Construção de signos matemáticos: uma proposta metodológica para séries iniciais do ensino fundamental
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Data
2006-11-29
Autores
Manechine, Selma Rosana Santiago [UNESP]
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
Esse trabalho tem como objetivo elaborar uma proposta didático-metodológica para o ensino e aprendizagem de Matemática tendo o contexto experiencial como elemento integrador entre as disciplinas de Matemática e Ciências Naturais. Fundamentamos o desenvolvimento e a análise das ações discentes/docentes, pelo referencial teórico da filosofia de Charlers Sanders Peirce (1839- 1914). Segundo a teoria peirceana o modo de apreensão de um fenômeno se dá de forma triádica: primeiridade, secundidade e terceiridade, de maneira que, o conhecimento se faz mediante signos no decorrer da experiência. Os níveis didáticos Sentir-Perceber/Relacionar/Conceituar idealizados a partir da tríade peirceana de interpretantes nortearam a investigação do processo de significação dos conceitos matemáticos e científicos apreendidos pelos alunos. Os conhecimentos matemáticos: (a) medida de comprimento; (b) construção e interpretação de gráficos de colunas; (c) escala; (d) noção de espaço (fronteira, localização e formas geométricas) e estimativa foram desenvolvidos (com 32 alunos de 3ª série do ensino fundamental de uma escola pública) a partir de situações experienciais com canteiros de plantas para apreensão dos conceitos de coexistência e competição entre seres vivos. No ensino de Ciências Naturais as habilidades de medir, estimar, representar e interpretar dados são usadas como ferramenta na elaboração e análise de experimentos e gráficos das proporções estabelecidas entre os fenômenos estudados. Essas habilidades dependem dos signos matemáticos apreendidos no estudo de medidas e tratamento de informações. Podemos ressaltar, entre os pontos analisados, que a proposta didáticometodológica desenvolvida permitiu aos educandos e educadores produzir interpretantes (emocional, energético e lógico). Dessa maneira, o processo de significação...
The objective of this doctorate thesis is to present a mathematics teaching project in which an experimental environment integrates the disciplines Mathematics and Natural Sciences. The development and analysis of the teachers and students’ actions are based on the Charles Sanders Pierce’s theory (1839-1914). According to the Peircean theory, understanding a phenomenon relies on a triad – Firstness, Secondness and Thirdness – and knowledge is built on experience. The learning stages Perceiving/Relating/Conceptualizing present in the Piercean theory of interpretants guided the investigation of the students’ learning mathematical and scientific concepts. The mathematics contents (a) length measuring, (b) column graphics making and reading, (c) scale, (d) concepts of space (boundary, localization and geometric forms) and estimate were taught to 32 9-year-old schoolchildren from a state school, using plant beds as a real environment where coexistence and competition between living beings are easily seen. In the Natural Science classes, measuring, estimating, representing and interpreting skills are used as tools for doing and analyzing experiments and graphics representing the phenomena studied. These skills were developed from the students’ interpreting the mathematical signs learned in the study of measures and data analysis. The mathematics teaching project designed in this thesis produced effective interpretants (emotional, energetic and logical). Thus the signifying process (Perceiving/Relating/Conceptualizing) took place due to the students’ drawing inferences on the abductive/inductive/deductive levels which could be noted in their interpreting the objects studied. We show that learning mathematical concepts and their signification are beyond representations and involve integrating mathematical, linguistic and scientific symbols.
The objective of this doctorate thesis is to present a mathematics teaching project in which an experimental environment integrates the disciplines Mathematics and Natural Sciences. The development and analysis of the teachers and students’ actions are based on the Charles Sanders Pierce’s theory (1839-1914). According to the Peircean theory, understanding a phenomenon relies on a triad – Firstness, Secondness and Thirdness – and knowledge is built on experience. The learning stages Perceiving/Relating/Conceptualizing present in the Piercean theory of interpretants guided the investigation of the students’ learning mathematical and scientific concepts. The mathematics contents (a) length measuring, (b) column graphics making and reading, (c) scale, (d) concepts of space (boundary, localization and geometric forms) and estimate were taught to 32 9-year-old schoolchildren from a state school, using plant beds as a real environment where coexistence and competition between living beings are easily seen. In the Natural Science classes, measuring, estimating, representing and interpreting skills are used as tools for doing and analyzing experiments and graphics representing the phenomena studied. These skills were developed from the students’ interpreting the mathematical signs learned in the study of measures and data analysis. The mathematics teaching project designed in this thesis produced effective interpretants (emotional, energetic and logical). Thus the signifying process (Perceiving/Relating/Conceptualizing) took place due to the students’ drawing inferences on the abductive/inductive/deductive levels which could be noted in their interpreting the objects studied. We show that learning mathematical concepts and their signification are beyond representations and involve integrating mathematical, linguistic and scientific symbols.
Descrição
Palavras-chave
Didática, Metodologia, Matemática, Semiótica Peirceana, Teaching, Methodology, Mathematics, Peircean semiotics
Como citar
MANECHINE, Selma Rosana Santiago. Construção de signos matemáticos: uma proposta metodológica para séries iniciais do ensino fundamental. 2006. 310 f. Tese (doutorado) - Universidade Estadual Paulista, Faculdade de Ciências, 2006.