An investigation into the development process of the division algorithm in fractions by 6'th grade students'

The purpose of this study is to design appropriate learning environments and to apply them to the designed teaching in order to conceptually construct the division algorithm with fractions, then to report and examine the quality of the information formation in this process. In the study, case study was used among the qualitative research methods. The students who participated in the research were determined by using the sampling method of objective sampling methods. The students who will participate in the study are the sixth grade students and have not yet learned to divide by fractions. "Fractional Success Test" was used to determine whether the students had the necessary preliminary knowledge to perform the activities designed to be used in the information creation process, including the results of the State Boarding and Scholarship Exam questions up to the division by fractions. "Math Attitude Scale" was applied to measure attitudes towards math. The study was conducted with 12 students who were determined by considering the results of the tests applied to 108th grade students, fifth grade notes, opinions of mathematics teachers and the willingness of students to participate in the study. The study was conducted with six groups determined according to mathematics achievement levels. The "Fractional Division Algorithm Creation Activity Paper"preprepared by the researcher was applied to student groups. Reinforcement was carried out two weeks after the actual application. Activities with the working groups were recorded in video and then the written text was transcribed. Descriptive analysis of the obtained data was performed using RBC + C model as an analytical tool. At the end of the research, almost all of the student groups were found to form the cross product rule for the partitioning algorithm with fractions. The duration and path of this creation process varied according to each group, and it was observed that the process was better internalized in the groups with higher and higher success levels. It is thought that the other success levels are caused by the lack of preliminary knowledge which is required to construct the algorithm later. When the students were asked about the meaning of the division process during the application, it was seen that they did not know the meaning of measurement, instead, they all mentioned equal division. Judging from the obtained data, it can be said that the activities prepared for partitioning by fractions contribute both to the information creation process because it includes both the meanings of the partitioning process and the algorithm creation process.