Critical thinking and creativity along with problem-solving skills have become basic competencies in an increasingly complex and technological world, in which an individual needs to be able to process information in a critical way, find alternative solutions, analyse complex problems, and formulate innovative solutions. As teachers, we train the children for occupations that have not been invented yet -- an aspect that thus becomes clear is that it is no longer sufficient for the young students to perfectly execute given tasks, but they need to be able to solve new problems. To achieve this, they need to be able to consider the problem from multiple angles, to weight alternatives, to look critically at what needs to be solved, and to make well-thought and well-argued decisions. With this perspective in mind, developing such skills in pupils should be an essential goal for the teachers. Yet, unfortunately, training teachers for developing critical thinking skills in pupils comes short, in the Romanian educational system. This article presents the results of a training course whose goal was to prepare mathematics schoolteachers to teach mathematics based on questioning and discovery, to help develop pupils' critical thinking skills. Analyzing the short- and long-term impact of our training course confirms the results obtained in OECD (2019) studies, namely that once teachers have been qualified to work in this way, they become more open to acting differently to stimulate the developing of critical thinking and creative skills in pupils.