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A utilização de tecnologia na resolução de problemas matemáticos : análise do perfil de resolvedores em geometria
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Orientador(es)
Resumo(s)
O presente estudo aborda três temáticas fundamentais ao ensino da Matemática:
Resolução de problemas, Geometria e Tecnologia. Tendo por base estes três aspectos
desenvolveu-se este estudo que pretende descrever holisticamente o perfil de dois tipos de
grupos de alunos, enquanto resolvedores de problemas de Geometria quando recorrem ao
Geometer's Sketchpad nessas resoluções.
Para este estudo foi construído um referencial para a escolha/selecção de dois tipos
de grupos de alunos. Um grupo I de alunos com notas acima da média da turma nas
disciplinas de Matemática, Língua Portuguesa, Inglês e TIC e outro grupo II de alunos com
classificações dentro da média ou ligeiramente abaixo. Neste referencial de escolha dos
grupos, os alunos responderam ainda a um inquérito sobre o seu gosto pela resolução de
problemas bem como resolveram um problema matemático, que influenciou a constituição
dos grupos.
Este estudo baseou-se no Modelo de Resolução de problemas de Polya e procurou
dar resposta às seguintes questões: (1) qual o perfil de resolvedores de problemas dos dois
tipos de grupos de alunos na etapa da compressão do problema?; (2) qual o perfil de
resolvedores de problemas dos mesmos dois tipos de grupos de alunos na etapa relativa ao
estabelecimento de um plano para resolver os problemas?; (3) qual o perfil de resolvedores
de problemas dos mesmos dois tipos de grupos de alunos na etapa da execução dos planos
de resolução dos problemas? e (4) qual o perfil de resolvedores de problemas dos mesmos
dois tipos de grupos de alunos na etapa da verificação da resolução dos problemas?
Utilizou-se uma metodologia de investigação qualitativa. Os instrumentos
utilizados para a recolha de dados foram: (a) registos vídeo da actividade dos grupos
durante a resolução das actividades; (b); registos feitos pelo investigador; (c) fichas de
registo de actividade elaboradas pelos grupos e (d) análise do histórico e ficheiros do
Geometer's Sketchpad.
Em termos de resposta às questões de investigação formuladas, podemos afirmar
que relativamente à primeira etapa do Modelo de Polya, os alunos do grupo 1 manifestaram
sempre grande preocupação por uma correcta compreensão das actividades, contrariamente
aos alunos do outro grupo que não dedicavam o tempo suficiente a esta etapa. A segunda
etapa de Polya manifestou-se como o principal problema dos dois grupos pois, em ambos,
raramente lhe foi dedicada especial atenção, com implicações óbvias nas seguintes etapas.
Na terceira etapa de Polya, execução dos planos de resolução, surgiram alguns problemas,
sobretudo no grupo II pelo facto dos alunos não realizarem a etapa anterior, em algumas
actividades. A quarta e última etapa do Modelo de Polya, verificação, foi realizada de
forma objectiva em apenas algumas actividades e somente pelos alunos do grupo 1.
Como principais conclusões do estudo podemos referir o seguinte: o Modelo de
Polya quando sugerido aos alunos do grupo 1 foi seguido com alguma atenção e os alunos
apresentaram melhorias ao nível das suas resoluções. Relativamente aos alunos do grupo
II, e durante a realização deste estudo, verificaram-se ligeiras melhorias apenas ao nível da
compreensão dos problemas.
Assim com um estudo desta natureza, podemos afirmar que o perfil de resolvedores
de problemas em geometria dos alunos do grupo 1 apresenta algumas melhorias
contrariamente aos alunos do grupo II onde estas melhorias são apenas pontuais.
