From this perspective, the research problem "To establish the characteristics of didactics based on problem solving through learning tasks of aspects associated with the semiotic representations of rational numbers in relation to the seventh grade students of the Madre Paula Montal School" is proposed. This research revolves around the teaching-learning processes related to rational numbers, focusing on the orientation of mathematics didactics, considering the bases of the methodological and theoretical design of problem solving, where from personal knowledge, knowledge is lived in the classroom and its formality and conventionality is naturally assumed as a privileged means to understand what students do. as well as to produce a didactic proposal adapted to the students' pre-knowledge.