Time for telling stories: narrative thinking with dynamic geometry

In his work on human cognition, Bruner (The culture of education, Harvard University Press, Cambridge, 1996) distinguishes between narrative and paradigmatic modes of thinking. While the latter is closely associated with mathematics, Bruner’s writings suggest that the former contributes non-trivially to the learning of mathematics. In this paper, we argue that the very nature of dynamic mathematical representations—being intrinsically temporal, occurring over time—offer very different opportunities for narrative thinking than do the static diagrams and pictures traditionally available to learners. Using examples from our research, we analyse these opportunities both in terms of their potential for enhancing understanding and for their relation to the kind of paradigmatic thinking that usually constitutes mathematical knowledge.