Una epistemología de usos de lo proporcional. Un estudio socioepistemológico en el contexto de la huerta escolar

Abstract

At present, there are scenarios located within the schools, but outside the classrooms that bring the reality of the learner to the classroom and that allow to establish a two-way relationship between the mathematics that is worked in the classroom and those that are used. in extracurricular contexts. One of these scenarios is the school garden, which, beyond being a learning laboratory, constitutes a sociocultural framework for the social dissemination of knowledge. The social knowledge associated with the school garden is closely related to the ways in which the peasants carry out their tasks, since the tasks developed in this scenario correspond to those tasks typical of agricultural processes. Research carried out in peasant contexts shows how, in the development of agricultural tasks, a series of arguments that contribute to the domain of proportional thinking become evident. Affirmation that reaffirms when identifying that in the tasks of the school garden the students incur in the development of recurrent mathematical manifestations, which bring with them an epistemological status in the social construction of the proportional. This is how the investigation deals with the uses of proportionality, since it considers this knowledge as one that is used with certain intentions in the development of the tasks of the school garden, a knowledge that is constructed in a school context mediated by the reality of the student. The investigation included a cyclical development of different stages, among which are the construction of the state of the question, the collection of information, the socioepistemological analysis and the resignification of the theoretical-epistemic framework. This construction led us to consider that it is through studies around popular, technical and cult knowledge that the current School Mathematics discourse is nourished, since the object-centered paradigm is modified and a proposal centered on practices is put into discussion. Therefore, Socioepistemology was considered to be the theoretical approach with which proportionality would be approached, considering that it shared the investigative principles and provided powerful theoretical elements for the interpretation of the information and the foundation of the proposal. The epistemology of uses proposed on the proportional is based on the existence of three uses of proportionality that live in the context of the school garden: comparisons, the use of patterns and construction of units of measurement and generalizations. In it, the practices that make up the social construction of knowledge account for the resignification of proportionality and allow us to recognize how cultural, technical and cultured knowledge in a use scenario leads to the democratization of learning.