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O presente relatório final de estágio foi realizado no âmbito do Mestrado em Ensino do 1.º Ciclo do Ensino Básico (CEB) e de Matemática e Ciências Naturais no 2.º CEB e pretende apresentar o trabalho desenvolvido nas unidades curriculares das Práticas de Ensino Supervisionadas desenvolvidas em ambos os ciclos, assim como o projeto de investigação na área disciplinar de Matemática, no âmbito do 2.º CEB. Este projeto de investigação teve como foco o ensino-aprendizagem da Matemática apresentando como questão problema Em que medida o recurso a materiais didáticos no ensino da Matemática no 2.º CEB potencia aprendizagens significativas?, tendo como objetivos identificar as potencialidades do uso de barras de Cuisenaire, tangram, espelhos, mira, papel vegetal e torre de Hanói, no ensino-aprendizagem da Matemática no 2.º CEB e conceber tarefas matemáticas com recurso a materiais didáticos que sejam potenciadoras de aprendizagens significativas. A partir da revisão detalhada da literatura sobre o tema, criou-se e analisou-se um conjunto de tarefas matemáticas, com recurso a materiais didáticos, apresentando-se propostas de roteiros numa perspetiva de ensino exploratório, sendo o público-alvo alunos do 2.º CEB. O estudo trata-se de uma Investigação Baseada em Design (IBD), apoiando-se numa experiência de prática pedagógica. Esta metodologia parte de uma hipótese, tratando-se neste caso da questão problema já mencionada anteriormente, à qual a investigação pretende dar resposta. As tarefas matemáticas construídas com base no ensino exploratório e com recurso a materiais didáticos, designadamente barras de Cuisenaire, tangram, espelhos, mira, papel vegetal e torre de Hanói, permitiram concluir que o uso de materiais didáticos é potenciador de aprendizagens significativas. As barras de Cuisenaire e o tangram apresentam potencialidades para trabalhar os números racionais não negativos. Todavia a tarefa apresentada com recurso às barras de Cuisenaire aborda o sentido da fração como relação parte-todo e medida, enquanto que a tarefa em que se utiliza o tangram trabalha-se o sentido da fração como medida. A tarefa com recurso a espelhos, mira e papel vegetal revelou potenciar aprendizagens significativas ao nível das isometrias do plano, nomeadamente nas simetrias de reflexão e rotação. Também, a tarefa apresentada com recurso à torre de Hanói demostrou proporcionar aprendizagens significativas nos conteúdos das sequências e regularidades e potências de expoente natural. As tarefas matemáticas apresentadas neste trabalho com utilização dos materiais didáticos potenciam aprendizagens significativas, dado o material facilitar a abordagem dos conteúdos curriculares, promover o trabalho em grupo e proporcionar ainda as discussões matemáticas coletivas, sendo estes aspetos caracterizadores do ensino exploratório.
This final internship report was made within the scope of the Master's in Teaching the 1st Cycle of Basic Education, and of Maths and Natural Sciences in the 2nd Cycle of Basic Education and intends to present the work developed in the curricular units of Supervised Teaching Practice, developed in both cycles, as well as the research project in the disciplinary area of mathematics, within the 2nd Cycle of Basic Education. This research project focused on the teaching and learning of mathematics, with the problem question To what extent the use of didactic materials in the teaching of mathematics in the 2nd Cycle of Basic Education promotes significant learning?, Its goals were to identify the potential of using Cuisenaire rods , tangram, mirrors, crosshairs, tracing paper and tower of Hanói, in the teaching and learning of mathematics in the 2nd Cycle of Basic Education and to design mathematical tasks using didactic materials that promote significant learning. Based on the detailed literature review on the subject, a set of mathematical tasks was created and analysed, using didactic materials, presenting proposals for roadmaps in an exploratory teaching perspective, being the target audience the 2nd Cycle of Basic Education. The study is a Design-Based Research based on a pedagogical practice experience. This methodology is based on a hypothesis, in this case the problem question mentioned above, to which the research aims to answer. The mathematical tasks based on exploratory teaching and using teaching materials, namely Cuisenaire rods, tangram, mirrors, crosshairs, tracing paper and tower of Hanói, led to the conclusion that the use of teaching materials promotes significant learning. The Cuisenaire rods and tangram have the potential to work with non-negative rational numbers. However, the task presented using Cuisenaire rods addresses the meaning of fraction as part-whole relationship and measure, while the task using tangram works the meaning of fraction as measure. The task using mirrors, crosshairs and tracing paper proved to enhance significant learning at the level of plane isometries, namely in reflection and rotation symmetries. Moreover, the task using the tower of Hanói provided significant learning in the contents of sequences and regularities and powers of natural exponent. The mathematical tasks included in this essay with the use of didactic materials enhance significant learning, since the material facilitates the approach to curriculum content, promotes workgroup, and also provides collective mathematical discussions, which are characteristic aspects of exploratory teaching.
This final internship report was made within the scope of the Master's in Teaching the 1st Cycle of Basic Education, and of Maths and Natural Sciences in the 2nd Cycle of Basic Education and intends to present the work developed in the curricular units of Supervised Teaching Practice, developed in both cycles, as well as the research project in the disciplinary area of mathematics, within the 2nd Cycle of Basic Education. This research project focused on the teaching and learning of mathematics, with the problem question To what extent the use of didactic materials in the teaching of mathematics in the 2nd Cycle of Basic Education promotes significant learning?, Its goals were to identify the potential of using Cuisenaire rods , tangram, mirrors, crosshairs, tracing paper and tower of Hanói, in the teaching and learning of mathematics in the 2nd Cycle of Basic Education and to design mathematical tasks using didactic materials that promote significant learning. Based on the detailed literature review on the subject, a set of mathematical tasks was created and analysed, using didactic materials, presenting proposals for roadmaps in an exploratory teaching perspective, being the target audience the 2nd Cycle of Basic Education. The study is a Design-Based Research based on a pedagogical practice experience. This methodology is based on a hypothesis, in this case the problem question mentioned above, to which the research aims to answer. The mathematical tasks based on exploratory teaching and using teaching materials, namely Cuisenaire rods, tangram, mirrors, crosshairs, tracing paper and tower of Hanói, led to the conclusion that the use of teaching materials promotes significant learning. The Cuisenaire rods and tangram have the potential to work with non-negative rational numbers. However, the task presented using Cuisenaire rods addresses the meaning of fraction as part-whole relationship and measure, while the task using tangram works the meaning of fraction as measure. The task using mirrors, crosshairs and tracing paper proved to enhance significant learning at the level of plane isometries, namely in reflection and rotation symmetries. Moreover, the task using the tower of Hanói provided significant learning in the contents of sequences and regularities and powers of natural exponent. The mathematical tasks included in this essay with the use of didactic materials enhance significant learning, since the material facilitates the approach to curriculum content, promotes workgroup, and also provides collective mathematical discussions, which are characteristic aspects of exploratory teaching.
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Keywords
Materiais didáticos Ensino exploratório da Matemática Aprendizagens significativas 2.º CEB Didactic materials Exploratory teaching of maths Significant learning 2nd Cycle of Basic Education