Contemporary Learning in the Interaction of the Human with Data, Via Technology-Mediated Graphics: The Discourse-Representation Dialogue in Mathematics

The (abstract) mathematical discourse originates in Greece. In the fourteenth century, the properties of movement began to be represented; this will be expanded to mathematical objects two centuries later, still privileging the abstract treatment. Subsequently, the search for the foundations of Infinitesimal Calculus departs from graphic reasoning in the arithmetization of Analysis process of the nineteenth century. Now, Socioepistemology recognizes the mathematical practices of different communities and the school-daily life mathematical reciprocity. Thus, it makes it possible to redesign the teaching-learning of mathematics, both for specialties and for the ordinary individual, recognizing that their interests are not necessarily those of the mathematical community. To do this, Socioepistemology distinguishes graphing as a natural linking mechanism, develops graphical argumentation to address phenomena, and deems graphing as important for the transversality of knowledge. However, we claim that, in fact, human beings process information in a dialogue of the discursive and graphical ways in which it is present. Nowadays, this requires managing technology to obtain adequate data representations and for the symbolic processing of the relationships at stake; in turn, to some extent, this shifts attention from computational routines and allows to focus on contemporary learning requirements: modelling, decision-making, computational thinking. Thus, a more complex scenario but an excellent opportunity for students and teachers alike.