İnvestigation of the middle school students development of the proportional reasoning in the hypothetical learning trajectory

In this study, it is aimed to examine the development of proportional reasoning skills of middle school sixth grade students in a teaching process based on GME approach based on hypothetical learning trajectory. In this context, a hypothetical learning trajectory has been established to determine the mathematical activities and to use the 5-week teaching sequence process based on the GME approach. The data of this qualitative study, which was designed according to the teaching experiment method, was performed with 39 students attending 6th grade. The results of the study show that the hypothetical learning trajectory provides a significant orientation for the planning of program design and evaluation for the development of the idea of proportional reasoning in students. In this study, the students' knowledge of the estimated learning situations, which is the evaluation scheme formed after the lesson based on the hypothetical learning trajectory prepared by the researcher, was evaluated. Estimated learning situations have been found to be less likely to be encountered in the course of the course, as well as to ensure that the teacher has a more rationalized learning route for subsequent courses. At the end of the teaching experiment, it was observed that the students increased their scores from the qualitative and quantitative questions related to the proportional reasoning questions according to the pre-teaching experiment.