Many empirical studies about STEM (science, technology, engineering, and mathematics) curriculum present problems for students to solve. This paper draws upon the data collected from the enactment of an integrated STEM curriculum to discuss problems as constitutive of problem spaces where four Grade 5 Singapore students engage with the materialities and relationships to generate solutions from these spaces. The study seeks to address the nature of the problem spaces in STEM inquiry. Derived from the emergent coding of 12 hours of lesson videos, the findings illuminated that problem spaces emerged from familiar and dissimilar contexts in the curriculum. These problem spaces embodied epistemic infrastructures and epistemic emotions within which students exercised agency to collaborate productively and learn. Implications for STEM curriculum making that foregrounded epistemic considerations, rather than outcome-based learning, were discussed. This paper helps to further the field of curriculum studies in STEM education by contributing to the theorization of STEM curriculum by applying a process lens to deepen understanding of problems as problem spaces.