Modelagem matemática no estudo de análise combinatória
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Data
2022-09
Autores
Orientador
Dullius, Maria Madalena
Banca
Quartieri, Marli Teresinha
Moro, Fernanda Teresa
Bisognin, Eleni
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Resumo
A presente pesquisa vinculada ao Programa de Pós-Graduação Doutorado e Mestrado Profissional em Ensino de Ciências Exatas (PPGECE), desenvolvida na Universidade do Vale do Taquari - Univates, Lajeado/RS, tem por objetivo explorar as possibilidades e os limites da Modelagem Matemática, como metodologia para o ensino da Análise Combinatória, correlacionando os fenômenos do cotidiano com os conceitos matemáticos, numa turma de cerca de trinta alunos do 2o ano do Ensino Médio de uma escola pública. A pesquisa se caracteriza como qualitativa, sendo os dados coletados através das gravações de áudio e vídeo, de encontros em sala de aula, pesquisa de campo e diário de bordo. O referencial teórico fundamenta-se em autores da Modelagem Matemática, enquanto o desenvolvimento da prática pedagógica ocorreu pelo “caso 2”, de Barbosa (2000). Para os procedimentos metodológicos, foram seguidos os passos de Biembengut e Hein (2021): Interação, Matematização e Modelo Matemático. Trazer a Modelagem como metodologia de ensino proporciona ao aluno uma visão de como a Matemática pode ser útil na vida fora do ambiente escolar e como ela interage com as demais áreas do conhecimento. O aluno passa a perceber a importância da Matemática para a compreensão de fenômenos naturais e como é possível “prever” acontecimentos utilizando fórmulas e modelos, o que desperta seu interesse pela ciência. Foi concluído que a Modelagem Matemática como metodologia de Ensino possibilita aos alunos a interpretação, a compreensão, a convivência e a cooperação em grupos e a correlação entre os fenômenos do cotidiano com os conceitos de Análise Combinatória, explorando os limites de uma sala de aula, com destaque ao produto educacional oriundo desta dissertação.
The present research linked to the Postgraduate Doctorate and Professional Master's Program in Teaching Exact Sciences (PPGECE) developed at the University of Vale do Taquari - Univates, Lajeado/RS, aims to explore the possibilities and limits of Mathematical Modeling as a methodology for the teaching of Combinatorial Analysis, correlating everyday phenomena with the mathematical concepts of a class of about thirty 2nd year high school students from a public school. The research is characterized qualitative and data were collected through audio and video recordings of classroom meetings, field research and logbook. The theoretical framework is based on authors of Mathematical Modeling and the development of pedagogical practice occurred through “case 2”, by Barbosa (2000). For the methodological procedures, the steps of Biembengut and Hein (2021) were followed, namely: Interaction, Mathematization and Mathematical Model. Bringing Modeling as a teaching methodology provides the student with a view of how Mathematics can be useful in their life outside the school environment and how it interacts with other areas of knowledge. The student begins to realize the importance of Mathematics for the understanding of natural phenomena, how it is possible to "predict" some events using formulas and models and this ends up arousing their interest in science. It was concluded that Mathematical Modeling as a teaching methodology allows students to interpret, understand, coexist and cooperate in groups and the correlation between everyday phenomena with the concepts of Combinatorial Analysis, exploring the limits of a classroom, highlighting the product education resulting from this dissertation.
The present research linked to the Postgraduate Doctorate and Professional Master's Program in Teaching Exact Sciences (PPGECE) developed at the University of Vale do Taquari - Univates, Lajeado/RS, aims to explore the possibilities and limits of Mathematical Modeling as a methodology for the teaching of Combinatorial Analysis, correlating everyday phenomena with the mathematical concepts of a class of about thirty 2nd year high school students from a public school. The research is characterized qualitative and data were collected through audio and video recordings of classroom meetings, field research and logbook. The theoretical framework is based on authors of Mathematical Modeling and the development of pedagogical practice occurred through “case 2”, by Barbosa (2000). For the methodological procedures, the steps of Biembengut and Hein (2021) were followed, namely: Interaction, Mathematization and Mathematical Model. Bringing Modeling as a teaching methodology provides the student with a view of how Mathematics can be useful in their life outside the school environment and how it interacts with other areas of knowledge. The student begins to realize the importance of Mathematics for the understanding of natural phenomena, how it is possible to "predict" some events using formulas and models and this ends up arousing their interest in science. It was concluded that Mathematical Modeling as a teaching methodology allows students to interpret, understand, coexist and cooperate in groups and the correlation between everyday phenomena with the concepts of Combinatorial Analysis, exploring the limits of a classroom, highlighting the product education resulting from this dissertation.
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Palavras-chave
Modelagem Matemática; Análise combinatória; Probabilidade; Placas de automóveis; Mathematical Modeling; Combinatorial analysis; Probability; Automobile plates
Citação
FILARDO, Sandra Maria. Modelagem matemática no estudo de análise combinatória. 2022. Dissertação (Mestrado) – Curso de Ensino de Ciências Exatas, Universidade do Vale do Taquari - Univates, Lajeado, 27 set. 2022. Disponível em: http://hdl.handle.net/10737/3510.