The aim of this study was to examine the mistakes made by freshman students of science teaching during the process of proving and the reasons for these mistakes. To this aim, the study, which was conducted via the case study method, was performed with 52 freshman students who were studying at the department of science teaching in a state university. A test composed of eight open-ended questions was used for data collection, and non-structured interviews oriented towards identifying the reasons for the mistakes made by the students were conducted with eight students. The content analysis technique was utilised in data analysis. It was found that many of the students made mistakes in terms of method, in other words, they used incorrect methods. In this regard, it was detected that more than half of the students regarded assigning numerical values as a method of proof, whereas a few of them made conceptual mistakes, algorithmic mistakes, misunderstood the questions, etc. Furthermore, it was determined that these mistakes resulted from reasons such as the fact that the students did not have any previous experience related to proof; they regarded assigning numerical values as a method of proof; and their lack of knowledge.