Trigonometria no triângulo retângulo: uma análise exploratória nos documentos curriculares brasileiros e em livros de história da matemática
Data
2023-07-07
Autores
Almeida Junior, Pedro Pereira de 
Orientadores
Pommer, Wagner Marcelo
Tipo
Dissertação de mestrado
Título da Revista
ISSN da Revista
Título de Volume
Resumo
A Trigonometria é um tema presente na atual Base Nacional Comum Curricular, descrita em
Brasil (2017). Este texto teve por objetivo verificar como o tema da Trigonometria no triângulo
retângulo é proposto e desenvolvido em documentos curriculares brasileiros da era democrática
brasileira e em livros de História da Matemática. Assim, discorremos sobre as razões que levaram
a esta investigação e aos desafios com que o ensino de Trigonometria tem se mostrado nos
espaços escolares os quais tem sido objeto de inúmeras discussões por parte da academia, em
especial aos pesquisadores em Educação Matemática. Em seguida apresentamos os referenciais
teóricos para uma discussão sobre alguns aspectos como as origens da Trigonometria, sua
etimologia bem como exemplos de definições. Adentramos brevemente a algumas definições
conceituais da academia sobre o que é currículo e as possibilidades e razões favoráveis para o uso
da História da Matemática no ensino básico. São trazidas considerações breves sobre as
classificações relativas aos livros de História da Matemática e a transposição didática a partir da
perspectiva de autores que discorreram sobre estes tópicos. Após isto, nos concentramos na
descrição das escolhas e procedimentos metodológicos para análise dos documentos oficiais
brasileiros e os dois livros de História da Matemática. Tomamos como referencial metodológico a
análise documental e a pesquisa qualitativa, apontada em Gil (2002) e Prodanov e Freitas (2013).
Assim, a partir da metodologia descrita foram analisados os documentos curriculares brasileiros e
os livros de História da Matemática. No que tange aos documentos oficiais brasileiros analisados
foi possível identificar características próprias em cada documento. Constatamos que estas vão
desde as etapas em que cada assunto da Trigonometria deveria ser ministrado, bem como as
abordagens com que estes deveriam ser tratados em sala de aula e aos pressupostos pedagógicos
propostos sejam nos currículos propriamente ditos ou nas propostas curriculares. Com relação a
análise histórica foram utilizados dois livros de História da Matemática: o primeiro de Carl Boyer
(1974) e o segundo de Roque (2012). Este material foi analisado a partir de um conjunto de
categorias dimensionadas para classificar as menções históricas levantadas a partir dos livros
escolhidos. Foram apresentadas as conclusões sobre as menções históricas contidas e identificadas
nas obras de História da Matemática, onde foi possível constatar elementos importantes que se
referem à forma com que os autores perceberam os dados históricos disponíveis, bem como sobre
os desdobramenos não lineares do desenvolvimento da Trigonometria no triângulo retângulo no
transcorrer dos séculos. Os livros revelaram que os povos antigos tiveram, em muitos casos, como
motivação de sua elaboração as necessidades práticas, tecnológicas ou como uma poderosa
ferramenta para a Astronomia. Porém, muitos estudiosos dos antigos gregos cultivavam um estudo
mais voltado aos aspectos teóricos, desvinculados nas necessidades pragmáticas. Finalizamos este
trabalho de pesquisa considerando que a partir dos dados apresentados é razoável supormos que
muitas das menções históricas concernentes a Trigonometria no triângulo retângulo trazem
consigo um potencial de uso em sala de aula, a depender dos objetivos e das adaptações feitas pelo
professor de Matemática em sala de aula.
