The importance of argumentation in educational activities is widely acknowledged in relation to cognitive as well as social development. However, concerning small children, psychological studies are divided between those which provide evidence for an early emergence of argumentation and those in which it is claimed that argumentative skills develop according to age and educational inputs. In order to solve this apparent contradiction, some authors advocate that understanding and evaluating argumentative skills is not possible without taking the process of argumentation into account as a situated activity. If the child is considered as a partner in conversation rather than as an object of research, a different account of children’s capacities for reasoning emerges. Notably, in order to fully understand what happens in conversation, one should take implicit background assumptions into account. In other words, the problem is understanding contextual and cultural premises that are left implicit by children – and adults discussing with them. Yet a systematic study of implicit in argumentation processes in which small children are involved has not been undertaken up to now. We find that theoretical and methodological tools are readily available for this purpose from recent developments of argumentation theory. As a consequence, we see that a new perspective is now possible for psycho-educational research on children’s argumentation via the integration of these tools from argumentation theory. Our project sets out to explore children’s contributions to argumentative discussions, with a particular focus on the role played by implicit premises. Our core theoretical and methodological innovation lies in the introduction of the Argumentum Model of Topics (Rigotti & Greco Morasso 2009, 2010) for the study of implicit premises in the general framework of an argumentation process understood as a critical discussion (van Eemeren & Grootendorst 2004, van Eemeren 2010). The advantages of the Argumentum Model of Topics (AMT) for the reconstruction of (partially) implicit premises of children’s argumentation revolve around two axes. Methodologically, the AMT represents a tool to reconstruct implicit in argumentation because the analyst can use the model as a grid to elicit premises of different types and then check if they hold. At the theoretical level, differently from other models, the AMT systematically distinguishes between premises of procedural (logical) nature and premises of material nature (which ground argumentation in the interlocutors’ supposedly shared knowledge). Procedural and material premises are intertwined in real-life argumentation; both are equally important because argumentation presupposes rationality (logical consistency) but it is anchored to the context in which interlocutors discuss. With the AMT, it will thus be possible to access children’s forms of reasoning (procedural component) but to do so in such a way that the situated nature of reasoning is also included in the analysis (material component). We will analyse small children’s (2-6 years) spontaneous argumentation in different settings (informal discussions, settings in which adults have defined the issues to be discussed, and settings in which material objects are present). The rationale for our research ultimately lies in the effort to contribute to foster argumentation in education. However, we believe that this goal will be better reached if, before planning how to foster argumentation, we step back and consider the inferential configuration of children’s arguments. At the present stage, there is a need to better understand why learning to argue seems so difficult to achieve in the formal settings of schools and yet it seems to be part and parcel of daily life. We expect our study to help clarify some problems in adult-child communication due to misunderstandings of implicit premises, thus opening new perspectives for research in education. The study will also contribute to advances in argumentation theory, in particular concerning children’s (knowledge-oriented and pragmatic) argumentation as well as the emergence of argumentative discussions from problematic issues before the establishment of clear-cut standpoints.