O jogo como ferramenta no trabalho com números negativos: um estudo sob a perspectiva da epistemologia genética de Jean Piaget

Abstract

The central theme of this work is the structuralism construtivist, in that detached the importance of the mathematical structure for the acquisition of the logical-mathematical knowledge. We began our study presenting an abbreviation summary on the life and work of Piaget, the theory of the knowledge exposing the theoretical arguments of the rationalism (Leibniz), of the empiricism (Locke), of the interacionismo (Kant) and the constructivism piagetian. The approached themes show the different forms of understanding the origin of the knowledge. Due to your importance for our work made a study about the structuralism piagetiano and mathematical structuralism. For the fact of the structuralism piagetiano to present a dynamic character related with the activity, organization, transformation, action coordination and construction looked for a model to assist her/it those requirements. In this sense, we opted for the study of the game in the vision piagetian, because he comes as an appropriate model of the algebraic structures or of the Mathematics in general. Thus, for understanding the shape to represent those models we made a study on semiotics in Peirce and Piaget, because the game presents a direct connection with the representation. In our work we presented two studies: the first was an exploratory study with semi-structured questionnaire and, in the second, we applied the game of the chess board with activities on the negative numbers; the activities were developed with ten teachers of public school of the state net of teaching that act in the 6a. series of the Fundamental Teaching. The study concludes that the game is a suitable tool, as it presents the structure of the negative numbers as well as it offers and different representation forms more clearly