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.
We discuss the similarities and differences between probabilistic and statistical thinking, arguing in favour of metaphorising them as arrows pointing in opposite directions. We base our argument and discussion on concrete examples, drawn from our teaching experience to a broad spectrum of learners at the University of Chile and inspired by Brousseau’s fundamental adidactic situation for inferential statistics in primary school, and our own fundamental adidactic situations for probability. Learners involved include first year humanistic university students, prospective math teachers, and in-service primary school teachers and their students.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.