A carregar...
Publicação
Explorações e investigações matemáticas e a aprendizagem da geometria
| Nome: | Descrição: | Tamanho: | Formato: | |
|---|---|---|---|---|
| 3.42 MB | Adobe PDF |
Orientador(es)
Resumo(s)
Este estudo analisa o modo como os alunos do 2º ciclo do ensino básico
desenvolvem a sua competência geométrica num contexto de actividades de carácter
exploratório e investigativo. Debruça-se sobre três questões: (a) De que modo os alunos
reconhecem e analisam propriedades de formas geométricas? (b) De que modo usam a
visualização e o raciocínio espacial? e (c) Como compreendem as características
mensuráveis dos objectos?
O quadro de referência teórico é constituído por duas grandes áreas: a Geometria
no currículo de Matemática e as actividades de cunho exploratório e investigativo. Na
primeira, a partir de uma breve perspectiva histórica sobre a Geometria no currículo de
Matemática, aprofundam-se o conceito de competência geométrica e discutem-se as
principais finalidades de cada aspecto dessa competência, considerados neste estudo: (a)
propriedades de formas geométricas; (b) visualização e raciocínio espacial e (c)
características mensuráveis dos objectos. Na segunda clarifica-se o modo de entender
uma actividade de carácter exploratório e investigativo e discutem-se estudos empíricos
desenvolvidos em Portugal que incidiram nesta temática.
O estudo segue uma metodologia qualitativa baseada num design de estudo de caso
de quatro alunos que trabalharam durante três meses, de forma ininterrupta, num
ambiente de verdadeira actividade Matemática. A proposta pedagógica implementada
na exploração de onze tarefas de carácter exploratório e investigativo. Os registos áudio
do trabalho realizado na aula, a observação participante e as entrevistas realizadas aos
alunos estudados individualmente constituíram as principais fontes de recolha de dados.
No entanto, foram usadas outras fontes de informação que incluíram documentos de
diversos tipos e um questionário inicial.
Os resultados do estudo confirmam as potencialidades das actividades de
carácter exploratório e investigativo no desenvolvimento de aspectos da competência
geométrica como os considerados nesta investigação.
This study analyses how eleven year old students develop their geometrical reasoning within an exploratory and investigative environment. It approaches three issues: a) How do students recognise and analyse the geometric forms properties? b) How do students use spatial visualization and reasoning? c) How they understand the objects’ measurable characteristics? The theoretical framework of the study integrates two main areas: Geometry in the Mathematic curriculum and the investigative and exploratory activities. Deriving from a brief historical perspective about geometry in the mathematic curriculum, the first area thoroughly examines the concept of geometric competence. The main purposes of each aspect of that competence considered in this study, are discussed: a) geometric forms properties; b) spatial visualization and reasoning; c) the objects measurable characteristics. The second area clarifies the understanding of exploratory and investigative activities and discusses Portuguese developed empirical studies which fell upon this thematic. The study follows a qualitative methodology based on a case study design of four students, working, uninterruptedly for three months, on a real mathematic environment. The pedagogical proposal executed was based on the explanation of eleven tasks of exploratory and investigative nature. The main source of the gathered data are: classroom accomplishments audio data, the participants observations and the individual interviews made to the students. Other sources of information were used, such as various types of documents and a starting formal list of questions. The results of this study confirms that the nature of exploratory and investigative activities have a great deal of potential in the development geometric reasoning aspects, such as the ones considered in this investigation.
This study analyses how eleven year old students develop their geometrical reasoning within an exploratory and investigative environment. It approaches three issues: a) How do students recognise and analyse the geometric forms properties? b) How do students use spatial visualization and reasoning? c) How they understand the objects’ measurable characteristics? The theoretical framework of the study integrates two main areas: Geometry in the Mathematic curriculum and the investigative and exploratory activities. Deriving from a brief historical perspective about geometry in the mathematic curriculum, the first area thoroughly examines the concept of geometric competence. The main purposes of each aspect of that competence considered in this study, are discussed: a) geometric forms properties; b) spatial visualization and reasoning; c) the objects measurable characteristics. The second area clarifies the understanding of exploratory and investigative activities and discusses Portuguese developed empirical studies which fell upon this thematic. The study follows a qualitative methodology based on a case study design of four students, working, uninterruptedly for three months, on a real mathematic environment. The pedagogical proposal executed was based on the explanation of eleven tasks of exploratory and investigative nature. The main source of the gathered data are: classroom accomplishments audio data, the participants observations and the individual interviews made to the students. Other sources of information were used, such as various types of documents and a starting formal list of questions. The results of this study confirms that the nature of exploratory and investigative activities have a great deal of potential in the development geometric reasoning aspects, such as the ones considered in this investigation.
Descrição
Tese de mestrado em Educação (Didáctica da Matemática), apresentada à Universidade de Lisboa através da Faculdade de Ciências, 2006
Palavras-chave
Geometria Aprendizagem Investigação matemática Teses de mestrado - 2006