Structural thinking: an approach from the first memoir of É. Galois

Structural thinking, defined as the identification of relationships among the elements of a system and their use to understand its functioning, is relevant in both scientific modelling and Mathematics Education. Due to the lack of explicit models to describe this type of thinking, this study aims to characterize the structural thinking present in Galois' first memoir, “Memoir on the Conditions for the Solvability of Equations by Radicals”. This treatise is significant for introducing the mathematical notion of group and the study of algebraic structures. Based on documentary analysis, the treatise and its historical context were examined, leading to the identification of three key characteristics of structural thinking: the study of structure–behavior relationships, isomorphism as a modelling mechanism, and the development of a macrostructural view.