O movimento universal, particular e singular existente entre as significações aritméticas, geométricas e algébricas: um estudo com enfoque no ensino fundamental
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Data
2021-06-11
Autores
Mame, Osvaldo Augusto Chissonde
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Universidade Estadual Paulista (Unesp)
Resumo
A presente tese tem por objetivo analisar o contexto peculiar quanto à organização do ensino de matemática – concepção angolana e do sistema Elkonin-Davidov-Repkin em que ocorre o movimento universal-particular-singular entre as significações aritméticas, algébricas e geométricas. A hipótese apresentada é de que a investigação sobre uma proposta dirigida ao ensino de matemática, da educação escolar primária, subsidie as decisões e a efetivação de ações para evitar os problemas com os quais os alunos se defrontam, atualmente, no processo de educação e ensino em Angola. Trata-se de uma investigação qualitativa, de base bibliográfica e de análise documental, que tem como referência duas obras que expressam a objetivação e orientação do sistema Elkonin-Davídov-Repkin e uma que explicita o modo de organização do ensino de matemática em Angola. Traz como fundamentos, mais especificamente, a psicologia pedagógica de base teórica histórico-cultural, porém sem perder de vista sua matriz, o Materialismo Histórico e Dialético. Os resultados da tese demonstram que, em termos pedagógicos, na proposição do sistema Elkonin-Davidov-Repkin, todas as tarefas anunciam a articulação entre as significações aritméticas, algébricas e geométricas, de forma articulada ao movimento universal, particular e singular. Em contrapartida, a mesma articulação não é verificada nas proposições angolanas, uma vez que suas tarefas, além de não explicitar a articulação entre as significações aritméticas, geométricas e algébricas, também não apresentam o movimento universal, particular e singular. Além disso, promove o ensino baseado na observação para constituição da ideia conceitual, isto é, voltado à promoção de aprendizagem de conteúdos apenas empíricos.
This thesis aims to analyze the peculiar context of the organization of mathematics teaching – Angolan conception and the Elkonin-Davidov system – Repkin in which there is the universal-particular-singular movement between arithmetic, algebraic and geometric meanings. The hypothesis presented is that the investigation of a proposal aimed at teaching mathematics, primary school education, subsidize decisions and implementation of actions to avoid the problems that students are currently facing in the education and teaching process in Angola. This is a qualitative research, bibliographically based and documental analysis, which has as reference two works that express the objectification and orientation of the Elkonin- Davídov – Repkin system and one that explains the way of organizing the teaching of mathematics in Angola. Its foundations are, more specifically, the pedagogical psychology of a cultural-historical theoretical basis, but without losing sight of its matrix, Historical and Dialectical Materialism. The results of the thesis demonstrate that, in pedagogical terms, in the proposition of the Elkonin-Davidov-Repkin system, all tasks announce the articulation between arithmetic, algebraic and geometric meanings, bringing together the universal, particular and singular movement. On the other hand, the same articulation is not verified in the Angolan propositions, since their tasks, in addition to not making explicit the articulation between arithmetic, geometric and algebraic meanings, also do not present the universal, particular and singular movement. In addition, it promotes observation-based teaching to build the conceptual idea, that is, aimed at promoting empirical content learning.
This thesis aims to analyze the peculiar context of the organization of mathematics teaching – Angolan conception and the Elkonin-Davidov system – Repkin in which there is the universal-particular-singular movement between arithmetic, algebraic and geometric meanings. The hypothesis presented is that the investigation of a proposal aimed at teaching mathematics, primary school education, subsidize decisions and implementation of actions to avoid the problems that students are currently facing in the education and teaching process in Angola. This is a qualitative research, bibliographically based and documental analysis, which has as reference two works that express the objectification and orientation of the Elkonin- Davídov – Repkin system and one that explains the way of organizing the teaching of mathematics in Angola. Its foundations are, more specifically, the pedagogical psychology of a cultural-historical theoretical basis, but without losing sight of its matrix, Historical and Dialectical Materialism. The results of the thesis demonstrate that, in pedagogical terms, in the proposition of the Elkonin-Davidov-Repkin system, all tasks announce the articulation between arithmetic, algebraic and geometric meanings, bringing together the universal, particular and singular movement. On the other hand, the same articulation is not verified in the Angolan propositions, since their tasks, in addition to not making explicit the articulation between arithmetic, geometric and algebraic meanings, also do not present the universal, particular and singular movement. In addition, it promotes observation-based teaching to build the conceptual idea, that is, aimed at promoting empirical content learning.
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Palavras-chave
Aritmética, Geometria, Álgebra, Matemática, Sistema Elkonin-Davidov-Repkin, Ensino fundamental, Arithmetic, Geometry, Elementary school, Mathematics, Elkonin-Davidov-Repkin system