Embodiment and metaphorising in the learning of mathematics

Abstract

In this paper we undertake a critical reading of the Ouroboric (circular) relationship between the guiding metaphors of artificial intelligence and those of natural human intelligence, which has evolved from a vicious circle, triggered by the metaphorising of cognition as information processing, to a virtuous one, fostered by the advent of the embodied and enactive turn in cognitive science. We describe then our own experimental and theoretical approach to mathematical thinking and learning, where metaphorization plays a key role, besides embodiment and enaction. We comment on some concrete examples of mathematical thinking with different types of learners, in combinatorics, arithmetic, geometry and probability, where idiosyncratic metaphorization emerges and enacting and embodiment make a dramatic difference. We outline finally some significant challenges to contemporary AI, cognitive sciences, and mathematics proper, suggested by our examples. These challenges involve metaphorising as the tip of the iceberg in human cognition, metaphorising in intelligent systems, Ouroboric circularity, mathematical collective improvisation as an analogue of musical improvisation, group creativity and human swarm intelligence.