Solving a problem requires and promotes a diversity of competencies, which include conceptual knowledge, technical and methodological knowledge, and transversal competencies. Everyday STEM-relevant problems are contextualized, ill structured, and multidisciplinary in nature. By focusing on daily life issues, they promote students’ engagement in the problem-solving process and enable them to perceive how science relates to their lives. This paper aims to characterize the processes followed by prospective primary school teachers when solving three STEM-relevant problems that have different features. The qualitative analysis of 77 participants’ answers showed that complete problem-solving pathways were one among a variety of other paths identified. Most strategies adopted by the participants led them to ignore the contextual conditions of the problem and to reach solutions that did not attend to them. The affective relationship with the object may increase the problem solver’s tendency to ignore the contextual conditions, but this issue deserves further research. The results shed some light on the features of the problems that teacher educators should select if they wish for their prospective teachers to learn and succeed in solving everyday STEM-relevant issues. This is required to promote their future students’ engagement in problem-based learning processes.