High and persistent dropout rates represent one of the biggest challenges for improving the efficiency of the educational system, particularly in underdeveloped countries. A range of features influence college dropouts, with some belonging to the educational field and others to non-educational fields. Understanding the interplay of these variables to identify a student as a potential dropout could help decision makers interpret the situation and decide what they should do next to reduce student dropout rates based on corrective actions. This paper presents SDA-Vis, a visualization system that supports counterfactual explanations for student dropout dynamics, considering various academic, social, and economic variables. In contrast to conventional systems, our approach provides information about feature-perturbed versions of a student using counterfactual explanations. SDA-Vis comprises a set of linked views that allow users to identify variables alteration to chance predefined students situations. This involves perturbing the variables of a dropout student to achieve synthetic non-dropout students. SDA-Vis has been developed under the guidance and supervision of domain experts, in line with some analytical objectives. We demonstrate the usefulness of SDA-Vis through case studies run in collaboration with domain experts, using a real data set from a Latin American university. The analysis reveals the effectiveness of SDA-Vis in identifying students at risk of dropping out and proposes corrective actions, even for particular cases that have not been shown to be at risk with the traditional tools that experts use.