Tarefas investigativas e metacognição no estudo de derivada
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Data
2024-06-27
Autores
Orientador
Quartieri, Marli Teresinha
Banca
Rehfeldt, Márcia Jussara Hepp
Giongo, Ieda Maria
Rosa, Cleci Teresinha Werner da
Silva, Jaime Carvalho e
Título do periódico
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Título do Volume
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Resumo
O estudo do Cálculo Diferencial tem se mostrado fundamental para a compreensão da aplicação de derivadas em variadas situações como taxa de variação e velocidade instantânea, problemas de otimização, máximo e mínimo de uma função e inclinação de uma reta tangente em um determinado ponto. Além disso, aprender os conceitos de derivada é importante para estudar fenômenos e resolver situações-problemas, por exemplo, das áreas de matemática, física, química, biologia, engenharia e economia. Nesta perspectiva, manifestou-se o seguinte problema de pesquisa: Que indícios de aprendizagem emergem sobre derivada quando exploradas tarefas investigativas combinadas a questões metacognitivas com alunos de Licenciatura em Matemática? Na busca de resposta para esta problemática, surgiu o objetivo geral de analisar indícios de aprendizagem dos alunos de Licenciatura em Matemática sobre derivada por meio da combinação de tarefas investigativas e questões metacognitivas. Os principais aportes teóricos utilizado neste trabalho de tese foram Brown (1978, 1980); Flavell (1971, 1976, 1979, 1987); Magalhães e Varizo (2016); Ponte, Brocardo e Oliveira (2019); Rosa (2011, 2014, 2017, 2020); Soares (2019, 2021, 2023), entre outros. A realização da pesquisa foi efetuada no Centro de Estudos Superiores de Tefé da Universidade do Estado do Amazonas – CEST/UEA na disciplina de Cálculo I, com uma turma de Licenciatura em Matemática, no primeiro semestre de 2023. No contexto metodológico, adotou-se uma abordagem qualitativa e a técnica utilizada foi a pesquisa participante. Para a coleta de dados foram desenvolvidas 8 tarefas investigativas, sendo 4 combinadas com questões metacognitivas, com a utilização dos instrumentos: questionário, caderno de anotações dos alunos e gravador de voz. Os dados coletados foram analisados pela técnica da análise descritiva qualitativa, norteada pela compreensão e interpretação da descrição detalhada dos resultados imbricados com o referencial teórico. Os resultados demonstraram que a exploração de tarefas investigativas combinadas com questões metacognitivas apresentou indícios de aprendizagem de derivada com a evocação dos elementos metacognitivos pessoa, tarefa, estratégia, planificação, monitoramento e avaliação. As respostas dos alunos destacaram que taxa de variação, velocidade instantânea e inclinação da reta tangente são conceitos da derivada. Pode-se inferir que a sequência didática explorando tarefas de investigação matemática associada a metacognição possibilitou a reflexão dos discentes sobre os caminhos para aprender melhor, pois utilizaram estratégias que produziram resultados e potencializaram a aprendizagem. A partir do desenvolvimento desta sequência didática foi produzido o Produto Educacional intitulado “Sequência didática para o ensino de derivada por meio de tarefas investigativas e metacognição”. O intuito do Produto é socializar a sequência didática que envolve tarefas investigativas e questões metacognitivas para o ensino de derivadas no Ensino Superior. O mesmo está disponível na página do Programa de Pós-graduação em Ensino de Ciências Exatas da Universidade do Vale do Taquari – Lajeado/RS.
