The intention is to check to what extend models of cognitive science can help us to describe, to explain or to understand pupils’ mathematical behaviour in a more appropriate way. To this purpose, at first such models (as e.g. “semantic networks” or “production systems”) are described in more detail. In the main part it is discussed which problems in mathematics education call for explanations using results from cognitive psychology, and which answers can be given; i.e. it is investigated how useful models of cognitive science are in research on mathematics education. Finally, more recent developments are discussed, as for instance the significance of expert knowledge, intelligent tutoring systems, metacognition, and cognitive strategies and structures.