Volume 18 · Number 2 · Pages 259–276
Random Walks as a Royal Road to E-STEAM in Math Education

Amaranta Valdés-Zorrilla, Daniela Díaz-Rojas, Leslie Jiménez & Jorge Soto-Andrade

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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 practicing 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 à 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 antidotal 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.

Erratum: In the last sentence of §111 "so fostering their metacognitive abilities" should have been deleted.

Key words: Bayes, choreography, cognitive bullying, cognitive abuse, dance, dynamical systems, embodiment, enaction, metaphor, random walks, Francisco Varela


Valdés-Zorrilla A., Díaz-Rojas D., Jiménez L. & Soto-Andrade J. (2023) Random walks as a royal road to e-steam in math education. Constructivist Foundations 18(2): 259–276. https://constructivist.info/18/2/259

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