Demonstrações matemáticas e a Educação Básica: um estudo em Hermenêutica Filosófica - Dias Filho, Carlos Alberto Tavares [UNIFESP] (2020)
In this research we investigated in a phenomenological approach around the guiding question: How to do mathematical demonstrations in basic education didactically? The research was built by an analysis in Philosophical Hermeneutics of mathematical demonstration, understood as tradition, that is, the historical construction of the human collective. In the first moment of analysis, we looked for signs of answers to the guiding question in texts of this tradition that were presented to us, from this moment we built the ground-text, the soil of the analysis. The second moment of analysis consisted of a hermeneutic reading of the ground-text and its organization in the form of questions and answers of what the ground-text reveals to us regarding the guiding question. The questions that are repeated in the ground-text highlight relevant aspects to what we are looking for and make up the open categories. We have three open categories that tell us about the tradition of mathematical demonstrations: P1 - What is the way of being of mathematical demonstration ?; P2 - Is the mathematical proof the only tool that communicates the mathematical truth ?; P3 - How do mathematical statements take place ?. We explain the excerpts of the ground-text that composse each open category, how the excerpts relate to each other and what they explain about the mathematical demonstration. From the construction and analysis of open categories, we perceive five aspects of didactic work with mathematical demonstrations: (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. Finally, we summarize our understanding of the listed aspects. In our final remarks, we reinforce the importance of argumentation and mathematical demonstration in basic education.