The central problem of this work addresses the difficulty faced by students of computer science and systems to understand and apply recursion in programming. Recursion is a fundamental tool to solve complex problems efficiently and its understanding is key to create code efficiently, its mastery is necessary for professional development in technological areas. However, traditional teaching, focused on laboratories and the direct use of programming languages, has shown several limitations: in the first instance it seems effective, in the long term it fails to consolidate the basic understanding of the underlying mathematical and logical concepts, this affects motivation and may increase student dropout. This research proposes a methodological framework based on genetic decomposition supported by APOE (Action, Process, Object and Scheme) theory that combines mathematical foundations and computer science. This approach allows modeling learning paths, designing activities and assessing the conceptual understanding of recursion to facilitate understanding at different levels of cognitive abstraction. The main results indicate that the use of genetic decomposition favors the efficient and structured understanding of recursion, guiding students from concrete action to the abstraction of complex schemes. The implications of this solution are significant, not only improving educational quality and student retention, but also contributing to the development of key skills for the business sector, thus contributing to the Sustainable Development Goals related to education and employment.