Entre plantas e árvores: uma articulação entre a resolução de problemas, a análise combinatória e um beija-flor
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Data
2022-12-15
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Universidade Estadual Paulista (Unesp)
Resumo
O que pode o voo de um beija-flor? Quais caminhos essa ave pode percorrer? Decorrente dessa ligação do beija-flor e pesquisador é nessa liberdade de voo que, mesmo com tempestades e ventos fortes como a pandemia e o distanciamento social, esse beija-flor se aventura em um voo sobre as árvores do ensino de Combinatória e da Resolução de Problemas. Com o objetivo principal de apresentar os resultados de uma pesquisa, cujo intuito foi o de compreender como pode a Metodologia de Ensino-Aprendizagem-Avaliação de Matemática através da Resolução de Problemas ajudar no desenvolvimento do raciocínio combinatório de futuros professores e contribuir para a reflexão sobre suas ações pedagógicas, esta pesquisa mostra como se deu esse caminho, passando por cada árvore ou planta, mostrando dificuldades e mudanças pois, como na pesquisa, o voo não é linear. O ensino de Combinatória ou Análise Combinatória trata noções matemáticas fundamentais e trabalha processos e habilidades cognitivas importantes para o desenvolvimento intelectual de ideias sobre conjuntos, contagem, organização de ideias, pensamento estratégico, etc. Apesar de não possuir um conceito aparentemente complexo, pois tem como base os Princípios Multiplicativo e Aditivo, a Combinatória ainda é vista como um conteúdo de difícil compreensão, tanto para alunos como para professores. Acreditamos que seja uma consequência da abordagem de ensino baseada na valorização de definições e fórmulas em detrimento de problemas que exijam raciocínio e criatividade. Dessa forma, inevitavelmente, futuros professores de Matemática podem repetir as práticas que lhes foram ensinadas pois essas foram as únicas. A produção de dados foi realizada de forma remota possuindo como elemento central problemas combinatórios por nós levantados e alguns adaptados de sites e livros de autores nacionais e internacionais. Os encontros utilizados como pano de fundo para a produção de dados contaram com a participação voluntária de oito alunos do curso de Licenciatura em Matemática de uma universidade estadual situada no interior de São Paulo. A análise dos dados produzidos com a implementação do trabalho com Combinatória através da Resolução de Problemas deu-se a partir das sugestões de resolução desenvolvidas por esses estudantes frente aos problemas propostos. Por meio dos elementos da prática, de uma Comunidade de Prática (CoP), pudemos entender como o raciocínio combinatório foi desenvolvido em grupo a cada problema. A análise dos dados sugere que o uso da Metodologia de Ensino-Aprendizagem-Avaliação de Matemática através da Resolução de Problemas dentro de uma CoP se mostrou pertinente para o trabalho fazendo uso de problemas com ênfase em aspectos-chave para do desenvolvimento raciocínio combinatório. Por outro lado, percebeu-se que os principais desafios encontrados estão relacionados à própria natureza dos problemas combinatórios, assim como a interpretação dos enunciados dos problemas.
What can the flight of a hummingbird do? What paths can this bird travel? As a result of this connection between the hummingbird and the researcher, it is in this freedom of flight that, even with storms and strong winds such as the pandemic and social distance, this hummingbird ventures out on a flight over the trees of the teaching of Combinatorics and Resolution of Problems. With the main objective of presenting the results of a research, whose aim was to understand how the Teaching-Learning-Assessment Methodology of Mathematics through Problem Solving can help in the development of combinatory reasoning of future teachers and contribute to the reflection on their pedagogical actions, this research shows how this path took place, passing through each tree or plant, showing difficulties and changes because, as in the research, the flight is not linear. The teaching of Combinatorics or Combinatorial Analysis deals with fundamental mathematical notions and works with important cognitive processes and skills for the intellectual development of ideas about sets, counting, organizing ideas, strategic thinking, etc. Despite not having an apparently complex concept, as it is based on the Multiplicative and Additive Principles, Combinatorics is still seen as a content that is difficult to understand, both for students and teachers. We believe that it is a consequence of the teaching approach based on valuing definitions and formulas at the expense of problems that require reasoning and creativity. In this way, inevitably, future Mathematics teachers can repeat the practices they were taught because these were the only ones. Data production was carried out remotely, having as a central element combinatorial problems raised by us and some adapted from websites and books by national and international authors. The meetings used as a background for the production of data had the voluntary participation of eight students of the Licentiate in Mathematics course at a state university located in the interior of São Paulo. The analysis of the data produced with the implementation of work with Combinatorics through Problem Solving was based on the solution suggestions developed by these students in the face of the proposed problems. Through the elements of practice, a Community of Practice (CoP), we were able to understand how combinatorial reasoning was developed in a group for each problem. Data analysis suggests that the use of the Teaching-Learning-Assessment Methodology of Mathematics through Problem Solving within a CoP proved to be relevant for the work making use of problems with an emphasis on key aspects for the development of combinatorial reasoning. On the other hand, it was noticed that the main challenges encountered are related to the very nature of combinatorial problems, as well as the interpretation of problem statements.
What can the flight of a hummingbird do? What paths can this bird travel? As a result of this connection between the hummingbird and the researcher, it is in this freedom of flight that, even with storms and strong winds such as the pandemic and social distance, this hummingbird ventures out on a flight over the trees of the teaching of Combinatorics and Resolution of Problems. With the main objective of presenting the results of a research, whose aim was to understand how the Teaching-Learning-Assessment Methodology of Mathematics through Problem Solving can help in the development of combinatory reasoning of future teachers and contribute to the reflection on their pedagogical actions, this research shows how this path took place, passing through each tree or plant, showing difficulties and changes because, as in the research, the flight is not linear. The teaching of Combinatorics or Combinatorial Analysis deals with fundamental mathematical notions and works with important cognitive processes and skills for the intellectual development of ideas about sets, counting, organizing ideas, strategic thinking, etc. Despite not having an apparently complex concept, as it is based on the Multiplicative and Additive Principles, Combinatorics is still seen as a content that is difficult to understand, both for students and teachers. We believe that it is a consequence of the teaching approach based on valuing definitions and formulas at the expense of problems that require reasoning and creativity. In this way, inevitably, future Mathematics teachers can repeat the practices they were taught because these were the only ones. Data production was carried out remotely, having as a central element combinatorial problems raised by us and some adapted from websites and books by national and international authors. The meetings used as a background for the production of data had the voluntary participation of eight students of the Licentiate in Mathematics course at a state university located in the interior of São Paulo. The analysis of the data produced with the implementation of work with Combinatorics through Problem Solving was based on the solution suggestions developed by these students in the face of the proposed problems. Through the elements of practice, a Community of Practice (CoP), we were able to understand how combinatorial reasoning was developed in a group for each problem. Data analysis suggests that the use of the Teaching-Learning-Assessment Methodology of Mathematics through Problem Solving within a CoP proved to be relevant for the work making use of problems with an emphasis on key aspects for the development of combinatorial reasoning. On the other hand, it was noticed that the main challenges encountered are related to the very nature of combinatorial problems, as well as the interpretation of problem statements.
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Palavras-chave
Resolução de problemas, Análise combinatória, Formação inicial de professores, Comunidade de prática, Problem solving, Combinatorial analysis, Initial teacher training, Community of practice