The present work proposes a framework based on STEM for the teaching and learning of programming with scope in modeling the problem in basic engineering sciences. The methodology for the framework is implemented in the competency-based curriculum for the line of Software Engineering in the training of professionals for the Engineering Computer Science at Catholic University of Temuco (Chile). We propose a case study with the STEM approach, following the Bloom's taxonomy steps in the modeling of systems with the coupling of the respective technologies in Web 1.0, Web 2.0 and Web 3.0.