowledge and geometric measurement knowledge of middle school students. The study was carried out on 9 students, three 8th grade, three 7th grade and three 6th grade students studying in one of the state middle schools in the north of Turkey. The study is in the nature of a case study and the study data were collected through one-on-one interviews and the collected data were analyzed using descriptive analysis. In the study, the interview form was applied to the students in two sessions and it was determined how the students used the area and length model of the fraction to determine the fraction, and their level of associating fraction information with geometric measurement information was examined. As a result of the findings, it was determined that the participants' fractional and geometric measurement knowledge was mostly in the pre-internalization profile which is one of the pre-interiorization, interiorization, condensation and reification profiles. It was observed that the students used different strategies and methods such as counting notches, counting points, counting intervals, deciding according to the appearance of the figure, counting unit squares, dividing the shape into parts and calculating with formulas in the length models of fractions and models of fractional area models. In the research, it can be suggested to mathematics teachers to design tasks that can integrate basic mathematical concepts, to establish links between different fields, and to use different segmented field models in textbooks.