This research is presented in a way that provides useful knowledge for successful problem posing by mathematics pre-service teachers. We present a review of the concept of mathematical creativity (by different authors) and review studies that underline the relevance of problem posing in teaching mathematics, studies that consider problem posing a way to identify students' learning patterns and to test them, and studies that relate mathematical competences to problem posing. Participants in the study were 10 pre-service teachers who were successful in problem solving. Data were gathered through qualitative techniques: classroom observations, sequences of tasks, questionnaires, student focus groups and discussion. The case study illustrated some of pre-service teachers' difficulties in problem posing: creating problems that students recognize as relevant to their everyday lives, problems adapted to the school curriculum at a specific educational level, and problems that can be self-corrected.