Mathematical objects, semiotic representations and senses

Abstract

In this paper we present results of a study on the emergence of mathematical objects from their representations and the difficulties encountered by some students to articulate the senses assigned by them to semiotic representations of the same mathematical object, obtained by transformations of treatment. We describe and analyze some processes of assigning senses achieved by students in grades 9 and 11 of the secondary education (Colombia) in relation to specific tasks that require such treatments performed between representations, and report some associated difficulties. In this study we include aspects of mathematical activity, communication on emerging mathematical objects and cognitive construction of mathematical objects.