The study of Differential Calculus has proven to be fundamental for understanding the application of derivatives in various situations such as rate of change and instantaneous speed, optimization problems, maximum and minimum of a function and slope of a tangent line at a given point. In addition, learning the concepts of derivatives is important for studying phenomena and solving problem situations, for example, in the areas of mathematics, physics, chemistry, biology, engineering and economics. In this perspective, the following research problem was expressed: What evidence of learning about derivatives emerges when exploratory tasks combined with metacognitive questions with undergraduate students in Mathematics? In the search for an answer to this problem, the general objective arose to analyze evidence of learning of undergraduate students in Mathematics about derivatives through the combination of investigative tasks and metacognitive questions. The main theoretical contributions used in this thesis work were Brown (1978, 1980); Flavell (1971, 1976, 1979, 1987); Magalhães and Varizo (2016); Ponte, Brocardo and Oliveira (2019); Rosa (2011, 2014, 2017, 2020); Soares (2019, 2021, 2023), among others. The research was carried out at the Center for Higher Education of Tefé of the State University of Amazonas - CEST/UEA in the discipline of Calculus I, with a class of Bachelor's Degree in Mathematics, in the first semester of 2023. In the methodological context, a qualitative approach was adopted and the technique used was participatory research. For data collection, 8 investigative tasks were developed, 4 of which were combined with metacognitive questions, using the following instruments: questionnaire, student notebook and voice recorder. The collected data were analyzed using the qualitative descriptive analysis technique, guided by the understanding and interpretation of the detailed description of the results intertwined with the theoretical framework. The results demonstrated that the exploration of investigative tasks combined with metacognitive questions presented evidence of learning about derivatives with the evocation of the metacognitive elements person, task, strategy, planning, monitoring and evaluation. The students' responses highlighted that rate of change, instantaneous speed and slope of the tangent line are concepts of the derivative. It can be inferred that the didactic sequence exploring mathematical investigation tasks associated with metacognition allowed the students to reflect on the ways to learn better, as they used strategies that produced results and enhanced learning. From the development of this didactic sequence, the Educational Product entitled “Didactic sequence for teaching derivatives through investigative tasks and metacognition” was produced. The purpose of the Product is to socialize the didactic sequence that involves investigative tasks and metacognitive questions for teaching derivatives in Higher Education. It is available on the website of the Postgraduate Program in Teaching Exact Sciences at the University of Vale do Taquari – Lajeado/RS.
The study of Differential Calculus has proven to be fundamental for understanding the application of derivatives in various situations such as rate of change and instantaneous speed, optimization problems, maximum and minimum of a function and slope of a tangent line at a given point. In addition, learning the concepts of derivatives is important for studying phenomena and solving problem situations, for example, in the areas of mathematics, physics, chemistry, biology, engineering and economics. In this perspective, the following research problem was expressed: What evidence of learning about derivatives emerges when exploratory tasks combined with metacognitive questions with undergraduate students in Mathematics? In the search for an answer to this problem, the general objective arose to analyze evidence of learning of undergraduate students in Mathematics about derivatives through the combination of investigative tasks and metacognitive questions. The main theoretical contributions used in this thesis work were Brown (1978, 1980); Flavell (1971, 1976, 1979, 1987); Magalhães and Varizo (2016); Ponte, Brocardo and Oliveira (2019); Rosa (2011, 2014, 2017, 2020); Soares (2019, 2021, 2023), among others. The research was carried out at the Center for Higher Education of Tefé of the State University of Amazonas - CEST/UEA in the discipline of Calculus I, with a class of Bachelor's Degree in Mathematics, in the first semester of 2023. In the methodological context, a qualitative approach was adopted and the technique used was participatory research. For data collection, 8 investigative tasks were developed, 4 of which were combined with metacognitive questions, using the following instruments: questionnaire, student notebook and voice recorder. The collected data were analyzed using the qualitative descriptive analysis technique, guided by the understanding and interpretation of the detailed description of the results intertwined with the theoretical framework. The results demonstrated that the exploration of investigative tasks combined with metacognitive questions presented evidence of learning about derivatives with the evocation of the metacognitive elements person, task, strategy, planning, monitoring and evaluation. The students' responses highlighted that rate of change, instantaneous speed and slope of the tangent line are concepts of the derivative. It can be inferred that the didactic sequence exploring mathematical investigation tasks associated with metacognition allowed the students to reflect on the ways to learn better, as they used strategies that produced results and enhanced learning. From the development of this didactic sequence, the Educational Product entitled “Didactic sequence for teaching derivatives through investigative tasks and metacognition” was produced. The purpose of the Product is to socialize the didactic sequence that involves investigative tasks and metacognitive questions for teaching derivatives in Higher Education. It is available on the website of the Postgraduate Program in Teaching Exact Sciences at the University of Vale do Taquari – Lajeado/RS.
Descrição
Palavras-chave
Tarefas Investigativas; Metacognição; Ensino de Derivada; Investigative Tasks; Metacognition; Teaching Derivatives
Citação
SOARES, Carlos José Ferreira. Tarefas investigativas e metacognição no estudo de derivada. 2024. Tese (Doutorado) – Curso de Ensino de Ciências Exatas, Universidade do Vale do Taquari - Univates, Lajeado, 27 jun. 2024. Disponível em: http://hdl.handle.net/10737/4524.