Habermas' construct of rationality is a tool adapted from social sciences into mathematics education to identify the difficulties in the proving process and to plan the teaching of proof for reducing these difficulties. According to Habermas, people engaged in an activity/action are considered to "act rationally" if they choose and use the available criteria and communication tools in the field to reach their aim. Habermas' construct is composed of three integrated components which are epistemic, teleological, and communicative rationality, and in this study, the proving process of university students was analyzed based on this construct. The aim was to identify the performance of students in the context of rationality components and explore the reasons for the difficulties students experience during the proving process. Freshmen mathematics teacher candidates participated in the study and the researchers focused on the field of geometry. The findings revealed that different interactions between the rationality components considerably affected the proving process of students. On the other hand, during the analysis, the modeling requirements of the epistemic rationality and communicative rationality components needed to be structured with new sub-components. It is thought that this expanded version of Habermas' construct of rationality can be used more effectively to identify the difficulties students have in mathematical activities such as problem solving, proving, and modeling.