El infinito en el aula de matemática. Un estudio de sus representaciones sociales desde la socioepistemología

Abstract

The research reported here is about infinity and its presence in the scholastic mathematics discourse. The socio-epistemological theory is the one chosen for this study, because it cares about the construction of mathematical knowledge as a result of the actions placed in particular scenario, analyzed from a systemic point of view. The core concept of this work is the infinite which is peculiar in nature and treatment within school, since it is not argued or defined explicitly as a mathematical concept, but is present without any doubt. The students are faced with different obstacles in the development of this idea and the others closely related to it. Nevertheless, in the Teachers Training College, Cantor’s study on infinite is presented, along with the study of infinite sets and transfinite numbers. From the socioepistemological point of view about the evolution and development of this concept we were able to find the processes, meanings and questions that made this idea emerge. In the end of that part of the research, we could detect the social practices, referential practices and meaning contexts for the two types of infinites that were found: the one related to algebra and the one related to calculus. The experience done with students form Teachers Training College and high schools lead us to the understanding that the concept we began working with, is so close to many others that allow it to have meaning within certain context. And we assume that these are the contexts we need to take back to school.