Trigonometry is a theme present in the current National Common Curricular Base, described in Brasil (2017). This text aimed to verify how the subject of Trigonometry in the right triangle is proposed and developed in Brazilian curriculum documents from the Brazilian democratic era and in History of Mathematics books. Thus, we discuss the reasons that led to this investigation and the challenges with which the teaching of Trigonometry has been shown in school spaces, which has been the subject of numerous discussions on the part of the academy, especially researchers in Mathematics Education. Then we present the theoretical references for a discussion on some aspects such as the origins of Trigonometry, its etymology as well as examples of definitions. We briefly enter some conceptual definitions of the academy about what is curriculum and the possibilities and favorable reasons for the use of the History of Mathematics in basic education. Brief considerations are made about classifications related to History of Mathematics books and didactic transposition from the perspective of authors who discussed these topics. After that, we focus on the description of methodological choices and procedures for analyzing official Brazilian documents and the two History of Mathematics books. We take documental analysis and qualitative research as a methodological reference, pointed out in Gil (2002) and Prodanov and Freitas (2013). Thus, based on the described methodology, Brazilian curriculum documents and History of Mathematics books were analyzed. With regard to the Brazilian official documents analyzed, it was possible to identify specific characteristics in each document. We found that these range from the stages in which each subject of Trigonometry should be taught, as well as the approaches with which these should be treated in the classroom and the pedagogical assumptions proposed either in the curricula themselves or in the curricular proposals. Regarding the historical analysis, two books on the History of Mathematics were used: the first by Carl Boyer (1974) and the second by Roque (2012). This material was analyzed based on a set of categories designed to classify the historical mentions raised from the chosen books. Conclusions were presented on the historical mentions contained and identified in the History of Mathematics works, where it was possible to verify important elements that refer to the way in which the authors perceived the available historical data, as well as on the non-linear developments of the development of Trigonometry in the right triangle over the centuries. The books revealed that the ancient peoples had, in many cases, practical and technological needs as a motivation for their elaboration, or as a powerful tool for Astronomy. However, many scholars of the ancient Greeks cultivated a study more focused on theoretical aspects, unrelated to pragmatic needs. We ended this research work considering that based on the data presented, it is reasonable to assume that many of the historical mentions concerning Trigonometry in the right triangle bring with them a potential use in the classroom, depending on the objectives and adaptations made by the Mathematics teacher in classroom.
Trigonometry is a theme present in the current National Common Curricular Base, described in Brasil (2017). This text aimed to verify how the subject of Trigonometry in the right triangle is proposed and developed in Brazilian curriculum documents from the Brazilian democratic era and in History of Mathematics books. Thus, we discuss the reasons that led to this investigation and the challenges with which the teaching of Trigonometry has been shown in school spaces, which has been the subject of numerous discussions on the part of the academy, especially researchers in Mathematics Education. Then we present the theoretical references for a discussion on some aspects such as the origins of Trigonometry, its etymology as well as examples of definitions. We briefly enter some conceptual definitions of the academy about what is curriculum and the possibilities and favorable reasons for the use of the History of Mathematics in basic education. Brief considerations are made about classifications related to History of Mathematics books and didactic transposition from the perspective of authors who discussed these topics. After that, we focus on the description of methodological choices and procedures for analyzing official Brazilian documents and the two History of Mathematics books. We take documental analysis and qualitative research as a methodological reference, pointed out in Gil (2002) and Prodanov and Freitas (2013). Thus, based on the described methodology, Brazilian curriculum documents and History of Mathematics books were analyzed. With regard to the Brazilian official documents analyzed, it was possible to identify specific characteristics in each document. We found that these range from the stages in which each subject of Trigonometry should be taught, as well as the approaches with which these should be treated in the classroom and the pedagogical assumptions proposed either in the curricula themselves or in the curricular proposals. Regarding the historical analysis, two books on the History of Mathematics were used: the first by Carl Boyer (1974) and the second by Roque (2012). This material was analyzed based on a set of categories designed to classify the historical mentions raised from the chosen books. Conclusions were presented on the historical mentions contained and identified in the History of Mathematics works, where it was possible to verify important elements that refer to the way in which the authors perceived the available historical data, as well as on the non-linear developments of the development of Trigonometry in the right triangle over the centuries. The books revealed that the ancient peoples had, in many cases, practical and technological needs as a motivation for their elaboration, or as a powerful tool for Astronomy. However, many scholars of the ancient Greeks cultivated a study more focused on theoretical aspects, unrelated to pragmatic needs. We ended this research work considering that based on the data presented, it is reasonable to assume that many of the historical mentions concerning Trigonometry in the right triangle bring with them a potential use in the classroom, depending on the objectives and adaptations made by the Mathematics teacher in classroom.