Our study aims to determine how Habermas' construct of rationality can serve to identify and interpret the difficulties experienced by university students in the mathematical problem-solving process. To this end, a problem which required modelling and solving a differential equation was used. The problem-solving processes of university students were analysed based on rationality components. The findings demonstrated that the problems in epistemic rationality such as predominance of the figure over the definition and/or theorems, use of dogmatic knowledge, intuitive generalizations, lack of prior knowledge, incorrect recognition of the differential equation prevented the choosing and using of an appropriate problem-solving method, leading to problems in teleological rationality. It was determined that the student performance in communicative rationality was negatively affected by problems in epistemic rationality such as using of knowledge acquired by rote and predominance of figure prototype on the definitions and/or theorems. Throughout the analysis, it is required to define two new sub-components, named "geometric" and "algebraic" representation under the modelling requirements of epistemic rationality. It is advised to use the extended version of Habermas' construct of rationality to examine the performance of students in mathematical activities to get more detailed and accurate results.