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Explorações e investigações matemáticas por alunos com insucesso escolar
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Orientador(es)
Resumo(s)
Este estudo analisa como reagem alunos com dificuldades na aprendizagem da
Matemática ao trabalho com tarefas de exploração e investigação. São três as questões
de investigação: (1) Como é a sua actividade matemática nestas tarefas? (2) Que
concepções têm e, eventualmente, alteram sobre a disciplina e as aulas de Matemática?
(3) Que relação estabelecem com a disciplina? A investigação segue uma abordagem
qualitativa com um design de estudo de caso múltiplo. Os três alunos participantes
apresentam forte resistência e dificuldades na aprendizagem da Matemática, com uma
história de insucesso repetido. No imcio do estudo não tinham experiência em tarefas de
exploração e investigação, tendo-se realizado cinco destas tarefas durante o ano lectivo
de 2003/04. As técnicas de recolha de dados foram a observação participante, a
entrevista e o diário de bordo. Analisaram-se também os registos dos alunos nas folhas
das tarefas. A análise foi feita em três fases: (a) redução de dados; (b) apresentação de
dados; e (c) interpretação e verificação.
Os resultados indicam que os alunos reagiram de forma favorável às tarefas.
Envolveram-se no trabalho demonstrando empenhamento, curiosidade e persistência.
Utilizaram processos matemáticos fundamentais como a formulação, teste e validação
de conjecturas e nalgumas situações conseguiram justificá-las. Na quarta tarefa
realizaram generalizações. A troca de ideias que de fornia espontânea se registou entre
eles proporcionou que argumentassem na defesa das suas ideias. Mobilizaram diversos
conhecimentos matemáticos, usando os conceitos de número, algarismo, múltiplo,
potência, ângulo, amplitude de um ângulo, simetria, perpendicularidade, quadrilátero e
polígono, recorreram ao cálculo mental e utilizaram as quatro operações aritméticas. As
principais dificuldades situaram-se nos registos escritos e nos processos de justificação
e generalização de conjecturas. Comprovou-se que as dificuldades na aprendizagem da
Matemática destes alunos estão directamente relacionadas com o seu desinteresse total
em relação à disciplina. Assim, os resultados do estudo sugerem que uma experiência de
trabalho regular com explorações e investigações pode motivar alunos com estas
características para a aprendizagem, levando-os a atribuir significado à actividade
matemática. Esta vivência favorece a mudança de concepções sobre o seu papel
enquanto alunos, reforça-lhes a auto estima e melhora a sua relação com a disciplina.
This study analyses how pupils with learning difficulties in Mathematics react to a job with exploration and investigation tasks. There are three investigation questions: 1) How is their mathematical activity in these tasks? 2) What conceptions do they have and, eventually, change about the subject and the classes? 3) What kind of relation do they establish with the subject? The investigation follows a qualitative approach with a multiple case study design. The three pupils which participate in this study show a strong resistance and difficulties in learning Mathematics, with a repeated unsuccessful history. In the beginning of the study they didn't have any experience in exploration and investigation tasks, and five of these tasks occured throughout the 2003/04 school year. Data collection techniques were the participant observation, the interview and the logbook. Students' tasks paper sheets were also analysed. This analysis was done in three phases: a) data reduction; b) data presentation; and c) interpretation and checking. The results show that students reacted in a favourable way to the tasks. They got involved in the woric, showing conunitment, curiosity and persistance. They have used fundamental mathematical process such as formulation, testing and validation conjectures and in some situations they were able to justify them. During the fourth task they evolved to generalization. The exchange of . ideas that spontaneously occured among the students allowed them to argue and to stend up for their ideas. They have mobilized severel mathematical knowledges, using the concepts of number, numeral, multiple, power, angle, angle s measure, symmetry, perpendicular line, quadrilaterol and polygon, used mental calculus and four arithmetic operations. Their main difficulties were in the written registrations and in the conjectures justification and generalization process. It was proved that the learning difficulties of these students are directly related with their lack of interest towards the school subject. So, the study results show that a regular work experience with explorations and investigations can motivate students with these characteristics to the learning activity, leading them to a meaningful mathematical activity. This experience favours the change of conceptions regarding their role as students reinforces their self-esteem and improves the relation with the school subject.
This study analyses how pupils with learning difficulties in Mathematics react to a job with exploration and investigation tasks. There are three investigation questions: 1) How is their mathematical activity in these tasks? 2) What conceptions do they have and, eventually, change about the subject and the classes? 3) What kind of relation do they establish with the subject? The investigation follows a qualitative approach with a multiple case study design. The three pupils which participate in this study show a strong resistance and difficulties in learning Mathematics, with a repeated unsuccessful history. In the beginning of the study they didn't have any experience in exploration and investigation tasks, and five of these tasks occured throughout the 2003/04 school year. Data collection techniques were the participant observation, the interview and the logbook. Students' tasks paper sheets were also analysed. This analysis was done in three phases: a) data reduction; b) data presentation; and c) interpretation and checking. The results show that students reacted in a favourable way to the tasks. They got involved in the woric, showing conunitment, curiosity and persistance. They have used fundamental mathematical process such as formulation, testing and validation conjectures and in some situations they were able to justify them. During the fourth task they evolved to generalization. The exchange of . ideas that spontaneously occured among the students allowed them to argue and to stend up for their ideas. They have mobilized severel mathematical knowledges, using the concepts of number, numeral, multiple, power, angle, angle s measure, symmetry, perpendicular line, quadrilaterol and polygon, used mental calculus and four arithmetic operations. Their main difficulties were in the written registrations and in the conjectures justification and generalization process. It was proved that the learning difficulties of these students are directly related with their lack of interest towards the school subject. So, the study results show that a regular work experience with explorations and investigations can motivate students with these characteristics to the learning activity, leading them to a meaningful mathematical activity. This experience favours the change of conceptions regarding their role as students reinforces their self-esteem and improves the relation with the school subject.
Descrição
Tese de mestrado em Educação (Didáctica da Matemática), apresentada à Universidade de Lisboa através da Faculdade de Ciências, 2005
Palavras-chave
Dificuldades de aprendizagem Investigação matemática Concepções dos alunos Teses de mestrado - 2005