Critical Paradigm of Research and Mathematical Modelling: Transformations that Challenge Conditions of Social Vulnerability

Abstract

In this reflexive paper, we aim to describe the mutual influence —and its consequences—between research based on a critical paradigm and mathematical modelling environments oriented by a socio-critical perspective, all carried out in a context of social and cultural diversity. To this end, we reflect on two doctoral theses whose data were produced in the same school context —a public school in the city of Bogotá, Colombia— at two different moments. The participants of the two investigations are students who live in a condition of social vulnerability, understood not only as economic and structural restrictions, but also from the (in)capacity to react to this condition. The dialectical relationship between the investigations and a series of pedagogical practices of modelling acted as an engine of transformations in mathematics classes, which started to consider the social, cultural and political reality of the students. The students’ condition of social vulnerability began to have visibility in mathematics classes as a source of themes for mathematical modelling environments, which occurred both during the investigations carried out there and in the absence of the researchers. From reflections and questionings made during the modelling environments, students were able to rethink their own actuation in society and their condition of social vulnerability, challenging it.