Many education professionals have realized that the traditional expository method and dogmatic type of teaching methodologies are an obsolete trend that prevent them from introducing new teaching styles to work on new contents, develop objectives, acquire competences, and achieve learning assessment, which are related, for example, to human cognition ability, skills, or capacity to solving problems, leadership, or strategic management. Instead, from the end of the 19th century and the beginning of the 20th century to nowadays, teachers introduce new teaching styles, as is the case of active methodologies, where students become the center of the educational process; the rote learning is completely rejected, thereby fostering their critical thinking based on the rationale behind scientific methods, while influencing their leadership development, communicative, and collaboration skills. Like this manner, knowledge could be reformulated and disciplines would acquire new specialized connotations in scientific fields such as scientific and distributed computing regarding blending learning. This paper, then, aims to explore the theme of a scientific and technological transformation that invests in communication modalities and semantics by assessing the effectiveness of Problem-Based Learning (PBL) strategy instruction on students' mathematical ability to solve the Fano Plane. To this end, we will conceive a set of phenomena that need to be explored and a puzzle-like problem that needs to be solved.