The Geometrical Argumentative Practice: from Intuition to Deductive Logic

Abstract

This article describes part of a research carried out with 17 students from the third high school of the Public School of Education of the State School Prefeito Jaime Toledo, located in the municipality of Caiana, in the state of Minas Gerais. The research was carried out in order to verify, according to the model proposed by Balacheff (1987), the level of geometric evidence found in the arguments of these students in view of the need to justify a certain proposed situation; As well as to analyze if starting from na activity of experimental proof is possible that these students develop a better understanding of a certain geometric property. For the construction of the experimente we used the activity of Greek adapted from the portal M³ Multimedia Mathematics of UNICAMP. The results show that the constructed arguments are in a type of Pragmatic proof, varying between Naive Empiricis mand Generic Example, and that the absence of a more advanced mathematical language in these arguments is related to the lack of mathematic maturity. We also verified that the proposed activity contributed significantly to the construction of the presented geometric concepts.