In recent years, the presence of the acronym STEAM has been growing in the educational field. All around the world we are faced with a growing demand for professional STEM skills, however, who has the responsibility to train future STEAM teachers? In this article, we explain the results of an investigation with university students pursuing a degree in primary education and Master's degree students in secondary education, with technology speciality, participating in a seminar about STEAM projects design in two consecutive academic calendar years (18/19 and 19/20). We analyse the responses to a questionnaire which was specifically designed to discover their knowledge about STEAM and the predisposition towards its extended study with a set of semi-structured interviews to delve into the causes of the responses. Previous knowledge about the meaning of STEM and the predisposition of pre-service teachers towards the future design of projects based on the STEAM disciplines are compared. The results show significant differences between the previous knowledge and the perceptions of the teachers from both specializations: primary and secondary level. The results also confirm the low levels of prior knowledge with a slight tendency towards improvement when two consecutive courses are compared. The findings emphasize the need to integrate STEAM teacher training into official curricula.