STEM education should be grounded in our knowledge of how students think in STEM-focused learning environments. However, little is currently known regarding specific types of thinking in these contexts. We explore the theoretical notion of STEM Ways of Thinking (SWoT) in interdisciplinary learning situations. Our primary focus is not on the curricular content of STEM education, but rather on the nature of the cognitive activity at play during STEM-focused activity. We give particular focus to students' claim making and reasoning during interdisciplinary STEM activity. Our framework focuses on the disciplines of science, engineering, and mathematics. While these disciplines have vastly different practices and epistemologies, we argue that claim making and reasoning provide an avenue for considering student thinking at their intersections. A brief literature review of SWoT is provided that illustrates trends and limitations amongst current theories and studies. After a detailed discussion of our own theoretical perspective of SWoT, we provide an illustrative learning segment to explore the explanatory and analytic power of our theoretical perspective. Implications of our work on curriculum and instruction are provided.