Abdução e a produção do conhecimento matemático
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Data
2020-03-09
Autores
Souza, Jesaías da Silva [UNESP]
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
Este trabalho investigou como o raciocínio abdutivo se mostra na produção do conhecimento matemático. Para tanto, consideramos o compreendido nas leituras de Charles Sanders Peirce (1839 – 1914) acerca desse tipo de raciocínio e, norteados pela postura fenomenológica, em um movimento hermenêutico, apresentamos o significado da Abdução como um modo de pensar do matemático, ou seja, como abertura de possibilidade à investigação. Partimos, portanto, da análise das ideias explicitadas pelos filósofos Peirce e Gadamer (1900–2002) para compreender o raciocínio Abdutivo e a hermenêutica, respectivamente. Entrevistamos um matemático do Instituto de Matemática e Estatística da Universidade de São Paulo – IME-USP. A entrevista nos permitiu um diálogo em torno do seu fazer matemático e, ao analisar o depoimento, identificamos aspectos relacionados ao raciocínio abdutivo que se destacaram em seu modo de fazer matemática e o que é a produção de conhecimento. Nesse sentido entendemos a necessidade de discutir o que é o pensar para Heidegger (1889 – 1976) a fim de compreendermos o que se mostrou durante a entrevista. Tratando-se de uma pesquisa qualitativa de abordagem fenomenológica, sua relevância está na exposição de compreensões sobre a produção do conhecimento matemático, evidenciando a expressão do pensar que, no diálogo com o outro, abre-se revelando modos de compreender a produção matemática.
This paper investigated how abductive reasoning is shown in the production of mathematical knowledge. Therefore, we consider the comprehension in Charles Sanders Peirce (1839 - 1914) readings about this kind of reasoning and, guided by the phenomenological posture, in a hermeneutic movement, we present the meaning of Abduction as a way of thinking of the mathematician, that is, as an opening of possibility to research. Therefore, we start with the analysis of explicit ideas by philosophers Peirce and Gadamer (1900 - 2002) to understand abductive reasoning and hermeneutics, respectively. We interviewed a mathematician, from the Institute of Mathematics and Statistics of the University of São Paulo - IME-USP, talking about his work and, analyzing the interview we identified aspects related to the abductive reasoning that stood out in his way of doing mathematics and what is the production of knowledge. We discussed thinking in Heidegger (1889 - 1976) to understand what was shown during the interview. Being a qualitative research with a phenomenological approach, its relevance is in the exposition of understandings about the production of mathematical knowledge, highlighting the expression of thinking that, in dialogue with the other, opens revealing ways of understanding mathematical production.
This paper investigated how abductive reasoning is shown in the production of mathematical knowledge. Therefore, we consider the comprehension in Charles Sanders Peirce (1839 - 1914) readings about this kind of reasoning and, guided by the phenomenological posture, in a hermeneutic movement, we present the meaning of Abduction as a way of thinking of the mathematician, that is, as an opening of possibility to research. Therefore, we start with the analysis of explicit ideas by philosophers Peirce and Gadamer (1900 - 2002) to understand abductive reasoning and hermeneutics, respectively. We interviewed a mathematician, from the Institute of Mathematics and Statistics of the University of São Paulo - IME-USP, talking about his work and, analyzing the interview we identified aspects related to the abductive reasoning that stood out in his way of doing mathematics and what is the production of knowledge. We discussed thinking in Heidegger (1889 - 1976) to understand what was shown during the interview. Being a qualitative research with a phenomenological approach, its relevance is in the exposition of understandings about the production of mathematical knowledge, highlighting the expression of thinking that, in dialogue with the other, opens revealing ways of understanding mathematical production.
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Palavras-chave
Educação matemática, Investigação, Pensar, Hermenêutica, Fenomenologia, Mathematical education, Investigation, Think, Hermeneutics, Phenomenology