Investigation of eleventh grade students' ways of thinking in problem solving process within the concept of function

Problem solving is one of the most basic skills at the center of school mathematics, as well as one of the most focused areas of study in the mathematics education literature. By definition of the problem, rather than the result found in the solution of a problem, the strategy put forward in the problem solving process, the way of thinking becomes important. In this direction, in this study, it is aimed to investigations the ways of thinking and the relationship between the ways of thinking and the context of the problem situation, if any, within the concept of function. The participants of the study are 10 of 11th grade students selected according to their academic success criteria. In the designed qualitative study, the data of the study were collected through clinical interview and the data obtained were analyzed using content analysis method. DNR (Duality-Necessity-Repeated Reasoning) framework was used in interpreting the ways of thinking from the data obtained. Since the ways of thinking of the participants in the problem solving process were examined in the problems based on the concept of function, mental action levels based on the concept of covariate reasoning were used in the determination of the problem solving strategies within the framework of DNR.