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As potencialidades do uso da geometria dinâmica no estudo da circunferência no 9º ano
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Esta investigação tem como objetivo compreender como é que os alunos desenvolvem o seu raciocínio geométrico quando recorrem ao ambiente de geometria dinâmica GeoGebra para resolver tarefas de construção, exploração e investigação. O propósito geral é melhorar a aprendizagem da disciplina de Matemática, tentando ir de encontro às dificuldades dos alunos e contribuir para que as superem, ou melhor ainda, contribuir para as evitar. O quadro teórico refere o contributo que os ambientes de geometria dinâmica (AGD) podem dar no ensino e aprendizagem da Matemática, mais especificamente da Geometria. Abordo ainda os processos de raciocínio em geral e geométrico em particular, com especial atenção à generalização e à justificação por parte dos alunos.
A intervenção foi feita no tema “Circunferência”, que consta do currículo do 9.º ano, e segue uma metodologia qualitativa e interpretativa, com observação participante. A recolha de dados foi efetuada numa turma cuja professora é a investigadora, sendo estudada a própria turma, durante toda a unidade de ensino. Na recolha de dados foram utilizados a observação de aulas, com registos em diário de bordo e em gravações áudio, e a recolha documental das produções dos alunos em suporte papel e também em suporte informático.
Os resultados indicam que os alunos, com tarefas de carácter exploratório e investigativo, num ambiente em que se analisam as figuras obtidas com o ambiente de Geometria dinâmica GeoGebra e se discutem ideias, formulam conjeturas e produzem generalizações com alguma facilidade. Também conseguem justificar as suas generalizações recorrendo a métodos descritivos ou mais formais desenvolvendo as suas competências nestas áreas. Os alunos induziram e justificaram todas as propriedades previstas nos descritores do programa em vigor, em vez de simplesmente as memorizarem e aplicarem na resolução de exercícios.
This research aims to understand how students develop their geometric reasoning when they resort to GeoGebra's dynamic geometry software to solve construction, exploration, and research tasks. The general purpose is to improve the learning of Mathematics, trying to meet the difficulties of the students and contribute to overcome them, or better yet, help them avoid it. The theoretical framework refers to the contribution the software of dynamic geometry could have in the teaching and learning of Mathematics, more specifically of Geometry. I also approach reasoning processes generally and geometric ones in particular, with special attention to generalization and proof by students. The intervention was made with the theme "Circumference", which is included in the 9th grade curriculum, and follows a qualitative and interpretative methodology, with participant observation. The data collection was carried out in a class whose teacher is the researcher, being studied the class itself, throughout the whole teaching unit. In the data collection, classroom observation was used, with logbooks and audio recordings, and the documental collection of the students' productions in paper format and also in computer support. The results indicate that the students, with exploratory and investigative tasks, in an environment in which the figures obtained with the GeoGebra dynamic geometry software are analyzed and ideas are discussed, formulate conjectures and produce generalizations with some ease. They can also justify their generalizations by using descriptive or more formal methods by developing their skills in these areas. Students have induced and justified all of the properties provided in the current program descriptors, rather than simply memorizing and applying them in solving exercises.
This research aims to understand how students develop their geometric reasoning when they resort to GeoGebra's dynamic geometry software to solve construction, exploration, and research tasks. The general purpose is to improve the learning of Mathematics, trying to meet the difficulties of the students and contribute to overcome them, or better yet, help them avoid it. The theoretical framework refers to the contribution the software of dynamic geometry could have in the teaching and learning of Mathematics, more specifically of Geometry. I also approach reasoning processes generally and geometric ones in particular, with special attention to generalization and proof by students. The intervention was made with the theme "Circumference", which is included in the 9th grade curriculum, and follows a qualitative and interpretative methodology, with participant observation. The data collection was carried out in a class whose teacher is the researcher, being studied the class itself, throughout the whole teaching unit. In the data collection, classroom observation was used, with logbooks and audio recordings, and the documental collection of the students' productions in paper format and also in computer support. The results indicate that the students, with exploratory and investigative tasks, in an environment in which the figures obtained with the GeoGebra dynamic geometry software are analyzed and ideas are discussed, formulate conjectures and produce generalizations with some ease. They can also justify their generalizations by using descriptive or more formal methods by developing their skills in these areas. Students have induced and justified all of the properties provided in the current program descriptors, rather than simply memorizing and applying them in solving exercises.
Descrição
Trabalho de projeto de mestrado, Educação (Área de especialidade em Didática da Matemática), Universidade de Lisboa, Instituto de Educação, 2018
Palavras-chave
Geometria Generalização (aprendizagem) Circunferências Ensino básico (3º Ciclo) Trabalhos de projeto de mestrado - 2018