Using enactivism as a methodology to characterise algebraic learning

Abstract

My purpose in this paper is to illustrate the way in which an enactivist methodological approach guided me as I conducted a two-case longitudinal study where the learning of algebra was explored in different contexts throughout time. Three groups of students in two different schools in the city of Puebla, Mexico, were followed from the last year of primary school (Year 6) to the second year of their secondary education (Year 8). Learning was characterised as the ongoing structural change that allows individuals or groups to act effectively in a changing environment [Maturana (GAIA, a way of knowing: political implications of the new biology. Lindisfarne, New York, pp 65–82, 1987)]. An enactivist methodology, which revolves around the idea of research being a form of learning [Reid (Proceedings of the 20th conference of the international group for the psychology of mathematics education. PME, Valencia, pp 203–209, 1996)], implied that, as I carried out the study, what I was doing was learning about how people learn algebra. My initial questions arose from my experiences with the teaching and learning of mathematics, which gave me a sense of the complexity involved in the learning processes. Later, as I became immersed in the process of investigation of the teaching and learning of algebra, my conceptions continually evolved. The meaning of the phrase ‘algebraic learning’, which I used as a way of maintaining a wide perspective that allowed me to explore the events in the classroom in a complex way, arose as I engaged with enactivist ideas about learning, with the research literature on the learning of algebra, in conversations with people and in interactions with the participants of my project. I went through a process of continual development and change which I describe in this paper.