A complementaridade entre sentido e referência dos símbolos da matemática

Abstract

This research aimed to discuss the reflections in Mathematical Education of the use of a semiotic approach focused on the complementarity between meaning and reference of symbols of mathematics. Therefore, it was analyzed the historical development of the semiotic representations in Mathematics and Sciences from the Scientific Revolution occurred in the 17th century, a period in which, according to Foucault, was based essentially on the understanding of the relative independence between sense and reference of the symbolic representations. We also analyzed the work of Cassirer, who recognized the importance of the Copernican Revolution of Kant's Epistemology, and the work of Descartes, who knew how to explore this new environment very well. The theoretical references were Kant (1787/2001), Peirce (1931-1935; 1958) and Otte (1993b; 2003a; 2012). The methodology was based on Semiotics, with the contribution of an analysis that allows the interweaving of events and facts from a theoretical perspective, seeking complementary characteristics. The complementary understanding of mathematics, perceived in the Axiomatic Theory developed by Grassmann (1844; 1861), and the work of Graeub, who introduced a new approach to Linear Algebra, complementary to the approach prevailing at the time, were also analyzed. As a result, implications for Mathematical Education were identified, such as the fact that the semiotic approach avoids the usual dichotomy between psychology and platonism, offering a synthetic view of how to learn and know mathematics.