Abstract The purpose of the research is to strengthen the competence of mathematical interpretation through the portfolio as a learning tool in an educational institution of the “Municipio de Gramalote, Norte de Santander, Colombia”. The research is carried out from the socio-critical approach, qualitative paradigm and the chosen method is action research. The information gathering process was developed using the techniques of: participant observation and focus group. The key informants were two high school mathematics teachers and eighth grade students. The results show that in the diagnosis the participants’ lack of knowledge regarding the process of mathematical interpretation was evidenced; elements of knowledge are identified from the previous knowledge of the students and the preparation of the researcher teacher in the didactic sequence. The use of a tool such as the portfolio made it possible to motivate the learning process and to evidence in an orderly manner the abilities and capacities empowered by the students; there was an appropriation of learning around the analysis and interpretation of mathematics from concrete situations in the daily lives of the students, taking up their previous knowledge and using didactic elements and resources from their environment.