The aim of this qualitative study was to explore the thoughts of primary and secondary prospective mathematics teachers about educating mathematically gifted students. For this purpose, this research was conducted with 40 prospective mathematics teachers, 17 of whom were secondary mathematics prospective teachers, and 23 were primary mathematics prospective teachers. The data was collected through (i) written explanations of all prospective teachers, (ii) one classroom discussion, and (iii) three focus group interviews. The data was analyzed by using content analysis. The findings indicated that prospective mathematics teachers mostly associated education of gifted students within the school context, such as what can be done in the classroom or out of the classroom for these students. It can be interpreted that the participants will tend to focus on out-of-class activities rather than in-class activities for the mathematically gifted students in their future classrooms.