Demonstrações Matemáticas e a Educação Básica: um estudo em hermenêutica filosófica

we are presenting the research around the guiding question: How to do mathematical demonstrations in basic education didactically? The analysis in Philosophical Hermeneutics first moment was the construction of the ground-text based on a hermeneutics reading of texts from the match tradition; the second moment we analysed the ground-text pointing to clues about the structures of the phenomenom. Then we described aspects of the didactical work of mathematical demonstrantions, summarized as: (a) definition of mathematical demonstration adopted from its purposes; (b) justification for the use of the mathematical demonstration, mainly because of the human limitation of understanding and the temporal limitation; (c) way of constructing the demonstration that is socially accepted as valid today, based on the purpose adopted; (d) the role of argumentation and naive demonstrations compared to formal demonstration and mathematical skills; and (e) the mathematical language, its writing and the language about mathematics.