Estudo da função quadrática com utilização do software GeoGebra na perspectiva da teoria histórico-cultural: transformações expansivas
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Data
2022-03-07
Autores
Xavier, José Fábio
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Universidade Estadual Paulista (Unesp)
Resumo
Esta tese busca compreender, em um mundo dialético, como se processa a aquisição de conceitos matemáticos necessários à compreensão das funções quadráticas para alunos dos primeiros anos do ensino médio do Instituto Federal de Rondônia, no campus Ariquemes, RO. Para entender o que ocorre no processo formativo foi utilizada a Teoria Histórico Cultural, iniciando por Vygotsky, e passando por Leontiev, Davidov, Zankov, Engestron. Buscamos entender também as relações entre tecnologia e sociedade, nos apoiaremos em Pierre Levy, Tikhomirov, entre outros para estabelecer tais relações. Esta tese tem como objetivo analisar como o software GeoGebra pode contribuir na apreensão e respectiva compreensão dos conceitos de função quadrática à luz da teoria da atividade, a partir de experimento formativo aplicado e desenvolvido com jovens educandos do primeiro ano do ensino médio do campus Ariquemes do Instituto Federal de Rondônia. A pergunta norteadora e, consequentemente, constituinte da problemática de pesquisa: se as novas tecnologias, especialmente as digitais, em alguma medida proporcionam reflexão crítica enquanto mediadoras dos processos de ensino-aprendizagem, de quais formas a ferramenta tecnológica GeoGebra facilita os processos de ensino-aprendizagem da matemática para jovens educandos do Ensino Médio, de modo a proporcionar transformações expansivas e respectivo desenvolvimento integral? Ao abordar diversos temas em ciências exatas as aplicações se tornam bem amplas, um dos assuntos que é possível verificar que o uso do GeoGebra enriquece muito as explicações é a aprendizagem de funções elementares, e no caso desta tese, com foco no ensino de funções quadrática. Pesquisa se caracteriza como Qualitativa com o uso de Triangulação, naturalística e com observação participante. Neste caso, esta pesquisa, foi realizada no Instituto Federal de Rondônia, Campus Ariquemes, nas turmas dos primeiros anos do ensino médio, na disciplina de matemática. Os alunos selecionados para realizarmos o experimento são oito. De modo geral, os educandos apresentaram sentimento de estarem sendo desafiados para o desenvolvimento de novas técnicas na utilização da ferramenta, em um processo de realização de autocríticas e, na dialética do consciente e inconsciente, se propuseram a romper com padrões de produção Matemática já tradicionalmente orientado pelo uso do lápis e papel, passando a buscar soluções para os problemas na utilização do software GeoGebra. Uma das conclusões a que se propõe esta tese é que os alunos utilizam consistentemente abstração e generalização para deduzir, sempre com a ajuda do professor, outros níveis de abstrações mais particulares e uni-las aos conceitos científicos, base das aprendizagens escolares, mas também as correlacionar com a realidade vivida. A tese que ao qual chegamos é que a abordagem da aprendizagem expansiva tem potencialidade de romper com o modelo tradicional escola uma vez da propositura de contínua e gradual ampliação do objeto e do contexto de aprendizagem que atendam as demandas dos educandos.