The present study approaches three fundamental thematic to the teaching of the Mathematics: Resolution of problems, Geometry and Technology. Basing in these three aspects, this study has been developed describe the profile of two types of students groups, while solvers of problems of Geometry when they fall back on to the Geometer's Sketchpad in those resolutions. For this study a referencial was built to the choice/selection of two types of students groups. A group I of students with classifications above the average of the group in the subjects of Mathematics, Portuguese Language, English and Computer Studies and another students group II with classifications inside of the average or lightly below. In this referencial of choice of the groups, the students have still answered to an inquiry on their fondness for the resolution of problems as well as they have solved a mathematical problem, that influenced the constitution of the groups. This study was based on the Model of Resolution of problems of Polya and tried to give answer to the following subjects: (1) What was the profile of the solvers of problems of the two types of students groups in the stage of the comprehension of problems?; (2) What was the profile of the solvers of problems of the same two types of students groups in the stage relative to the establishment of a plan to solve the problems?; (3) What was the profile of the solvers of problems of the same two types of students groups in the stage of the execution of the plans of resolution of the problems? and (4) What was the profile of the solvers of problems of the same two types of students groups in the stage of the checking of the resolution of the problems? A methodology of qualitative investigation was used. The instruments used for the sathering of data were: (a) video records of the activity of the groups during the resolution of the activities; (b); records done by the investigator; (c) records of activity sheets elaborated by the groups and (d) analysis of the report and files of Geometer's Sketchpad. In answer terms to the investigation subjects formulated, we can affirm that relatively to the first stage of the Model of Polya, the students of the group I have always manifested great concern for a correct understanding of the actividades, opposite to the students of the other group that didn't dedicate the enough time to this stage, even when requested. The second stage of Polya was showed as the principal problem of the two groups because, in both, special attention was rarely dedicated to this stage, with obvious implications in the following stages. In the third stage of Polya, execution of the resolution plans, some problems appeared, mainly in the group II because the students didnn't realize not to accomplish the previous stage in same activities. The fourth and last stage of the Model of Polya, checking, was accomplished in an objective was in just some activities and only by the students of the group I. As main conclusions of the study, we can refer the following: the Model of Polya when suggested to the students of the group I their was followed with some attention and the students showed improvements at the level of their resolutions. Relatively to the students of the group II, and during the accomplishment of this study, light improvements were verified at the level of the understanding of the problems. Therefore with a study of this nature, the Profile of solvers of problems in the students of the group I geometry has some improvements opposite to the students of the group II where these are just punctual improvements.
The present study approaches three fundamental thematic to the teaching of the Mathematics: Resolution of problems, Geometry and Technology. Basing in these three aspects, this study has been developed describe the profile of two types of students groups, while solvers of problems of Geometry when they fall back on to the Geometer's Sketchpad in those resolutions. For this study a referencial was built to the choice/selection of two types of students groups. A group I of students with classifications above the average of the group in the subjects of Mathematics, Portuguese Language, English and Computer Studies and another students group II with classifications inside of the average or lightly below. In this referencial of choice of the groups, the students have still answered to an inquiry on their fondness for the resolution of problems as well as they have solved a mathematical problem, that influenced the constitution of the groups. This study was based on the Model of Resolution of problems of Polya and tried to give answer to the following subjects: (1) What was the profile of the solvers of problems of the two types of students groups in the stage of the comprehension of problems?; (2) What was the profile of the solvers of problems of the same two types of students groups in the stage relative to the establishment of a plan to solve the problems?; (3) What was the profile of the solvers of problems of the same two types of students groups in the stage of the execution of the plans of resolution of the problems? and (4) What was the profile of the solvers of problems of the same two types of students groups in the stage of the checking of the resolution of the problems? A methodology of qualitative investigation was used. The instruments used for the sathering of data were: (a) video records of the activity of the groups during the resolution of the activities; (b); records done by the investigator; (c) records of activity sheets elaborated by the groups and (d) analysis of the report and files of Geometer's Sketchpad. In answer terms to the investigation subjects formulated, we can affirm that relatively to the first stage of the Model of Polya, the students of the group I have always manifested great concern for a correct understanding of the actividades, opposite to the students of the other group that didn't dedicate the enough time to this stage, even when requested. The second stage of Polya was showed as the principal problem of the two groups because, in both, special attention was rarely dedicated to this stage, with obvious implications in the following stages. In the third stage of Polya, execution of the resolution plans, some problems appeared, mainly in the group II because the students didnn't realize not to accomplish the previous stage in same activities. The fourth and last stage of the Model of Polya, checking, was accomplished in an objective was in just some activities and only by the students of the group I. As main conclusions of the study, we can refer the following: the Model of Polya when suggested to the students of the group I their was followed with some attention and the students showed improvements at the level of their resolutions. Relatively to the students of the group II, and during the accomplishment of this study, light improvements were verified at the level of the understanding of the problems. Therefore with a study of this nature, the Profile of solvers of problems in the students of the group I geometry has some improvements opposite to the students of the group II where these are just punctual improvements.
Descrição
Tese de mestrado em Ciências da Educação (Área de Especialização em Tecnologias Educativas), apresentada à Universidade de Lisboa, através da Faculdade de Psicologia e de Ciências de Educação, 2006
Palavras-chave
Teses de mestrado - 2006 Tecnologia educativa Problemas de matemática - soluções Metacognição Trabalho de grupo Geometria