The implementation of Science, Technology, Engineering, and Mathematics (STEM) at school is one of the challenges of education in the twenty-first century, especially concerning the development of critical thinking during argumentative interactions. In this paper, I refer to an interdisciplinary approach with the aim to analyze the implicit inferential reasoning emerging in argumentative discussions among children during scientific activities. The study involved 25 preschool children at a kindergarten engaged in three problem solving tasks. The first activity was to build a tunnel, the second to build a bridge--both with the use of Lego©--and the third to build an hourglass with recycled materials. The tasks were video-recorded and the discussions transcribed. The analysis implied different steps: first, I identified the argumentative structure of each exchange according to the pragma-dialectical approach; then, I found the implicit premises using the Argumentum Model of Topics; afterward, I analyzed the argumentative discussions according to a sociocultural approach. The findings show a predominance of arguments based on causal relationships and indicate how children reason regarding complex aspects of a problem, such as the negative consequences of an action, the adequacy of the available tools, and the (possible) future conditions connected to the scientific activity they are involved in. The study opens a possibility to shift from how to implement STEM activities to what children already do when engaged in scientific tasks. It also encourages the adoption of an interdisciplinary approach to investigating the complex process of argumentation in preschool children.