This thesis seeks to understand, in a dialectical world, how the acquisition of mathematical concepts necessary for the understanding of quadratic functions for students in the first years of high school at the Federal Institute of Rondônia, Ariquemes campus, RO, is processed. In order to understand what occurs in the formative process, the Cultural Historical Theory was used, starting with Vygotsky, and going through Leontiev, Davidov, Zankov, and Engestron. We also seek to understand the relationships between technology and society, we will rely on Pierre Levy, Tikhomirov, among others to establish such relationships. This thesis aims to analyze how the GeoGebra software can contribute to the apprehension and respective understanding of the quadratic function concepts in the light of the activity theory, from a formative experiment applied and developed with young students of the first year of high school at the Ariquemes campus of the Federal Institute of Rondônia. The guiding question and, consequently, constituting the research problematic: if the new technologies, especially the digital ones, in some measure provide critical reflection as mediators of the teaching-learning processes, in what ways the technological tool GeoGebra facilitates the teaching-learning processes of mathematics for young students in high school, in order to provide expansive transformations and their respective integral development? One of the subjects that can be verified that the use of GeoGebra greatly enriches the explanations is the learning of elementary functions, and in the case of this thesis, focusing on the teaching of quadratic functions. Research is characterized as Qualitative with the use of Triangulation, naturalistic and with participant observation. In this case, this research was carried out at the Federal Institute of Rondônia, Ariquemes Campus, in the first year high school classes, in the subject of mathematics. The students selected for the experiment were eight. In general, the students presented a feeling of being challenged to develop new techniques in the use of the tool, in a process of self-criticism and, in the dialectic of conscious and unconscious, they proposed to break with patterns of mathematical production already traditionally guided by the use of pencil and paper, starting to look for solutions to problems in the use of GeoGebra software. One of the conclusions of this thesis is that students consistently use abstraction and generalization to deduce, always with the help of the teacher, other levels of more particular abstractions and link them to scientific concepts, the basis of school learning, but also to correlate them with lived reality. The thesis we have reached is that the expansive learning approach has the potential to break with the traditional school model since it proposes a continuous and gradual expansion of the learning object and context that meets the demands of the students.
This thesis seeks to understand, in a dialectical world, how the acquisition of mathematical concepts necessary for the understanding of quadratic functions for students in the first years of high school at the Federal Institute of Rondônia, Ariquemes campus, RO, is processed. In order to understand what occurs in the formative process, the Cultural Historical Theory was used, starting with Vygotsky, and going through Leontiev, Davidov, Zankov, and Engestron. We also seek to understand the relationships between technology and society, we will rely on Pierre Levy, Tikhomirov, among others to establish such relationships. This thesis aims to analyze how the GeoGebra software can contribute to the apprehension and respective understanding of the quadratic function concepts in the light of the activity theory, from a formative experiment applied and developed with young students of the first year of high school at the Ariquemes campus of the Federal Institute of Rondônia. The guiding question and, consequently, constituting the research problematic: if the new technologies, especially the digital ones, in some measure provide critical reflection as mediators of the teaching-learning processes, in what ways the technological tool GeoGebra facilitates the teaching-learning processes of mathematics for young students in high school, in order to provide expansive transformations and their respective integral development? One of the subjects that can be verified that the use of GeoGebra greatly enriches the explanations is the learning of elementary functions, and in the case of this thesis, focusing on the teaching of quadratic functions. Research is characterized as Qualitative with the use of Triangulation, naturalistic and with participant observation. In this case, this research was carried out at the Federal Institute of Rondônia, Ariquemes Campus, in the first year high school classes, in the subject of mathematics. The students selected for the experiment were eight. In general, the students presented a feeling of being challenged to develop new techniques in the use of the tool, in a process of self-criticism and, in the dialectic of conscious and unconscious, they proposed to break with patterns of mathematical production already traditionally guided by the use of pencil and paper, starting to look for solutions to problems in the use of GeoGebra software. One of the conclusions of this thesis is that students consistently use abstraction and generalization to deduce, always with the help of the teacher, other levels of more particular abstractions and link them to scientific concepts, the basis of school learning, but also to correlate them with lived reality. The thesis we have reached is that the expansive learning approach has the potential to break with the traditional school model since it proposes a continuous and gradual expansion of the learning object and context that meets the demands of the students.
Descrição
Palavras-chave
Teoria histórico-cultural, Educação matemática, Transformações expansivas, Funções quadráticas, Cultural-historical theory, Mathematics education, Expansive transformations, Quadratic functions
Como citar
XAVIER, José Fábio. Estudo da função quadrática com utilização do software GeoGebra na perspectiva da teoria histórico-cultural: transformações expansivas. Universidade Estadual Paulista (Unesp), 2022.