The main theme of this research is problem solving and the study of graphs, combined with the use of Information and Communication Technologies (ICT) as facilitating tools during the classroom work. The subjects involved are first-year technical high school students, who performed, in the classroom and in the computer lab, a didactic sequence developed by the teacher-researcher in order to investigate the contributions of the Teaching-Learning-Assessment (TEAE) methodology of mathematics through problem solving, aiming to introduce the concept of function, from its graphs. The instruments used were online questionnaires and the students' own resolutions, prepared with pencil and paper, and later with the help of spreadsheets. Reports and observations, which occurred during the development of the methodology used, also contributed to the analysis and interpretation of the results obtained. In the conclusion of this work it was possible to notice that the students identify and participate in innovative classes that make use of ICT.