“Now I get it !”: Eureka experiences during the acquisition of mathematical concepts

Many famous scientists have reported anecdotes where a new understanding occurred to them suddenly, in an unexpected flash. Do people generally experience such “Eureka” moments when learning science concepts, and how do these episodes relate to learning mechanisms? To address these questions, we developed a new paradigm where participants learned a mathematical concept in the lab, in a single experimental session. Participants were given 1 to 7 lessons introducing the concept of geodesic, which generalizes the common notion of straight line to straight trajectories drawn on curved surfaces. They were then tested on their understanding of geodesics in several tasks requiring increasing levels of generalization from the information taught in the lessons. Our findings indicate that insight experiences are common when learning mathematics, as such experiences were reported by about 61% of our participants. Moreover, the participants who experienced insights performed better in a generalization test where they needed to identify a type of geodesic that had not been presented in the lessons, and this, even after controlling for their confidence in their own understanding. Based on these findings, we suggest that concept learning involves mechanisms that generally are not accessible to introspection, except when the process reaches key computational steps and insights are triggered.