Imaginary significations and mathematical modeling: questions of meaning

Abstract

Considering Mathematical Modeling Environments (MMEs) from a socio-critical perspective (Barbosa, 2001) involves recognizing their nature as social —and therefore discursive— practices. In this context, a mathematical model has two essential dimensions: a referential one, linked to a topic and its meaning, and an evaluative one, related to the sense it acquires within the social practices in which the model is embedded. This paper aims to present a semiotic relationship —drawing on Bakhtin (2000) and Voloshinov (2009)— between MMEs and the meanings constructed for such models. It also proposes that social imaginary significations (Castoriadis, 1975), understood as both instituting and instituted elements of social practices, offer a deeper understanding of the evaluative richness found in the discursive practices within MMEs, as these significations precede and underpin such practices. To this end, the paper begins with a discussion of mathematical modeling in relation to mathematical, technological, and reflective knowledge. It then explores sense as an evaluative complement to the referential character of a mathematical model, connecting it to imaginary significations, since both exist as responses to questions. The concept of imaginary significations (Castoriadis, 1975) is considered as a response to humanity’s fundamental questions, as an organizing framework for representational possibilities in society, and as a simultaneously instituted and instituting configuration of that society. Finally, the notion of exotopy (the I-other interaction) is presented as a fundamental condition for generating surplus vision and promoting social transformation through Mathematical Modeling Environments. The role of imaginary significations is also acknowledged as a determining factor in the possibilities of exotopy.