STEAM is a coupling of the well-known STEM-disciplines of science, technology, engineering and mathematics with the arts. This conception of education builds on the foundations of STEM-curricula but complements it with a focus on innovation, creativity, novelty etc. Those in favor of STEAM education emphasize the importance of this shifted focus in better preparing the future generations for the complex challenges to come. However, a portion of the discourse on STEAM tends to reduce this approach to education to a means towards market-oriented ends. In opposition to such a discourse and primarily informed by Koestler's work on imagination and discovery in science, art and other domains of human creativity, we develop and defend a pedagogical conception of imagination. By connecting this conception of pedagogical imagination to insights from Tyson Lewis and Peter Hyland, we propose a protocol-based educational practice which can be incorporated in STEAM education.