This paper introduces the term "explorative mathematical argumentation" (EMA), signifying a concept for describing and analysing learners' mathematical argumentation processes. Despite multiple recent empirical evidence for argumentation promoting learning in science education, still little is known about the development of early mathematical argumentation skills and their role within early learning processes. The widely varying use of the term argumentation impedes respective research efforts. The concept of explorative mathematical argumentation offers an approach that takes into account the explorative nature of learners' knowledge construction as well as specific aspects of mathematical argumentation. The concept of EMA promotes mathematical argumentation as a separate competence facet within which different forms and tools of reasoning can be deployed. It is suitable for describing and analysing learners' mathematical argumentation processes from an early age onwards, as is illustrated by an exemplary situation with 4- and 5-year-old preschool children. Eventually, methods for identifying and analysing learners' explorative mathematical argumentation processes are presented for discussion.