It is often argued by educators and researchers that access to the arts leads to increased academic performance. However, it is not clear why such access does so. We here use autopoietic enactive embodied cognition and ecological psychology to explain the relationship between dance training and conceptual problem-solving. We investigate four features of dance training that are beneficial for conceptual problem-solving and critical thinking: empathy, affordance exploration, attention change, and habit breaking. In each case, we will see that the embodied sensorimotor skills developed through dance practice are a form of affordance exploration that can carry over into the realm of conceptual problem-solving. Hence, since some of the skills needed in conceptual problem-solving are the same ones developed and trained through dancing, when we train dance, we also train some of the relevant skills for conceptual problem-solving and critical thinking.