O ENSINO DE DERIVADAS DE FUNÇÕES REAIS MEDIADO PELO USO DO GEOGEBRA PARA APRENDIZAGEM SIGNIFICATIVA: CONTRIBUIÇÕES DE UMA SEQUÊNCIA DIDÁTICA
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Data
2024
Autores
Orientador
Rehfeldt, Márcia Jussara Hepp
Banca
Quartieri, Marli Teresinha
Dullius, Maria Madalena
Grossi, Luciane
Kuhn, Malcus Cassiano
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Resumo
Esta tese teve como objetivo investigar quais características de uma sequência didática (SD) mediada pelo uso do GeoGebra podem favorecer a aquisição, a construção e a retenção de conhecimentos com estudantes do Curso de Engenharia Agronômica (CEA) do Instituto Federal Baiano (IF Baiano) – Campus Teixeira de Freitas/BA, bem como proporcionar indícios de aprendizagem significativa das derivadas de funções reais. Para tanto, foi elaborada uma SD, composta por sete atividades, além de uma de revisão, que abordam conceitos, definições e propriedades do citado objeto matemático, por meio da resolução de situações-problema, a qual foi explorada durante duas intervenções pedagógicas com estudantes do CEA, em distintos momentos. A fundamentação teórica que sustenta esta pesquisa está baseada na Teoria da Aprendizagem Significativa (TAS), de Ausubel (1963; 1968; 2003) e colaboradores, bem como nas contribuições e influências das Tecnologias Digitais (TD) nos processos de ensino e de aprendizagem do Cálculo. A metodologia adotada é de caráter qualitativo, com aspectos de estudo exploratório e, no que tange aos procedimentos técnicos, com aproximações de um estudo de casos múltiplos. Os instrumentos usados na construção dos dados foram: pareceres dos professores avaliadores da SD; questionário de conhecimentos prévios; diário de campo do professor investigador; manuscritos dos estudantes; gravações dos encontros e questionário de sondagem. As análises dos dados construídos a partir das explorações da SD foram descritivas. Os resultados apontam que as tarefas propostas na SD apresentam aspectos de um material potencialmente significativo. Ademais, foram identificadas características de uma SD que podem favorecer a construção de conhecimentos, tais como: potencialidade para diagnosticar e revisar conhecimentos matemáticos obliterados nas estruturas cognitivas dos estudantes; proposição de um conjunto de situações-problema contextualizado na área de formação dos discentes; planejamento de aulas expositivas, dialogadas, participativas e com experimentação, usando as ferramentas e recursos do GeoGebra; estímulo aos estudantes para que desenvolvam grupos de estudos; disponibilização de atividades potencialmente significativas, com suas respectivas resoluções; utilização de organizadores prévios, por meio de videoaulas, com o propósito de reforçar e facilitar os estudos e a aprendizagem; construção, análise e interpretação de gráficos; avaliação como processo não acabado, isto é, para medir a aprendizagem, mas de forma processual, contínua, com reflexões e mudanças. Foram identificados alguns indícios de aprendizagem significativa, contribuições para a melhoria dos processos de ensino e de aprendizagem com significado do Cálculo Diferencial e Integral (CDI), mediados pelo uso do GeoGebra. Associado à pesquisa, elaborou-se um Produto Educacional (PE) intitulado, ensino e aprendizagem das derivadas de funções reais, por meio de uma SD mediada pelo GeoGebra, disponível para professores e estudantes de CDI, com o objetivo de incentivá-los a usar este software, para ensinar e aprender as derivadas de funções reais.
