This study examined the pedagogical content knowledge of pre-service preschool teachers on quantity concepts in terms of children's mistakes. A total of 94 pre-service teachers who were attending a teacher training program at a state university, in Turkey, participated this study. 52 of them were second-year, and 42 of them were third-year pre-service teachers. The case study method, which is one of the qualitative research methods, was applied. Five different vignettes were used as a data collection tool developed by the researchers. The summative content analysis technique was used to analyze the data. It was observed that the third-year pre-service teachers who took the preschool mathematics education course were partially successful in identifying children's mistakes regarding the quantity concepts. The second-year preservice teachers who did not take the preschool mathematics education course failed to identify the mistakes. The results of the study showed that the preservice preschool teachers were not adequately prepared to eliminate children's mistakes. The second-year pre-service teachers mostly preferred direct instruction and demonstration methods to eliminate children's mistakes. The third-year pre-service teachers mostly preferred the meaningful learning, educational game and direct instruction methods to eliminate children's mistakes. [This study was presented in the 'International Conference on Mathematics and Mathematics Education (ICMME-2018)' (27-29 June 2018, Ordu).]