The purpose of the present study is to examine the mathematical reasoning and the argumentation process of 7th-grade students during problem-solving and their views on this process. The case study method was employed in line with the purpose. The study group was determined by criterion sampling. Considering the criteria of students' scores on the Problem-Solving Achievement Test (PSAT) and teachers' opinions, two students were chosen for the study group. PSAT, routine and non-routine problems, and a semi-structured interview form were used as data collection tools. After the problems were implemented, the interviews with the students took place. The data obtained from the problems were analyzed by following a predetermined framework. Consequently, the students used creative reasoning in most non-routine problems, whereas they used imitative reasoning in all routine problems. Considering the solution process of all the problems, they employed the most claim component and the least backing and rebuttal components. The students generally used the most argument component when they used creative reasoning and delimiting algorithmic reasoning, and the least when they used memorized reasoning or familiar algorithmic reasoning. In addition, some of the argument components differed according to the reasoning types, while others generally did not.