O pensamento diferencial-com-GeoGebra de estudantes do ensino médio
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Data
2021-08-06
Autores
Domingues, Ana Rita
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Universidade Estadual Paulista (Unesp)
Resumo
Esta pesquisa tem como objetivo investigar aspectos do Pensamento Diferencial (PD) emergentes em um grupo de estudantes do Ensino Médio ao pensar-com-GeoGebra atividades que envolvem a investigação da área de regiões limitadas por eixos e curvas e o cálculo do volume de regiões limitadas por superfícies planas e curvas. Este trabalho está apoiado na noção de investigação matemática e no construto teórico seres-humanos-com-mídias. A pesquisa é de cunho qualitativo e visa observar e compreender a manifestação de quatro aspectos do PD. São eles: Noção de limite e continuidade, Noção de infinitésimo, Conceito de integral definida e Concepção visual-geométrica. Foram realizadas duas sessões de experimentos de ensino com duas duplas de estudantes do Ensino Médio de uma escola pública estadual do interior de São Paulo. Foram elaboradas cinco atividades nesta pesquisa, sendo as duas primeiras exploradas por estudantes do primeiro ano e as três últimas por estudantes do terceiro ano. Os procedimentos metodológicos de registro das sessões foram: filmagens do ambiente, captação de tela do computador e de webcam e os arquivos gerados pelos estudantes no GeoGebra. Os resultados da pesquisa indicam que o processo de pensar-com-GeoGebra oferece meios para o desenvolvimento de elementos investigativos, nos quais os estudantes elaboraram conjecturas, testando-as e (re)pensaram as estratégias de soluções utilizadas de maneira dinâmica. Quanto à emersão dos aspectos do PD, em particular, identificou-se indícios de que eles se complementam e manifestam-se em conjunto, atribuindo complexidade aos processos de pensamentos dos estudantes-com-tecnologias. Esta pesquisa contribui à Educação Matemática no que se refere a produção de conhecimentos acerca do uso de tecnologias digitais voltado ao ensino de Cálculo no Ensino Médio.
This research aims to investigate the aspects of Differential Thinking (DT) emerging in a group of high school students when they think-with-GeoGebra on activities that involve an investigation of the area of regions limited by axes and curves and the calculation of the volume of regions bounded by flat and curved surfaces. This work is supported by the notion of mathematical investigation and by the theoretical construct human-beings-with-media. The research is qualitative and aims to observe and understand the manifestation of four aspects of DT. They are: Notion of limit and continuity, Notion of infinitesimal, Concept of definite integral and Visual-geometric conception. Two teaching experiments were carried out with two pairs of high school students from a state public school in the interior of São Paulo. Five activities were developed in this research; the first two were explored by first-year students and the last three by third-year students. Methodological procedures for recording the sessions were: filming of the environment, capture of computer and webcam screens and files generated by students in GeoGebra. The results indicate that thinking-with-GeoGebra offers means for the development of investigative elements, in which the students elaborated conjectures, testing them and (re)thinking the solutions used in a dynamic way. As for the emergence of aspects of the DT, in particular, it was found that they complement each other and manifest themselves together, attributing complexity to the thinking processes of students-with-technologies. This research contributes to Mathematics Education regarding the production of knowledge about the use of digital technologies in the context of teaching Calculus in High School.
This research aims to investigate the aspects of Differential Thinking (DT) emerging in a group of high school students when they think-with-GeoGebra on activities that involve an investigation of the area of regions limited by axes and curves and the calculation of the volume of regions bounded by flat and curved surfaces. This work is supported by the notion of mathematical investigation and by the theoretical construct human-beings-with-media. The research is qualitative and aims to observe and understand the manifestation of four aspects of DT. They are: Notion of limit and continuity, Notion of infinitesimal, Concept of definite integral and Visual-geometric conception. Two teaching experiments were carried out with two pairs of high school students from a state public school in the interior of São Paulo. Five activities were developed in this research; the first two were explored by first-year students and the last three by third-year students. Methodological procedures for recording the sessions were: filming of the environment, capture of computer and webcam screens and files generated by students in GeoGebra. The results indicate that thinking-with-GeoGebra offers means for the development of investigative elements, in which the students elaborated conjectures, testing them and (re)thinking the solutions used in a dynamic way. As for the emergence of aspects of the DT, in particular, it was found that they complement each other and manifest themselves together, attributing complexity to the thinking processes of students-with-technologies. This research contributes to Mathematics Education regarding the production of knowledge about the use of digital technologies in the context of teaching Calculus in High School.
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Palavras-chave
Pensamento diferencial, Pensar-com-GeoGebra, Ensino médio, Educação matemática, Differential thinking, Think-with-GeoGebra, High school, Mathematics education