Research in the psychology of mathematics education has been confronted with the fact that people blatantly fail to solve tasks they are supposed to be able to solve correctly given their available domain-specific knowledge and skills. Also researchers in cognitive psychology have encountered such phenomena. In this paper, theories that have been developed in both fields to account for these findings are discussed. After giving a summary of the state of the art in both fields, we argue that bringing together these largely separately developed (sets of) theories creates opportunities for both domains and we suggest a way in which this can be done.