Epistemological Study of the Object Group: A Piagetian Perspective in the Light of The Onto- Semiotic Approach to Mathematics Cognition (2017)
This article presents an epistemological analysis on the historic evolution of the object Group in accordance with Piaget and García perspective. In this sense, some mechanisms in the evolution process of this mathematical object are described. They are based on the premise that knowledge is produced by the interaction of the individual with his/her environment and it is ruled by some structures that are part of the individual. Thus, according to the evolution analysis of the object Group, meanings attributed to this notion appeared throughout its evolution history until finding the meaning of Group as in Galois Theory – Later on as Abstract group -. As a result of the epistemological analysis of the mathematical object, this text presents in general form some of the issues that gave rise to the meanings of the algebraic structure in question. The research of the meanings was carried out on the basis of the Onto-semiotic approach to mathematics cognition, given that it is important, both for teachers and Group theory researchers and for mathematics students – graduates in mathematics and mathematicians -. The method used for the study of the meanings is determined by theoretical tools belonging to the onto-semiotic approach.