Analysis of proof process based on Habermas rational behaviour construct

Habermas' construct of rational behaviour is one of the means whose adaptation is made with the aim of determining the difficulties learners go through in the process of proof and arranging the proof teaching to reduce these difficulties. According to Habermas, if a person involved in an activity/action chooses and uses the criteria and communication tools available in the field in line with his/her purpose, that person is said to "act rationally". In this approach, "rationality" consists of three integrated components i.e. epistemic, teleological, and communicative rationality. Epistemic rationality is related to the content of statements, their use, their association with one another, and consciously sustaining their validity in accordance with common premises and reasoning processes. Teleological rationality is related to choosing consciously and using the appropriate means to reach the goal. Communicative rationality is related to communicative practices in a community in which members can communicate amongst themselves. The aim of this study is to analyze university students' processes of proofs according to Habermas' construct of rational behaviour. The study aims to determine the components at which students are good and weak and, this way, put forward the reasons behind the difficulties they experience in the process of proofs. In the study, freshmen mathematics teacher candidates were worked with in the fields of geometry and algebra. In the course of the study, new subcomponents in the model were needed and were added to the scopes of epistemic and communicative components. The data analysis showed that the components in Habermas' construct of rational behaviour has a strong interaction between one another, and this interaction showed variety in the fields of geometry and algebra. In addition, it was seen that different interactions of the components in the model and that one component is stronger or weaker than the others substantially affected students' process of proofs.