Several learning principles have emerged from cognitive science research that have direct applications for education (e.g., interleaved practice, worked examples, etc.). However, applying these principles at scale in education is complicated, as the principles fail to specify how they should be applied in different content areas, curricula, and classroom contexts. We summarize several challenges we have faced when attempting to apply and study the efficacy of cognitive learning principles in STEM educational contexts: 1) design challenges, e.g., how to enact the principle in new materials, 2) contextual/practical challenges, e.g., feasibility of implementation, scalability; 3) study-design challenges, e.g., implementation variability, data collection considerations; and 4) theory-specification, i.e., areas where principles may be underspecified for application. We aim to provide concrete suggestions and lessons learned related to translating cognitive principles, as well as spark discussion that could lead to new research and advance theory specification.