The study, conducted to determine the argumentation levels of social studies undergraduate and graduate students on socio-scientific issues in the spring term of 2020-2021 with a total of 12 students, was designed as a case study from qualitative research approaches. Convenience sampling was used for the participant selection. A worksheet consisting of open-ended questions with argumentation components was used as a data collection tool. Positive changes in the argumentation levels were observed from the first practices to the last ones. The parts that the students had difficulty in creating argument components were determined. While the claim component of the participants' arguments consisted of certain but incomplete initially, it was determined to consist of conclusive and complete claims in the last weeks. While they could not associate and interpret the claim and data initially, they could not associate their claims with other study data and interpret them sufficiently in the last practices. For the support component, while the participants were observed not to include studies supporting their claims in the initial practices, it was determined that they benefited from scientific data and researches supporting their claims, albeit in a small number, in the last practices. Similarly, while they were observed not to include different opinions contradicting their claims regarding the rebuttal component initially, they used multiple rebuttals in the later practices. Based on the results of the study, it has been suggested to teachers as a model for socioscientific issues to be used in their lessons to improve students' argument levels.