The prediction and explainability of student dropout in degree programs is an important issue, as it impacts students, families, and institutions. Nevertheless, the main efforts in this regard have focused on predictive power, even though explainability is more relevant to decision-makers. The objectives of this work were to propose a novel explainability model to predict dropout, to analyze its descriptive power to provide explanations regarding key configurations in academic trajectories, and to compare the model against other well-known approaches in the literature, including the analysis of the key factors in student dropout. To this effect, academic data from a Computer Science Engineering program was used, as well as three models: (i) a traditional model based on overall indicators of student performance, (ii) a normalized model with overall indicators separated by semester, and (iii) a novel configuration model, which considered the students’ performance in specific sets of courses. The results showed that the configuration model, despite not being the most powerful, could provide accurate early predictions, as well as actionable information through the discovery of critical configurations, which could be considered by program directors could consider when counseling students and designing curricula. Furthermore, it was found that the average grade and rate of passed courses were the most relevant variables in the literature-reported models, and that they could characterize configurations. Finally, it is noteworthy that the development of this new method can be very useful for making predictions, and that it can provide new insights when analyzing curricula and and making better counseling and innovation decisions.