The insertion of the language dimension in the analysis of the teaching problem

Abstract

The purpose of this article is to insert the language dimension into the analysis of the didactic problem with the same degree of relevance attributed to the epistemological, ecological and economic dimensions when studying a mathematical object. We planned a meeting with twelve Engineering and Mathematics students from two public universities in the interior of Bahia and proposed a task with the theme Double Integral of a Quadric Surface, the hyperbolic paraboloid. As theoretical assumptions we take as a contribution the Anthropological Theory of Didactics (TAD) and Peircean Semiotics and the construct elaborated by the authors of the four languages: counterfactual, dictated, in course, in (dis) course. Five of the students solved the task, three from Engineering, who created a question in the context of their degree, the other two, from the Mathematics Degree, focused on developing calculations. The results obstained revealed that future engineers strongly applied counterfactual and (dis)course language, while those in the bacherlor’s degree used dictated and in course language; the twelvw students experienced difficulties in co-authoring the elaboration, solution, and analysis of the activities, as they did not find similar models in textbooks and the media. We infer that the language dimension was relevant for the development of abductive reasoning and for the student’s co-authorship in the creation and solution of Double Integral question statements.