Imagining how could it be the reflexive knowing of the Bernabé Bernal ones

Abstract

The present article is based on the version of the research project “Reflective knowing in mathematical modeling contexts from a social-critical perspective”, focusing its attention, as a research problem, on the question: What would characterize the reflective knowledge of the Bernabé Bernal's if in their school history mathematical modeling from a social-critical perspective turned out to be a regular means in their training? In particular, this article seeks to report the analysis of a classroom experience based on a mathematical modeling environment, thought from a social-critical perspective, which sought to relate characteristics of reflective knowledge developed by a group of eleventh grade students in a public school in Bogota - Colombia. It starts with a methodological idea of research called critical investigation, which takes into consideration that in an investigation it could be taken into account not only what is happening but also what could have happened and what could be imagined. The data (recorded in audio and video recordings, interviews, students' writings and productions) were analyzed, considering the notion of dialogical acts. It is then presented to reflective knowledge and mathematical modelling from a political perspective of Mathematical Education. In this way, the context in which students develop such knowledge is considered an element of the starting point that we must take into account in our pedagogical and research practices. Thus, several reflections are highlighted, understood as an opening for discussion around four distinctive features of the process developed by students: thinking of the other, critical reading and Mathematics, practices with mathematics and the community. With this framework, such features are described as characteristics of the reflective knowledge