O software GeoGebra no ensino de funções para licenciandos em matemática: uma abordagem sociocultural
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Data
2019-03-20
Autores
Lucas, Rodrigo Dantas de
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Universidade Estadual Paulista (Unesp)
Resumo
Nesta tese investigamos como ocorreu a produção de significados em estudantes de licenciatura em Matemática utilizando uma sequência didática propostas para serem desenvolvidas com um software de geometria dinâmica (no presente trabalho foi utilizado o software GeoGebra), visando verificar o nível de domínio e apropriação dos conceitos de funções de uma variável real. A fundamentação teórica, baseada na teoria da ação mediada de James Wertsch, tem como foco o estudo sociocultural da mente e a memória coletiva sobre os aspectos históricos mediados pelas ferramentas culturais concernentes ás instituições formais de ensino. Wertsch propõe uma abordagem sociocultural à mente, onde as vozes da psicologia e da semiótica possam entrar em um diálogo produtivo com as vozes de outras disciplinas para a compreensão dos processos mentais e seus contextos culturais, históricos e institucionais. O público alvo consistiu em doze (12) estudantes (50% do sexo feminino) do curso de Licenciatura em Matemática da Universidade Estadual Paulista - UNESP, localizada na cidade de Bauru, no estado de São Paulo, Brasil. A pesquisa teve caráter qualitativo, caracterizada como um estudo de caso, pois envolveu a busca por significados atribuídos aos sujeitos da pesquisa relativos às suas vivências e experiências pessoais. Registrou-se o áudio das falas e a tela do computador dos estudantes que formaram grupos de três (03) e duas pessoas (02) com o objetivo de coletar as descrições, conversas e diálogos , bem como os apontamentos feitos por escrito com o intuito, também, de preservação dos dados coletados para uma posterior análise. As atividades foram desenvolvidas em quatro (04) módulos: 1) Atividades com funções quadráticas; 2) Atividades com funções racionais; 3) Atividades com funções exponenciais e logarítmicas e 4) Atividades com funções trigonométricas. As atividades com o software de geometria dinâmica contribuíram para a experimentação, a criação de estratégias, a produção de conjecturas, a argumentação qualitativa e a dedução de propriedades matemáticas relativas aos conteúdos de funções de uma variável real. Os estudantes com uma maior base teórica em Matemática exploraram os recursos computacionais com maior destreza, acuidade e precisão conseguindo, dessa forma, um aprofundamento nos conteúdos explorados. Esses alunos apresentaram, ainda, um detalhamento em suas explicações sobre os conteúdos abordados cometendo poucos erros de notação simbólica. Como uma extensão do trabalho, um Ambiente Virtual de Aprendizagem (AVA) está sendo elaborado com vistas à divulgação e disponibilização da metodologia e estratégias educacionais desenvolvidas.
In this thesis we investigated how the production of meanings occurred in undergraduate students in Mathematics using a didactic sequence proposed to be developed with software of dynamic geometry (in the present work was used GeoGebra software), aiming to verify the level of domination and appropriation of the concepts of functions of a real variable. The theoretical foundation, based on James Wertsch's theory of mediated action, focuses on the sociocultural study of the mind and collective memory on the historical aspects mediated by the cultural tools concerning formal educational institutions. Wertsch proposes a sociocultural approach to the mind, where the voices of psychology and semiotics can enter into a productive dialogue with the voices of other disciplines for the understanding of mental processes and their cultural, historical and institutional contexts. The target audience consisted of twelve (12) female students (50% female) of the Mathematics Undergraduate course at Universidade Estadual Paulista - UNESP, located in the city of Bauru, in the state of São Paulo, Brazil. The research had a qualitative character, characterized as a case study, since it involved the search for meanings attributed to the research subjects related to their experiences and personal experiences. The audio of the speeches and the computer screen of the students who formed groups of three (03) and two people (02) were recorded in order to collect the descriptions, conversations and dialogues, as well as the notes made in writing with the intention , also, of preservation of the data collected for later analysis. The activities were developed in four (04) modules: 1) Activities with quadratic functions; 2) Activities with rational functions; 3) Activities with exponential and logarithmic functions and 4) Activities with trigonometric functions. The activities with dynamic geometry software contributed to the experimentation, the creation of strategies, the production of conjectures, the qualitative argumentation and the deduction of mathematical properties related to the contents of functions of a real variable. Students with a greater theoretical base in Mathematics explored computational resources with greater dexterity, acuity and precision, thus achieving a deepening in the contents explored. These students also presented a detail in their explanations about the contents addressed with few errors of symbolic notation. As an extension of the work, a Virtual Learning Environment (VLE) is being developed with a view to disseminating and making available the methodology and educational strategies developed.
In this thesis we investigated how the production of meanings occurred in undergraduate students in Mathematics using a didactic sequence proposed to be developed with software of dynamic geometry (in the present work was used GeoGebra software), aiming to verify the level of domination and appropriation of the concepts of functions of a real variable. The theoretical foundation, based on James Wertsch's theory of mediated action, focuses on the sociocultural study of the mind and collective memory on the historical aspects mediated by the cultural tools concerning formal educational institutions. Wertsch proposes a sociocultural approach to the mind, where the voices of psychology and semiotics can enter into a productive dialogue with the voices of other disciplines for the understanding of mental processes and their cultural, historical and institutional contexts. The target audience consisted of twelve (12) female students (50% female) of the Mathematics Undergraduate course at Universidade Estadual Paulista - UNESP, located in the city of Bauru, in the state of São Paulo, Brazil. The research had a qualitative character, characterized as a case study, since it involved the search for meanings attributed to the research subjects related to their experiences and personal experiences. The audio of the speeches and the computer screen of the students who formed groups of three (03) and two people (02) were recorded in order to collect the descriptions, conversations and dialogues, as well as the notes made in writing with the intention , also, of preservation of the data collected for later analysis. The activities were developed in four (04) modules: 1) Activities with quadratic functions; 2) Activities with rational functions; 3) Activities with exponential and logarithmic functions and 4) Activities with trigonometric functions. The activities with dynamic geometry software contributed to the experimentation, the creation of strategies, the production of conjectures, the qualitative argumentation and the deduction of mathematical properties related to the contents of functions of a real variable. Students with a greater theoretical base in Mathematics explored computational resources with greater dexterity, acuity and precision, thus achieving a deepening in the contents explored. These students also presented a detail in their explanations about the contents addressed with few errors of symbolic notation. As an extension of the work, a Virtual Learning Environment (VLE) is being developed with a view to disseminating and making available the methodology and educational strategies developed.
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Palavras-chave
Ensino de Matemática, Tecnologias digitais, Funções elementares, GeoGebra, Ensino superior, Mathematics teaching, Digital technologies, Elementary functions, Superior education