This thesis aimed to investigate which characteristics of a Didactic Sequence (DS) mediated by the use of GeoGebra can favor the acquisition, construction and retention of knowledge with students from the Agricultural Engineering Course (AEC) at the Federal Baiano Institute (IF Baiano) – Campus Teixeira de Freitas-BA, as well as providing evidence of significant learning from the derivatives of real functions. To this end, a DS was created, consisting of seven activities, in addition to a review, which address concepts, definitions and properties of the aforementioned mathematical object, through the resolution of problem situations, which was explored during two pedagogical interventions with students of the AEC, at different times. The theoretical foundation that supports this research is based on the Theory of Meaningful Learning (TML), by Ausubel (1963; 1968; 2003) and collaborators, as well as on the contributions and influences of Digital Technologies (DT) in the teaching and learning processes of Calculation. The methodology adopted is qualitative in nature, with aspects of an exploratory study and, with regard to technical procedures, with approximations of a multiple case study. The instruments used in the construction of the data were: opinions of the DS evaluating teachers; prior knowledge questionnaire; field diary of the research teacher; student manuscripts; recordings of meetings and survey questionnaire. The analyzes of the data constructed from DS explorations were descriptive. The results indicate that the tasks proposed in DS present aspects of potentially significant material. Furthermore, characteristics of a DS were identified that can favor the construction of knowledge, such as: potential to diagnose and review mathematical knowledge obliterated in students' cognitive structures; proposition of a set of problem situations contextualized in the students’ training area; planning expository, dialogued, participatory and experimental classes, using GeoGebra tools and resources; encouraging students to develop study groups; availability of potentially significant activities, with their respective resolutions; use of previous organizers, through video classes, with the purpose of reinforcing and facilitating studies and learning; construction, analysis and interpretation of graphs; assessment as a non-finished process, that is, to measure learning, but in a procedural, continuous way, with reflections and changes. Some signs of significant learning were identified, contributions to the improvement of teaching and learning processes with significance in Differential and Integral Calculus (DIC), mediated by the use of GeoGebra. Associated with the research, an Educational Product (EP) was created entitled, teaching and learning the derivatives of real functions, through a DS mediated by GeoGebra, available to DIC teachers and students, with the aim of encouraging them to use This software, to teach and learn the derivatives of real functions.
This thesis aimed to investigate which characteristics of a Didactic Sequence (DS) mediated by the use of GeoGebra can favor the acquisition, construction and retention of knowledge with students from the Agricultural Engineering Course (AEC) at the Federal Baiano Institute (IF Baiano) – Campus Teixeira de Freitas-BA, as well as providing evidence of significant learning from the derivatives of real functions. To this end, a DS was created, consisting of seven activities, in addition to a review, which address concepts, definitions and properties of the aforementioned mathematical object, through the resolution of problem situations, which was explored during two pedagogical interventions with students of the AEC, at different times. The theoretical foundation that supports this research is based on the Theory of Meaningful Learning (TML), by Ausubel (1963; 1968; 2003) and collaborators, as well as on the contributions and influences of Digital Technologies (DT) in the teaching and learning processes of Calculation. The methodology adopted is qualitative in nature, with aspects of an exploratory study and, with regard to technical procedures, with approximations of a multiple case study. The instruments used in the construction of the data were: opinions of the DS evaluating teachers; prior knowledge questionnaire; field diary of the research teacher; student manuscripts; recordings of meetings and survey questionnaire. The analyzes of the data constructed from DS explorations were descriptive. The results indicate that the tasks proposed in DS present aspects of potentially significant material. Furthermore, characteristics of a DS were identified that can favor the construction of knowledge, such as: potential to diagnose and review mathematical knowledge obliterated in students' cognitive structures; proposition of a set of problem situations contextualized in the students’ training area; planning expository, dialogued, participatory and experimental classes, using GeoGebra tools and resources; encouraging students to develop study groups; availability of potentially significant activities, with their respective resolutions; use of previous organizers, through video classes, with the purpose of reinforcing and facilitating studies and learning; construction, analysis and interpretation of graphs; assessment as a non-finished process, that is, to measure learning, but in a procedural, continuous way, with reflections and changes. Some signs of significant learning were identified, contributions to the improvement of teaching and learning processes with significance in Differential and Integral Calculus (DIC), mediated by the use of GeoGebra. Associated with the research, an Educational Product (EP) was created entitled, teaching and learning the derivatives of real functions, through a DS mediated by GeoGebra, available to DIC teachers and students, with the aim of encouraging them to use This software, to teach and learn the derivatives of real functions.
Descrição
Palavras-chave
Derivada; Resolução de situações-problema; Sequência didática; GeoGebra; Aprendizagem significativa; Derivative; Resolution of problem situations; Following teaching; GeoGebra; Meaningful learning
Citação
BISPO, Joselito da Silva. O ENSINO DE DERIVADAS DE FUNÇÕES REAIS MEDIADO PELO USO DO GEOGEBRA PARA APRENDIZAGEM SIGNIFICATIVA: CONTRIBUIÇÕES DE UMA SEQUÊNCIA DIDÁTICA. 2024. Tese (Doutorado) – Curso de Ensino de Ciências Exatas, Universidade do Vale do Taquari - Univates, Lajeado, 29 fev. 2024. Disponível em: http://hdl.handle.net/10737/4361.