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., The 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.