O pensar algébrico: uma perspectiva fenomenológica
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Data
2024-02-08
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Universidade Estadual Paulista (Unesp)
Resumo
Nesta tese de doutorado, o autor buscou, trilhando um percurso fenomenológico inspirado em Husserl, compreender a questão fundamental de como a Álgebra se desvela em seus modos de ser. O estudo situa a Álgebra no contexto da Matemática, destacando sua inter-relação com outras áreas dessa ciência. A tese se desenvolveu em seis seções, explorando a fenomenologia, a crise nas ciências europeias, a presença da Álgebra na BNCC, a abordagem de Freudenthal sobre a Álgebra, a simbolização da Álgebra ao longo da história, e, finalmente, a teoria das multiplicidades sob a perspectiva husserliana. Nesta teoria, a Álgebra é concebida como uma área da Matemática a qual dá conta de mencionar generalidades, ao definir axiomaticamente seus objetos, que abarcam as idealidades e, portanto, aqueles objetos do pensar que são livres de qualquer posição de fato. Por fim, a tese enfatiza a necessidade de compreender a Álgebra para além de sua instrumentalização, buscando desvelar suas propriedades e sua presença na evolução do pensamento matemático.
In this doctoral thesis, the author, following a phenomenological path inspired by Husserl, sought to comprehend the fundamental question of how Algebra reveals itself in its modes of being. The study situates Algebra within the context of Mathematics, highlighting its interrelation with other areas of this science. The thesis unfolds in six sections, exploring phenomenology, the crisis in European sciences, the presence of Algebra in the BNCC (National Curriculum Common Core), Freudenthal's approach to Algebra, the symbolization of Algebra throughout history, and finally, the theory of multiplicities from the Husserlian perspective. In this theory, Algebra is conceived as a branch of Mathematics that addresses generalities by axiomatically defining its objects, encompassing idealities and, therefore, those objects of thought that are free from any actual position. Ultimately, the thesis emphasizes the need to understand Algebra beyond its instrumentalization, aiming to unveil its properties and its presence in the evolution of mathematical thought.
In this doctoral thesis, the author, following a phenomenological path inspired by Husserl, sought to comprehend the fundamental question of how Algebra reveals itself in its modes of being. The study situates Algebra within the context of Mathematics, highlighting its interrelation with other areas of this science. The thesis unfolds in six sections, exploring phenomenology, the crisis in European sciences, the presence of Algebra in the BNCC (National Curriculum Common Core), Freudenthal's approach to Algebra, the symbolization of Algebra throughout history, and finally, the theory of multiplicities from the Husserlian perspective. In this theory, Algebra is conceived as a branch of Mathematics that addresses generalities by axiomatically defining its objects, encompassing idealities and, therefore, those objects of thought that are free from any actual position. Ultimately, the thesis emphasizes the need to understand Algebra beyond its instrumentalization, aiming to unveil its properties and its presence in the evolution of mathematical thought.
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Fenomenologia, Álgebra, Pensamento algébrico, Educação Matemática, Phenomenology, Algebra, Algebraic thinking, Mathematics Education