This research had as objective to design a methodology that would appreciate and characterize the occurrence of the insight types in convergent and divergent of mathematical thinking in the process of the solutions of problems for students, in the classes in a course of the bachelor’s degree in mathematics teaching in the Antonio Narino University. A qualitative approach was used in a case study two times between the years 2015 and 2016. As part of the analysis and discussion of the results obtained, it was possible to identify and characterize three types of insight. The same occurs when students have found solutions successfully.