Studies of argumentation in education have increased in the last few decades, to analyze how people learn to argue, and how it is possible to improve practices of arguing to learn. Overall, these studies have shown that argumentation at school rarely occurs spontaneously, in contrast to the dialogical practices in informal settings, although the argumentative capacities of young children, even at preschool level, have been already highlighted. Other studies have been specifically devoted to examining the role of teachers in establish the conditions to engage pupils in argumentation: how to present instruction, how to motivate them to argue, how to guarantee a proper collaboration. Although we recognize the interest of looking at the role of the adult (teacher) in designing argumentative activities at school, in this paper we intend to analyze whether the presentation of a task requiring argumentative exchange is taken by children as a useful occasion to start arguing. To attend this goal, we will refer to an interdisciplinary approach, combining the pragma-dialectics and a discursive perspective to analyze the children’s reasoning emerging in the classroom while the teacher is presenting a task. A total of 44 preschool children (3-5 years old) were asked to interact in small groups of two or three people at the kindergarten in order to solve three tasks (to build a tunnel, a bridge and an hourglass – by using different materials) supposed to solicit argumentative exchanges among the participants. The activities were video-recorded and the interactions transcribed. The qualitative analysis implied two steps: the identification of the argumentative structure of each exchange according to the pragmadialectical approach; and the interpretation of the beginning of the argumentative discussions, through a discursive approach. The findings show that, while the teacher is presenting the task and asking participants to solve it, the children already engage themselves in reasoning about some aspects of the activity (e.g., alternative ways to solve the problem, possible use of other tools, etc.). Beyond expectations, children immediately start to argue about the task, advancing their ideas and comparing the possibilities offered by the available objects. As a consequence, the teacher is requested to re-organize the plan, to consider the children’s argumentative attempts, and to arrange the situation in order to pursue the goal and, at the same time, to take into account the children’s interest. As scientists in the field of teacher education, we suggest that teachers should consider not only their need to set out in advance the setting for the activity to be proposed at school, but also the opportunity to look first at what children already do when engaging in interactions. This will allow a better understanding of the relevance of cognitive-oriented argumentative activities in classroom, in which children can immediately enter and develop arguments even before the teacher manages to present the activity. Further studies should contribute to develop these aspects and to train pre- and in-service teachers to consider such a situation, to analyze it and to implement strategies devoted to favor cognitive argumentation at school.