### Factors Effecting Seventh Grade Students’ Proportional Reasoning in Mathematical Modelling Processes

#### Abstract

In this study, the factors which affect 7th grade students’ mathematizing proportional relations within the process of applying mathematical modelling activities have been investigated. Theoretical framework of the study has been structured by taking mathematical modelling perspective and horizontal and vertical mathematizing (Treffers, 1987) -the two dimensions in mathematizing- as the central motives in the study. The participants of the study consist of six 7th grade students with good mathematics competence. The activities, which are related to seventh grade mathematics lesson objectives on ratio and proportion, have been developed and employed by the researcher. The participants worked in groups of three. The data of the study consist of discussions during problem-solving process, video and audio recordings having been used in presentations, researcher’s observations notes and students’ study notes. In the study, it has been figured out that some factors such as distinguishing between proportional and non-proportional situations, expecting to find a whole number, regarding multiplicative relations conceptually, not getting feedback from the real life situation following operational mistakes, making transitions from daily life into mathematics and making transitions from mathematical results into daily life have shaped the modelling process based on proportional reasoning. The results of the research have dealt with these factors within horizontal and vertical mathematizing processes.

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