As funções da Geometria em outros campos da Matemática: uma análise de livros didáticos
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Data
2020-05-06
Autores
Gentil, Liara Alves
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Universidade Estadual Paulista (Unesp)
Resumo
O principal objetivo deste trabalho é investigar as funções que a Geometria desempenha em campos não-geométricos em livros didáticos dos Anos Finais do Ensino Fundamental, aprovados pelo Programa Nacional do Livro Didático 2017. A partir dele foram delineados dois objetivos específicos, a saber: analisar como os conteúdos de Geometria estão estruturados (introdução, abordagem e desenvolvimento) em capítulos não-geométricos; mapear, em capítulos não-geométricos, as tarefas que fazem uso da Geometria em seus enunciados. A base teórica que fundamentou esta pesquisa foram os estudos de Flores (2003, 2010, 2013) acerca da cultura visual, entendida como as concepções inerentes à cultura de uma sociedade, manifestas em sua forma visual. Dentro da cultura visual, foi assumido o termo visualidade, definido como os discursos que informam sobre o modo como nós vemos. Pautada numa abordagem qualitativa, foram analisadas, nesta dissertação, três coleções de livros didáticos, totalizando 12 obras. Todo o conteúdo de Geometria que permeava os capítulos de Álgebra, Aritmética, Probabilidade e Estatística foi classificado de acordo com as funções que exerce, a saber: função ilustrativa, formativa, explicativa, demonstrativa, representativa e imagem mental. Resultados reforçam o caráter histórico e cultural da Geometria ao pontuar o uso de figuras geométricas como parte do discurso visual da sala de aula. Em alguns conteúdos de Álgebra e Aritmética, a Geometria se estabeleceu como prática visual que compõe os modos de olhar dos alunos da Educação Básica. Nesse sentido, é possível afirmar que a Geometria e as figuras geométricas são articuladas aos outros campos da Matemática com o propósito de favorecer a aprendizagem. Por diversas vezes, a Geometria é inserida, principalmente nos campos Álgebra e Aritmética, como uma tentativa de facilitar o ensino de alguns conceitos abstratos, ilustrando-os por meio de figuras geométricas. Também foi possível observar que há um processo de “desgeometrização”, ou seja, há uma tendência em diminuir a quantidade de figuras geométricas em função do rigor algébrico.
The main goal of this paper is to investigate the functions Geometry performs in non-geometric fields in textbooks of the last years of Elementary School, approved by the National Textbook Program 2017. From it, two specific objectives were outlined: to analyze how geometry contents are structured (introduction, approach and development) in non-geometric chapters; to map, in non-geometric chapters, the tasks that make use of geometry in their tasks. The theoretical basis that underpinted this research was Flores' studies (2003, 2010, 2013) about visual culture, understood as the conceptions inherent to the culture of a society, manifested in its visual form. Within the visual culture, the term visuality was assumed, defined as the discourses that inform us about the way we see. Based on a qualitative approach, three collections of textbooks were analyzed in this research, totaling 12 books. All the content of Geometry that permeated the chapters of Algebra, Arithmetic, Probability and Statistics was classified according to the functions it performs, namely: illustrative, formative, explanatory, demonstrative, representative and mental image function. Results reinforce the historical and cultural character of Geometry by highlighting the use of geometric figures as part of the visual discourse of the classroom. In some contents of Algebra and Arithmetic, Geometry has established itself as a visual practice that composes the ways students of basic education look at it. Therefore, it is possible to affirm that Geometry and geometric figures are linked to other fields of Mathematics with the purpose of favoring learning. Geometry is inserted several times, mainly in Algebra and Arithmetic fields, as an attempt to facilitate teaching of some abstract concepts, illustrating them by geometric figures. Also, it was observed that there is a process of “degeometrization”, meaning, there is a tendency to decrease the amount of geometric figures due to algebraic rigor.
The main goal of this paper is to investigate the functions Geometry performs in non-geometric fields in textbooks of the last years of Elementary School, approved by the National Textbook Program 2017. From it, two specific objectives were outlined: to analyze how geometry contents are structured (introduction, approach and development) in non-geometric chapters; to map, in non-geometric chapters, the tasks that make use of geometry in their tasks. The theoretical basis that underpinted this research was Flores' studies (2003, 2010, 2013) about visual culture, understood as the conceptions inherent to the culture of a society, manifested in its visual form. Within the visual culture, the term visuality was assumed, defined as the discourses that inform us about the way we see. Based on a qualitative approach, three collections of textbooks were analyzed in this research, totaling 12 books. All the content of Geometry that permeated the chapters of Algebra, Arithmetic, Probability and Statistics was classified according to the functions it performs, namely: illustrative, formative, explanatory, demonstrative, representative and mental image function. Results reinforce the historical and cultural character of Geometry by highlighting the use of geometric figures as part of the visual discourse of the classroom. In some contents of Algebra and Arithmetic, Geometry has established itself as a visual practice that composes the ways students of basic education look at it. Therefore, it is possible to affirm that Geometry and geometric figures are linked to other fields of Mathematics with the purpose of favoring learning. Geometry is inserted several times, mainly in Algebra and Arithmetic fields, as an attempt to facilitate teaching of some abstract concepts, illustrating them by geometric figures. Also, it was observed that there is a process of “degeometrization”, meaning, there is a tendency to decrease the amount of geometric figures due to algebraic rigor.
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Palavras-chave
Cultura visual, Visualidade, Ensino Fundamental, Desgeometrização, Visual culture, Visuality, Last years of Elementary School, Degeometrization