Do triângulo ao trapézio semiótico: Uma análise do pensamento metafórico em problemas de aplicação da matemática

Abstract

The main question of this article concerns the search for a theoretical and empirical foundation to the argument, increasingly reaffirmed, according to which modelling and applications provide adequate contexts for meaningful mathematics learning. The framework adopted to address the question brings in the role of metaphorical thinking in human cognition and its articulation with the phenomenon of meaning making in light of the peircean theory of semiosis. The semiotic triangle suggested by Peirce is used to envision a new semiotic model of metaphorical meaning – the semiotic trapezoid.

The duplication of referential domains is seen as a key concept in the production and interpretation of metaphors. The application of the trapezoidal semiotic model is illustrated in the analysis of a protocol extracted from a set of data regarding the work of a group of students on an applied problem during an introductory calculus course. Data analysis leads to the formulation of conclusions both related to the viability and usefulness of the proposed theoretical model and to the understanding of the production of metaphors within the processes of solving applied problems. The instances of metaphorical thinking are found to be determinant in the generation of meaning for mathematical models and concepts.