Research in psychology and in mathematics education has documented the ubiquity of "intuition traps" -- tasks that elicit non-normative responses from most people. Researchers in cognitive psychology often view these responses negatively, as a sign of irrational behaviour. Others, notably mathematics educators, view them as necessary steps towards deeper understanding, but still as obstacles to be overcome. Still others, especially those with evolutionary bend, view them as the outcome of an intelligent system that has been tricked by atypical conditions (hence our term "traps"). As researchers and practitioners in mathematics education, we tend to sympathize with the latter and, moreover, consider these intuition traps as a potentially fertile resource in the mathematics classroom. This article thus presents theoretical and practical support for the two sides of the same coin: Intuition traps as representing a good "source" and a good "resource."