The aim of this paper is to present some ideas in order to construct designs for studying argumentation. Our specific focus is on learning processes involving peer interactions and adult-children activities. We consider argumentation as a context-bounded activity, at the crossroads of different lines of research, such as the neo-piagetian and neo-vygotskian concerns for the socio-cognitive development of higher psychological processes, and the socio-cultural approach of participative interactions within goal-directed activities. In this paper we offer some elements to implement designs around two on-going research lines in order to pay attention to quasi-experimental and observational studies. Firstly we present the task of liquid conservation assuming that a revisitation of this classical study could offer a possibility to consider the argumentation in children's talk beyond Piaget's logicism. The second line concerns an educational situation designed to observe learning through argumentation in classroom contexts; inspired by a piagetian task for studying physics quantities, a sequence is planned to offer students an educational setting to commit into argumentative interactions.