In this article, we characterized the forms of reasoning of French high school students (from Terminal Scientifique) in the course of an exchange of messages around the solution of a mathematical problem. Our goal was to determine whether or not the students make use of creative and investigative forms of reasoning. The results show that in the experimental conditions of the ‘mathematical correspondence,’the students displayed an unusual mathematical problem-solving activity, one that is indeed more creative and investigative than those typically found in a classroom activity. The results are accompanied by an effort to explain the conditions that allowed for this unusual activity to develop and to suggest some paths to use this setting in the classroom, so as to facilitate better learning in problem-solving contexts and the transition from high school to university. (ZDM/Mathdi)