Random Walks as a Royal Road to E-STEAM in Math Education

Context Millions of learners worldwide experience mathematics nowadays as an inescapable tool of cognitive abuse and punitive selection. Most traditional teaching thwarts natural human cognitive resources. Problem We would like to contribute to alleviating the aforementioned cognitive abuse, sharing the insights afforded by our exploration of enactive and metaphorical approaches to learning and teaching, inspired by E (embodied, enactive, extended, embedded, ecological)-cognition. We aim at understanding mathematical thinking processes and practic-ing an experimental epistemology of mathematics, not just prescribing actions to be undertaken in the classroom. Method Our theoretical scope is E-cognition. Our main research method is based on enactivism (enaction a la Varela) including metaphorical analysis, participant observation, and semi-structured interviews. Moreover, we discuss illustrative examples of learning activities related to random walks and STEAM (Science, Technology, Engineering, Art & Mathematics), particularly physics and art (dance and choreography). Results. Embodiment, enacting and metaphorising make a dramatic difference in mathematics learning processes. Learning activities related to random walks and deterministic dynamical systems enacted through dance and choreography can play a significant anti-dotal and remedial role against cognitive abuse in the teaching of mathematics. Beneficial insights are triggered, for students, teachers, and mathematics educators. Implications We suggest new horizons for research and practice in mathematics education informed by E-cognition and metaphorisation, with an antidotal and therapeutic effect against cognitive abuse in teaching. Further research is commendable on the often-stressful transition process from an abusive and repressive education to a more open enactivist education, which could use micro-phenomenological interviews among other techniques. It could involve scaling up our experimentation, particularly with prospective and in-service teachers. Limitations are related to the small number of students and teachers hitherto involved. Constructivist content Our research aims at developing a radically enactivist mathematics education inspired by Varela's enaction.