The importance of STEAM education in preparing students to deal with societal challenges is nowadays an international recommendation. We may find different perspectives concerning STEAM education and the integration of its disciplines. A possible pathway to achieve a balanced integration is through Engineering Design (ED), starting from problems of reality that enable the articulated mobilization of concepts from various disciplinary areas, promoting interdisciplinary where teamwork and context play a fundamental role. This article reports a study with primary preservice teachers (6-12 years old) that aims to analyze the learning displayed and the difficulties underlying the usage of ED in solving STEAM problems. The participants were 45 preservice teachers. We adopted a qualitative methodology, and data were collected through observation, documents, artifacts, and photos. The preliminary results show a very positive reaction of the participants to the experience of solving real context problems collaboratively and mobilizing mathematical and physical science concepts in an integrated way. We identified active engagement, persistence, and motivation in the creation of a model that fulfilled the requested conditions. Difficulties were evidenced in the identification of some concepts and the mobilization of adequate scientific language in the argumentation of decisions.