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Estratégias para determinar a área de uma superfície irregular no 2.º ciclo do ensino básico
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Abstract(s)
A aprendizagem dos conteúdos de Geometria e Medida, particularidade a medição de áreas, está fortemente marcada no ensino básico pela sua abordagem apenas em figuras geométricas planas e regulares e pela introdução de fórmulas para o seu cálculo sem a atribuição de qualquer significado, o que geralmente resulta em inúmeras dificuldades relacionadas com o entendimento conceptual deste conteúdo.
Tendo em consideração a problemática levantada, definiu-se como objetivo principal de investigação analisar quais as estratégias que os alunos definem para medir a área de uma superfície irregular, tal como a folha de uma árvore, num contexto de conexão externa com o mundo real. O estudo apresenta como questão geral de investigação: Quais as estratégias desenvolvidas pelos alunos do 2.º ciclo do ensino básico para determinarem a área de uma superfície irregular?
O estudo foi realizado numa turma do 6.º ano do 2.º ciclo do ensino básico, composta por um total de 21 alunos, com idades compreendidas entre os 11 e os 12 anos, numa escola do concelho de Loulé. De acordo com a questão de investigação e os objetivos definidos, utilizou-se para a realização do estudo uma metodologia de caráter qualitativo, englobando procedimentos metodológicos próximos dos da investigação-ação. Os instrumentos de recolha de dados foram: (i) as observações diretas, com registos áudios e fotográficos, e (ii) a análise documental das produções dos alunos.
Através da análise dos resultados obtidos, foi possível identificar cinco estratégias utilizadas pelos alunos para a medição da área numa superfície irregular: (i) subdividir; (ii) quantificar; (iii) estruturar espacialmente; (iv) enquadrar figuras geométricas regulares; e (v) aplicar fórmulas. Mediante os resultados de cada grupo, verificou-se que quantas mais estratégias aplicadas para medir a área de uma superfície irregular, maior é a complexidade de raciocínio utilizado para realizar tal medição.
The learning of Geometry and Measurement contents, particularly the measurement of areas, is strongly marked in primary schools by its approach only in plane and regular geometric figures and by the introduction of formulas for its calculation without the attribution of any meaning, which usually results in numerous difficulties related to the conceptual understanding of this content. Considering the problem raised, it was defined as the main research objective to analyse which strategies students define to measure the area of an irregular surface, such as the leaf of a tree, in a context of external connection with the real world. The study presents as general research question: What are the strategies developed by students of the 2nd cycle of basic education to determine the area of an irregular surface? The study was carried out in a 6th grade class of the 2nd cycle of basic education, composed of a total of 21 students, aged between 11 and 12, in a school in the municipality of Loulé. In accordance with the research question and objectives defined, a qualitative methodology was used to conduct the study, encompassing methodological procedures close to those of action research. The data collection instruments were: (i) direct observations, with audio and photographic records, and (ii) documentary analysis of the students' productions. Through the analysis of the results obtained, it was possible to identify five strategies used by students for the measurement of the area on an irregular surface: (i) subdivide; (ii) quantify; (iii) structure spatially; (iv) frame regular geometric figures; and (v) apply formulas. Through the results of each group, it was found that the more strategies applied to measure the area of an irregular surface, the greater the complexity of reasoning used to perform such measuremen
The learning of Geometry and Measurement contents, particularly the measurement of areas, is strongly marked in primary schools by its approach only in plane and regular geometric figures and by the introduction of formulas for its calculation without the attribution of any meaning, which usually results in numerous difficulties related to the conceptual understanding of this content. Considering the problem raised, it was defined as the main research objective to analyse which strategies students define to measure the area of an irregular surface, such as the leaf of a tree, in a context of external connection with the real world. The study presents as general research question: What are the strategies developed by students of the 2nd cycle of basic education to determine the area of an irregular surface? The study was carried out in a 6th grade class of the 2nd cycle of basic education, composed of a total of 21 students, aged between 11 and 12, in a school in the municipality of Loulé. In accordance with the research question and objectives defined, a qualitative methodology was used to conduct the study, encompassing methodological procedures close to those of action research. The data collection instruments were: (i) direct observations, with audio and photographic records, and (ii) documentary analysis of the students' productions. Through the analysis of the results obtained, it was possible to identify five strategies used by students for the measurement of the area on an irregular surface: (i) subdivide; (ii) quantify; (iii) structure spatially; (iv) frame regular geometric figures; and (v) apply formulas. Through the results of each group, it was found that the more strategies applied to measure the area of an irregular surface, the greater the complexity of reasoning used to perform such measuremen
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Keywords
2.º ciclo do ensino básico Matemática Superfície irregular Área Conexões internas e externas