Educação matemática crítica permeando capítulos de geometria em livros didáticos: entre direcionamentos, contextos e enunciados
Carregando...
Data
2022-12-21
Autores
Título da Revista
ISSN da Revista
Título de Volume
Editor
Universidade Estadual Paulista (Unesp)
Resumo
Os livros didáticos de Matemática são materiais que fazem parte do cotidiano escolar e evidenciam aspectos advindos de contextos sociais e culturais, além dos educacionais. Eles ainda podem ser vistos enquanto recursos passíveis de análise, no âmbito de investigações científicas. Sendo assim, assumindo uma perspectiva crítica da Educação Matemática para a pesquisa trazida nesta dissertação, objetivamos compreender como a Educação Matemática Crítica (EMC) permeia duas coleções de livros didáticos do Ensino Médio, no horizonte da Geometria. Para atender esse objetivo, alguns ‘conceitos’ da EMC foram colocados em discussão, seguindo a abordagem proposta por Ole Skovsmose. Logo, vemos ‘conceitos’ como expressões que dão conta de explicitar significados e qualificar interpretações sobre os dados, não conferindo um arcabouço teórico rígido para caracterizar a EMC. Dentre alguns desses, elegemos: a democracia e o papel sociopolítico da Educação Matemática; a ideologia da certeza; a matemacia; e os ambientes de aprendizagem. No que tange aos materiais analisados, escolhemos os capítulos destinados à abordagem da Geometria em livros didáticos de Matemática aprovados no edital de 2018 do Programa Nacional do Livro e do Material Didático. O recorte dado à Geometria nesses recursos deu-se pela falta de estudos identificada na revisão de literatura, quando os livros são tomados à luz da EMC, bem como devido ao escopo do nosso grupo de pesquisa, que possui como uma das preocupações investigar a presença da Geometria nesses materiais. Em termos metodológicos, foi adotada uma abordagem de investigação qualitativa com o delineamento da análise documental. Diante dessa conjuntura, e pensando em formas de apresentar os resultados da investigação, três eixos temáticos emergiram da análise, quais sejam: ‘livro didático de Matemática como direcionador da prática do professor e da aprendizagem dos alunos’; ‘Geometria como fonte de produção de contextos’; e ‘o papel dos enunciados sobre Geometria nos livros didáticos: do determinismo à formatação’. Como resultados, identificamos que entre direcionamentos, contextos e enunciados, o que se revelou nos dados evidencia um permear da EMC nos capítulos de Geometria dos materiais perquiridos, tanto diante de aspectos positivos, quanto de negativos. Tais aspectos foram compreendidos, por um lado, enquanto força que (re)produz uma ideologia da certeza matemática, fundamentada na perspectiva fechada que submete os alunos a ordens e que amarra o professor na limitação de outras formas de abordar conteúdos geométricos. Por outro lado, houve passagens nesses materiais que possibilitaram um desenvolvimento inicial da matemacia, considerada importante para a cidadania crítica e a competência democrática, além de fornecer situações em que investigações, diálogos e críticas sejam bases para reflexões sobre o conteúdo, suas aplicações, bem como suas implicações em aspectos sociais. Consideramos, a partir do exposto, que a pesquisa trouxe contribuições ao campo da Educação Matemática, em particular para a análise de livros didáticos e discussões teóricas alusivas aos conceitos da EMC utilizados. Ademais, vemos que preocupações voltadas aos processos de ensino e de aprendizagem de Matemática com qualidades críticas e reflexivas podem se tornar um meio para levar professores, estudantes e autores de livros didáticos a considerar e (re)pensar suas perspectivas.
