Prova e demonstração em geometria: uma busca da organização matemática e didática em livros didáticos de 6ª a 8ª séries de Moçambique

Abstract

This study aimed to understand the approach of proof and proving of properties of triangles present in textbooks for the 6th to the 8th series of Mozambique. The properties, the object of study, are the sum of internal angles, the relationship between the external and the internal angle non-adjacent and the relationship of congruence between triangles. Thus, the study sought to answer the following question: How do the texbtbook in use in schools (Mozambique) present the organization of the study about triangles and how they tech this object with a focus on proof and proving. The study was based on the work of Nicolas Balacheff about the processes of validation tests, Raymond Duval works about records of semiotic representations and Yves Chevallard works about the praxeological organization. The research has methodological procedure as the collection and analysis of bibliographic data. The study results showed that in the textbooks examined predominantly pragmatic proof. The authors emphasize the records figural and discursive in natural and symbolic language in these books and they have clear tasks with the technological-theoretical discourse available. But, the study results show that conversions are not adequately explored in the study of triangles and the reconfiguration is not fully exploited to produce arguments that could support intellectual proof