Our work investigated how six primary school students used a non-traditional method for adding and subtracting: the ABN method, a Spanish acronym for Open (method) Based on Numbers. Commognitive theory [Sfard, A. 2008. "Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing." New York: Cambridge University Press] was employed to study the students' mathematical routines. In particular, we studied whether their routines were exploratory or ritualised and found that four students had a ritualised use of the ABN method, while two others showed some signs of incipient exploratory use (manifested as an increase in flexibility, applicability, performer's agentivity, and substantiability). The results show some of the problems that students have when applying this method.