Potencialidades e limitações de material didático para explorar resolução de problemas matemáticos
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Data
2015-01
Autores
Orientador
Dullius, Maria Madalena
Banca
Dullius, Maria Madalena
Giongo, Ieda Maria
Schuck, Rogério
Amado, Nélia Maria Pontes
Título do periódico
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Título do Volume
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Resumo
Esta dissertação enfatiza a resolução de problemas como metodologia para o ensino de Matemática. Para aprofundar os conhecimentos acerca do estudo, foi fundamental o apoio teórico de diversos autores, entre os quais destacam-se Carvalho (2012), Diniz (2001) e Krulik e Reys (1997), Onuchic, Polya (1995), Lopes (2009), além dos PCN’s. Essa investigação visou diagnosticar como e para que os professores do 1º ano do Ensino Médio de seis escolas estaduais do Vale do Taquari usam os livros didáticos de Matemática e perceber como estes materiais apresentam a resolução de problemas. Além disso, objetivou-se criar um material didático para os professores abordarem Matemática através da resolução de problemas. Para atingir os objetivos propostos, foi realizado um estudo qualitativo em que os pesquisadores estiveram constantemente envolvidos durante o processo. Inicialmente, foi realizada uma entrevista com 10 professores de Matemática para perceber a importância que estes profissionais atribuem aos livros didáticos no planejamento e no desenvolvimento de suas aulas e identificar suas percepções em relação à abordagem da resolução de problemas no contexto atual. Posteriormente, foi realizada uma análise dos livros didáticos da série envolvida, adotados nas escolas contempladas nas entrevistas iniciais. Por fim, foi produzido o material para intervenção pedagógica com intuito de auxiliar os professores a utilizarem esta metodologia de forma diferenciada. O material foi experimentado e problematizado por sete professores e seus respectivos alunos. Como principal instrumento de coleta de dados foram utilizados os relatos, escritos e falados, dos professores de Matemática sujeitos da pesquisa. Esses relatos, após análise, resultaram em diferentes categorias. Como resultados, é possível destacar que os livros didáticos são utilizados pelos professores sob diferentes aspectos e que apresentam algumas inovações, mas os problemas vêm, na maioria das vezes, vinculados a algum conteúdo específico. Percebeu-se que os educadores apresentaram muita capacidade para inovar mostrando, portanto, que o apoio a partir de material concreto pode ser bastante significativo. Concluiu-se, também, que um profissional sozinho apresenta maior dificuldade em diversificar sua prática, porém, com pequenos incentivos é capaz de realizar inovações positivas que beneficiam a aprendizagem de seus alunos. Considera-se, portanto, que esta pesquisa possibilitou reflexões e até mesmo mudanças na percepção dos docentes quanto à metodologia da resolução de problemas.
This thesis emphasizes the problem solving as a methodology to the Mathematics teaching. In order to increase the knowledge about the study, theoretical support of several authors was fundamental, and among those Carvalho (2012), Diniz (2001) and Krulik and Reys (1997), Onuchic, Polya (1995), Lopes (2009) stand out, beyond the PCNs. This research aimed to diagnose how and what for teachers of the 1st year of High School, from six public schools in Vale do Taquari use Mathematics textbooks and to understand how these materials feature the problem solving. In addition, it aimed to create a teaching material for teachers to approach Mathematics through problem solving. In order to achieve the proposed objectives, we conducted a qualitative study in which researchers were continually involved in the process. Initially, an interview was conducted with 10 Mathematics teachers to realize the importance these professionals attribute to textbooks in planning and development of their classes and identify their perceptions of the approach to problem solving in the current context. Subsequently, an analysis of the textbooks of the series involved was held, adopted in schools included in the initial interviews. Finally, the material for educational intervention was produced to help teachers to use this methodology in different ways. The material was tested and questioned by seven teachers and their students. The main data collect instruments were written and spoken reports from the subjects of the research, the Mathematics teachers themselves. These reports, after analysis, resulted in different categories. As a result, it is possible to point out that textbooks are used by teachers under different aspects and that they present some innovations, but the problems are, in most cases, linked to some specific content. It was possible to notice that the teachers had a substantial capacity to innovate by showing, therefore, that the support from factual material can be quite significant. It was also possible to conclude that a professional, working alone, is harder to diversify his practice, but with some incentives he can accomplish positive innovations that benefit the learning of his students. It is considered, therefore, that this research allowed reflections and even changes in the perception of teachers as to methodology of problem solving.
This thesis emphasizes the problem solving as a methodology to the Mathematics teaching. In order to increase the knowledge about the study, theoretical support of several authors was fundamental, and among those Carvalho (2012), Diniz (2001) and Krulik and Reys (1997), Onuchic, Polya (1995), Lopes (2009) stand out, beyond the PCNs. This research aimed to diagnose how and what for teachers of the 1st year of High School, from six public schools in Vale do Taquari use Mathematics textbooks and to understand how these materials feature the problem solving. In addition, it aimed to create a teaching material for teachers to approach Mathematics through problem solving. In order to achieve the proposed objectives, we conducted a qualitative study in which researchers were continually involved in the process. Initially, an interview was conducted with 10 Mathematics teachers to realize the importance these professionals attribute to textbooks in planning and development of their classes and identify their perceptions of the approach to problem solving in the current context. Subsequently, an analysis of the textbooks of the series involved was held, adopted in schools included in the initial interviews. Finally, the material for educational intervention was produced to help teachers to use this methodology in different ways. The material was tested and questioned by seven teachers and their students. The main data collect instruments were written and spoken reports from the subjects of the research, the Mathematics teachers themselves. These reports, after analysis, resulted in different categories. As a result, it is possible to point out that textbooks are used by teachers under different aspects and that they present some innovations, but the problems are, in most cases, linked to some specific content. It was possible to notice that the teachers had a substantial capacity to innovate by showing, therefore, that the support from factual material can be quite significant. It was also possible to conclude that a professional, working alone, is harder to diversify his practice, but with some incentives he can accomplish positive innovations that benefit the learning of his students. It is considered, therefore, that this research allowed reflections and even changes in the perception of teachers as to methodology of problem solving.
Descrição
Palavras-chave
Resolução de problemas; Ensino de matemática; Livro didático
Citação
KLIEMANN, Geovana Luiza. Potencialidades e limitações de material didático para explorar resolução de problemas matemáticos. 2015. Dissertação (Mestrado) – Curso de Ensino de Ciências Exatas, Universidade do Vale do Taquari - Univates, Lajeado, jan. 2015. Disponível em: http://hdl.handle.net/10737/802.