For some years a problematic situation has been occurring in some chairs dedicated to the teaching of mathematics at the university level, and which is requiring solutions from all members of the educational community. In some research papers written by professionals specialized in the educational area and published in peer-reviewed journals, they report with concern the recurrent form that is occurring in each academic period, of a significant number of deferred students and dropouts in subjects related to mathematics in the first stages of the university career. Faced with this critical scenario in the university academic reality, the present author undertook a research work that aimed to develop an educational proposal from a constructivist perspective, taking into account the metacognitive processes, self-efficacy and goals of students, linking them with a didactic approach focused on mathematical problem solving and ICTs.