IDEAS PREVIAS A LA CONSTRUCCIÓN DEL INFINITO EN ESCENARIOS NO ESCOLARES

This work presents a study on the intuitive ideas associated to the infinite concept, generated in non scholar situations. The aim of this investigation is to detect the way these ideas arise and how they behave like part of the mental model that the student forms for the infinite, affecting the construction of the mathematical infinite. The ideas we are referring to are generated in natural situations of social coexistence, thus the investigation is centered in the socioepistemological approach, which considers the social component as one of the components of the construction of the mathematical knowledge. Because the center of this thesis is the construction of ideas in social surroundings, the line of investigation to which it adheres to is the Social Construction of the Knowledge, understanding all construction of knowledge as the result of the interactions that occur within a social group, which shares a common culturalbaggage. Three stages of action are made to be able to obtain the proposed objective: the study of previous investigations, with the purpose of detecting common starting points, the study of historical happening of the concept, in different cultures, to identify some of the answers that the students present; and finally, an experimentation with students of high school, to analyze what they say, think, do and understand regarding the infinite