Mathematics textbooks are materials that are part of everyday school life and show aspects arising from social and cultural contexts, in addition to educational ones. They can still be seen as resources that can be analyzed in the context of scientific investigations. Thus, assuming a critical perspective of Mathematics Education for the research presented in this dissertation, we aim to understand how Critical Mathematics Education (CME) permeates two collections of high school textbooks, in the horizon of Geometry. In order to meet this objective, some CME ‘concepts’ were discussed, following the approach proposed by Ole Skovsmose. Therefore, we see ‘concepts’ as expressions that explain meanings and qualify interpretations of data, not providing a rigid theoretical framework to characterize CME. Among some of these, we chose: democracy and the sociopolitical role of Mathematics Education; the ideology of certainty; mathemacy; and milieus of learning. With regard to the analyzed materials, we chose the chapters intended to approach Geometry in Mathematics textbooks approved in the 2018 public notice of the National Textbook and Teaching Material Program. The cut given to Geometry in these resources was due to the lack of studies identified in the literature review, when the textbooks are taken in the light of the CME, as well as due to the scope of our research group, which has as one of its concerns to investigate the presence of Geometry in these materials. In methodological terms, a qualitative research approach was adopted with the outline of documental analysis. Faced with this situation, and thinking about ways to present the results of the investigation, three thematic axes emerged from the analysis, namely: ‘Mathematics textbook as a guide for teacher practice and student learning’; ‘Geometry as a source of production of contexts’; and ‘the role of statements about Geometry in textbooks: from determinism to formatting’. As a result, we identified that between directions, contexts and statements, what was revealed in the data shows a permeation of CME in the Geometry chapters of the surveyed materials, both in terms of positive and negative aspects. Such aspects were understood, on the one hand, as a force that (re)produces an ideology of mathematical certainty, based on the closed perspective that submits students to orders and that binds the teacher in limiting other ways of approaching geometric contents. On the other hand, there were passages in these materials that enabled an initial development of mathemacy, considered important for critical citizenship and democratic competence, in addition to providing situations in which investigations, dialogues and criticisms are bases for reflections on the content, its applications, as well as its implications in social aspects. We consider, based on the above, that the research brought contributions to the field of Mathematics Education, in particular for the analysis of textbooks and theoretical discussions alluding to the concepts of CME used. In addition, we see that concerns related to the teaching and learning processes of Mathematics with critical and reflective qualities can become a means to lead teachers, students and authors of textbooks to consider and (re)think their perspectives.
Mathematics textbooks are materials that are part of everyday school life and show aspects arising from social and cultural contexts, in addition to educational ones. They can still be seen as resources that can be analyzed in the context of scientific investigations. Thus, assuming a critical perspective of Mathematics Education for the research presented in this dissertation, we aim to understand how Critical Mathematics Education (CME) permeates two collections of high school textbooks, in the horizon of Geometry. In order to meet this objective, some CME ‘concepts’ were discussed, following the approach proposed by Ole Skovsmose. Therefore, we see ‘concepts’ as expressions that explain meanings and qualify interpretations of data, not providing a rigid theoretical framework to characterize CME. Among some of these, we chose: democracy and the sociopolitical role of Mathematics Education; the ideology of certainty; mathemacy; and milieus of learning. With regard to the analyzed materials, we chose the chapters intended to approach Geometry in Mathematics textbooks approved in the 2018 public notice of the National Textbook and Teaching Material Program. The cut given to Geometry in these resources was due to the lack of studies identified in the literature review, when the textbooks are taken in the light of the CME, as well as due to the scope of our research group, which has as one of its concerns to investigate the presence of Geometry in these materials. In methodological terms, a qualitative research approach was adopted with the outline of documental analysis. Faced with this situation, and thinking about ways to present the results of the investigation, three thematic axes emerged from the analysis, namely: ‘Mathematics textbook as a guide for teacher practice and student learning’; ‘Geometry as a source of production of contexts’; and ‘the role of statements about Geometry in textbooks: from determinism to formatting’. As a result, we identified that between directions, contexts and statements, what was revealed in the data shows a permeation of CME in the Geometry chapters of the surveyed materials, both in terms of positive and negative aspects. Such aspects were understood, on the one hand, as a force that (re)produces an ideology of mathematical certainty, based on the closed perspective that submits students to orders and that binds the teacher in limiting other ways of approaching geometric contents. On the other hand, there were passages in these materials that enabled an initial development of mathemacy, considered important for critical citizenship and democratic competence, in addition to providing situations in which investigations, dialogues and criticisms are bases for reflections on the content, its applications, as well as its implications in social aspects. We consider, based on the above, that the research brought contributions to the field of Mathematics Education, in particular for the analysis of textbooks and theoretical discussions alluding to the concepts of CME used. In addition, we see that concerns related to the teaching and learning processes of Mathematics with critical and reflective qualities can become a means to lead teachers, students and authors of textbooks to consider and (re)think their perspectives.
Descrição
Palavras-chave
Livro didático, Educação matemática crítica, Geometria, Análise documental, PNLD, Textbook, Critical mathematics education, Geometry, Documental analysis