An investigation of proportional and algebraic reasoning of seventh grade middle school students and the relationship between them

At the secondary school level, between the primary school level and the high school level, it is aimed to transition from concrete thinking skills to abstract thinking skills. In this process, providing students with many mathematical thinking skills is one of the main goals of middle school mathematics teaching. Proportional reasoning and algebraic thinking are two of the important thinking skills that are aimed to be acquired by students. Proportional reasoning and algebraic thinking are interrelated and developmentally support each other. However, when we look at the historical development of algebra and the literature on mathematics education, it is seen that proportional reasoning has an important role in the development of algebraic thinking. This study aims to examine seventh grade students' proportional and algebraic reasoning and the relationship between them. For this purpose, the research design was determined as a qualitative case study. The data of the study were collected from nine seventh-grade participants selected by criterion sampling method through proportional reasoning problems test and clinical interviews. The data obtained were analyzed with the three-stage qualitative data analysis method developed by Miles and Hüberman. As a result of the analysis, it was observed that the participants, who generally reflected the mental acts of third-level proportional reasoning, differed in the mental acts of obtaining an equivalent ratio and realizing the invariance of the ratio, and their algebraic thinking skills were below the expected level at the seventh grade level. In addition, it was concluded that there is a mutual and mutually supportive relationship between proportional reasoning and algebraic thinking. Keywords: Proportional reasoning, Algebraic thinking, Middle school students