Abstract

We are interested in exploring and developing an enactivist approach to problem- posing and problem-solving. We use here the term “enactivist approach” to refer to Varela’s radically nonrepresentationalist and pioneering “enactive approach to cognition” (Varela et al., he embodied mind: Cognitive science and human experience. Cambridge, MA: The MIT Press, 1991), to avoid confusion with the enactive mode of representation of Bruner, which is still compatible with a representationalist view of cognition. In this approach, problems are not standing “out there” waiting to be solved, by a solver equipped with a suitable toolbox of strategies. They are instead co-constructed through the interaction of a cognitive agent and a milieu, in a circular process well described by the metaphor of the Ouroboros (the snake eating its own tail). Also, cognition as enaction is metaphorized by Varela as “lying down a path in walking.” In this vein, we present here some paradigmatic examples of enactivist, and metaphorical, approaches to problem-solving and problem-posing, involving geometry, algebra, and probability, drawn from our didactical experimenting with a broad spectrum of learners, which includes humanities-inclined university students as well as prospective and in-service maths teachers. Our examples may be metaphorized as cognitive random walks in the classroom, stemming, and unfolding from a situational seed.