Investigação matemática no ensino de derivadas em uma turma de licenciatura em matemática
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Data
2019-12
Autores
Orientador
Quartieri, Marli Teresinha
Banca
Amado, Nélia Maria Pontes
Rehfeldt, Márcia Jussara Hepp
Giongo, Ieda Maria
Título do periódico
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Título do Volume
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Resumo
O presente trabalho de cunho científico teve como objetivo analisar estratégias e conjecturas que os alunos da disciplina de Cálculo I de uma turma de licenciatura em Matemática elaboram ao utilizarem tarefas investigativas envolvendo derivadas. Como base teórica, este estudo esteve pautado em Ponte, Brocardo e Oliveira (2016), Magalhães e Varizo (2016) em relação aos fundamentos da Investigação Matemática.
A metodologia da pesquisa foi qualitativa, assistida pela observação participante e pela análise descritiva. Os dados foram coletados por meio das anotações dos alunos e questionário. O estudo foi realizado com 24 alunos de uma turma de 2º período de graduação em Licenciatura de Matemática da Universidade do Estado do Amazonas – UEA, localizada no município de Tefé – AM. Foram desenvolvidas atividades de cunho investigativo com o intuito de desafiar os alunos a utilizar diferentes estratégias e a formular conjecturas, em relação ao conteúdo abordado que foi derivada. Em especial, foi enfocado taxa de variação, máximos e mínimos. Os resultados enfatizam que o desenvolvimento de tarefas investigativas em sala de aula, contribui para que o aluno seja ativo na busca da construção de conhecimento matemático, assumindo o protagonismo na sua formação educacional. Especificamente, por meio deste trabalho, observou-se que os alunos construíram conhecimentos referente aos conceitos de derivadas a partir da exploração de taxa de variação, máximo e mínimo mediante simulações padronizadas envolvendo áreas de terreno, volume de caixas e
perímetro. Para a formulação de conjecturas utilizaram as seguintes estratégias de representações simbólica e numérica: simulações por meio da construção de quadros, desenhos, modelagem de funções e uso do excel.
The present work of scientific nature is aimed to analyze strategies and conjectures that students of the discipline of Calculus I of a class of degree in Mathematics elaborate when using investigative tasks involving derivatives. As a theoretical basis, this study was based on Ponte, Brocardo and Oliveira (2016), Magalhães and Varizo (2016) in relation to the foundations of Mathematical Research. The methodological research was qualitative, assisted by participant observation and descriptive analysis. Data were collected through student notes and a questionnaire. The study was carried out with 24 students from a class of 2nd semester undergraduate Mathematics degree from the Amazonas State University - UEA, located in the town of Tefé - AM. Investigative activities were developed in order to challenge students to use different strategies and formulate conjectures, in relation to the content that was derived. In particular, the rate of change, maximum and minimum, was focused. The results emphasize that the development of investigative tasks in the classroom, contributes for the student to be active in the search for the construction of mathematical knowledge, assuming the protagonist in his educational formation. Specifically, through this work, it was observed that the students built knowledge regarding the concepts of derivatives from the exploration of the rate of change, maximum and minimum through standardized simulations involving areas of land, volume of boxes and perimeter. For the formulation of conjectures, the following strategies were used symbolic and numerical representations: simulations through the construction of charts, drawings, function modeling and use of Excel.
The present work of scientific nature is aimed to analyze strategies and conjectures that students of the discipline of Calculus I of a class of degree in Mathematics elaborate when using investigative tasks involving derivatives. As a theoretical basis, this study was based on Ponte, Brocardo and Oliveira (2016), Magalhães and Varizo (2016) in relation to the foundations of Mathematical Research. The methodological research was qualitative, assisted by participant observation and descriptive analysis. Data were collected through student notes and a questionnaire. The study was carried out with 24 students from a class of 2nd semester undergraduate Mathematics degree from the Amazonas State University - UEA, located in the town of Tefé - AM. Investigative activities were developed in order to challenge students to use different strategies and formulate conjectures, in relation to the content that was derived. In particular, the rate of change, maximum and minimum, was focused. The results emphasize that the development of investigative tasks in the classroom, contributes for the student to be active in the search for the construction of mathematical knowledge, assuming the protagonist in his educational formation. Specifically, through this work, it was observed that the students built knowledge regarding the concepts of derivatives from the exploration of the rate of change, maximum and minimum through standardized simulations involving areas of land, volume of boxes and perimeter. For the formulation of conjectures, the following strategies were used symbolic and numerical representations: simulations through the construction of charts, drawings, function modeling and use of Excel.
Descrição
Palavras-chave
Investigação Matemática; Derivada; Ensino Superior; Mathematical Investigation; Derivative; University education
Citação
SOARES, Carlos José Ferreira. Investigação matemática no ensino de derivadas em uma turma de licenciatura em matemática. 2019. Dissertação (Mestrado) – Curso de Ensino de Ciências Exatas, Universidade do Vale do Taquari - Univates, Lajeado, 20 dez. 2019. Disponível em: http://hdl.handle.net/10737/2808.