A reflection of the structure of teachers' and student-teachers' perception of qualitative proportional reasoning

Ability to relate all the essential features of a situation in the form of zooming in or out represents thought in a relative form. The emergence of relative thinking, is the prognosis for the beginning of building a bridge to fill the gap between collective and multiplicative structures. Relative thinking is a cognitive function that describes the ability to analyze the change in relative conditions. The ability to lead and work with qualitative aspects leads to the strengthening of quantitative proportional thinking. Studying the quality of teachers’ perception is a perspective of how learners create and develop conceptual structures. With the aim of determinning the qualitative characteristics of knowledge of content pedagogy of qualitative proportional reasoning, this study examined the knowledge of related representations among the research participants. It was a descriptive study with survey design. The research sample consisted of 180 primary school teachers, first cycle high school math teachers and student-teachers. The research tool was the researcher-made test and the evaluation was done under the framework of the theories of this field through a mixed-methods analysis. Based on the results, the closeness of the performance of student-teachers and the primary school teachers could be pointed out, i.e., almost half of each of these two groups had a successful performance. The most correct interpretations were presented by high school teachers, student-teachers and primary school teachers, respectively.Paying attention to the preliminaries and necessities of the process of developing proportional reasoning by teachers, deepening its investigation by researchers and demanding it in the educational designs of teacher training centers were emphasized by the researchers of this study.Regarding the training of future teachers, developing sensitivity to the consequences of the delay in the emergence of students' proportional thinking is necessary.