Semiotic representation in Mathematics: history, epistemology, learning

Abstract

Since the works of Raymond Duval, the question regarding the role of records of semiotic representation in the learning of Mathematics has been an object of research. There is no doubt that records of semiotic representation are essential for the creation of mathematical objects, as well as for the learning of Mathematics. The subject of this text is, therefore, to offer some reflections on the way of thinking which gives foundation to this hypothesis. How did the idea of representation, particularly semiotic representation, become the model for the acquisition of knowledge within a specific line of thought? It can be said that the representation records theory, elaborated by Duval, for the learning of Mathematics, has modern thought as a base: a cognoscenti subject, a cognoscible object and a dual theory of signs. This analysis becomes particularly important for making possible a deeper reflection, especially in the education of Mathematics teachers, in regard to the learning theories which are employed, as well as the formation of the knowledge which is taught in Mathematics. Key words: Representation. Semiotics. History of Mathematics. Mathematics Education.