Recently, people prefer learning information operationally rather than conceptually. In this context, this study was carried out to uncover how preservice math teachers construct in their minds the conceptual definition of limit within the scope of the Calculus Course. The participants of this study consisted of 62 (30 female, 32 male) sophomore students studying in the Elementary Mathematics Teacher Education Department at Uludag University Faculty of Education in the 2016-2017 academic year. Midterm and final exam questions requiring the use of prior knowledge were used to help collect data. Interviews were conducted with three participants who were chosen for their success. In these interviews, five questions were asked by the researchers to uncover the mathematical thinking levels and abstraction processes of the participants. The methods of semi-structured interviews and observations were used to collect data. The data were video-recorded and transcribed. The transcripts were analyzed and interpreted according to the cognitive actions of the RBC-model and the steps in Sfard's theory of mathematics learning. Based on the analysis, the participants were found to be more successful in operational information than in conceptual information. Although the preservice teachers were able to accomplish operational learning, it can be said that they could not fully accomplish conceptual learning because they could not identify algebraic representations and could not use reasoning on these representations. Interviews with the participants revealed that they memorized the characteristics of the concept of limit to be successful in the exams. However, conceptual learning did not take place. Understanding how participants learn is believed to benefit the educators who teach the concept of limit.