In Geneva canton (Switzerland) a course deals especially with inquiry based mathematics education. During 45 minutes a week, teachers have to foster students' problem solving competencies. More exactly, the aim is to install scientific debate rules and to encourage students to use scientific processes of thinking such as the pattern of “try - conjecture - test and prove”. Meanwhile teachers have to assess students frequently. For that, the problem solving narration activity has been chosen as a means to assess students' problem solving competencies. But assessing such productions remains problematic. So our main concern is about how assessment based on problem solving narration activity can strengthen students' problem solving competencies. In that way, we are trying to know teachers' practices about assessment in this particular context and are working with two of them to develop a tool for assessing students on their problem solving competencies for both summative and formative purpose.