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Advisor(s)
Abstract(s)
O conceito de função acompanha os alunos durante todo o seu percurso escolar,
evidenciando-se muitas dificuldades na sua aprendizagem. Com este estudo, no qual sou
professora e investigadora, pretendo analisar de que forma tarefas de investigação e
exploração, recorrendo ao software GeoGebra, podem contribuir para a aprendizagem
das funções e para o seu uso na interpretação de situações e na resolução de problemas.
O estudo decorreu no contexto de uma unidade de ensino, leccionada por mim, que se
compunha de cinco tarefas de exploração/investigação. Em três das referidas tarefas,
usou-se o GeoGebra. A investigação seguiu uma metodologia qualitativa, através de
estudos de caso de pares de alunos. A recolha de dados envolveu a realização de duas
entrevistas, uma no início e outra no final do estudo, aos pares de alunos objecto de
estudos de caso, e a análise dos registos dos alunos na resolução das tarefas, bem como
da discussão realizada em grande grupo. Foram ainda analisadas as fichas de avaliação
de que foram alvo, no final do estudo.
Os resultados do estudo mostram que os alunos apresentam dificuldades na
apreensão e aplicação do conceito de função mas que podem ser minimizadas quando
são usadas várias representações. Mostra, também, que os alunos sentem dificuldade em
lidar com símbolos formais algébricos e em relacionar as várias representações. É na
ligação entre fórmulas, gráficos, diagramas e expressões verbais das relações, como na
interpretação de gráficos e na manipulação de símbolos, que residem as dificuldades
sentidas. Estas dificuldades são atenuadas com a realização de tarefas que envolvem os
diversos sistemas de representação. As tarefas usadas permitem aos alunos uma abrangência
de formas de representar a mesma situação, uma vez que a compreensão do conceito
só é possível quando se alcança a coordenação das várias representações. A utilização
de um software constituiu um factor motivador para as aulas de Matemática. No
entanto, a sua utilização fica aquém do esperado, preferindo os alunos utilizar, sempre
que podem, processos de raciocínio numérico.
The concept of function accompanies students throughout all their school years but they experience many difficulties in learning it. With this study, in which I am a teacher and researcher, I analyze how investigation and exploration tasks, using the software GeoGebra, contributes to the learning of functions and their use in interpreting situations and solving problems. The study was carried out in the context of a teaching unit, taught by me, consisting of five exploration/investigation tasks. In three of these tasks, I used GeoGebra. The investigation followed a qualitative methodology, through case studies of pairs of students. Data collection involved two interviews, one in the beginning and one at the end of the study, of pairs of students subject of case studies, the records done students while solving tasks, as well as large group discussion held. I also analyzed the evaluation sheets that were administered at the end of the study. The study results show that students have difficulties in understanding and applying the concept of function that, however, can be minimized with the introduction of multiple representations. It also shows that students find it difficult to deal with formal algebraic symbols and to relate the various representations. It is in the connection between formulas, graphs, diagrams and verbal expressions of relationships, such as interpreting graphs and manipulating symbols, which lay the difficulties. These difficulties can be overcome using tasks involving various systems of representation. This type of work enables students to represent the same situation in multiple ways; therefore they understand better the concept. The use of software was a motivating factor for math classes. However, it seems that students prefer to use processes of numerical reasoning, and less the representation of functions with GeoGebra.
The concept of function accompanies students throughout all their school years but they experience many difficulties in learning it. With this study, in which I am a teacher and researcher, I analyze how investigation and exploration tasks, using the software GeoGebra, contributes to the learning of functions and their use in interpreting situations and solving problems. The study was carried out in the context of a teaching unit, taught by me, consisting of five exploration/investigation tasks. In three of these tasks, I used GeoGebra. The investigation followed a qualitative methodology, through case studies of pairs of students. Data collection involved two interviews, one in the beginning and one at the end of the study, of pairs of students subject of case studies, the records done students while solving tasks, as well as large group discussion held. I also analyzed the evaluation sheets that were administered at the end of the study. The study results show that students have difficulties in understanding and applying the concept of function that, however, can be minimized with the introduction of multiple representations. It also shows that students find it difficult to deal with formal algebraic symbols and to relate the various representations. It is in the connection between formulas, graphs, diagrams and verbal expressions of relationships, such as interpreting graphs and manipulating symbols, which lay the difficulties. These difficulties can be overcome using tasks involving various systems of representation. This type of work enables students to represent the same situation in multiple ways; therefore they understand better the concept. The use of software was a motivating factor for math classes. However, it seems that students prefer to use processes of numerical reasoning, and less the representation of functions with GeoGebra.
Description
Tese de mestrado, Educação (Didáctica da Matemática), Universidade de Lisboa, Instituto de Educação, 2010
Keywords
Didáctica da matemática Funções (Matemática) Tecnologias educativas Teses de mestrado - 2010