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O pensamento geométrico nas provas de avaliação externa de matemática
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Na aprendizagem da Matemática as tarefas são um aspeto determinante do trabalho dos alunos, direcionando a sua atenção para conteúdos particulares e para formas específicas de processamento de informação. No caso particular do ensino e da aprendizagem da Geometria, as tarefas constituem um contexto natural para o desenvolvimento do raciocínio culminando no trabalho de demonstração. Neste estudo, tive como objetivos a análise dos conceitos necessários à resolução de tarefas, as representações e os processos cognitivos solicitados e utilizados pelos alunos, no âmbito da Geometria, em provas de avaliação externa em Matemática. Para o efeito, foram consideradas as provas de aferição (2010 e 2011) e as provas finais do 2.º ciclo (2013 e 2014), da primeira fase. Face aos objetivos definidos e às questões formuladas, o estudo seguiu uma metodologia de investigação de natureza descritiva e interpretativa. A recolha de dados recorreu à compilação documental (produções dos alunos) e a entrevistas semiestruturadas subsequentemente à realização das provas externas, registadas em áudio e vídeo, tendo como base uma amostra intencional. Os dados foram analisados tendo por base categorias, a partir da literatura convocada sobre o tema. A análise e compreensão do pensamento geométrico, exigiu, entre outros aspetos, ter em consideração os constrangimentos inerentes ao próprio ambiente em que as provas ocorreram, entre os quais o de haver um tempo limitado para a sua resolução e ainda o de os resultados obtidos nas provas finais serem considerados no cômputo da classificação final de um determinado ano letivo. De uma forma geral, os resultados obtidos evidenciaram que os alunos enfrentaram várias dificuldades e, como era de esperar, estas variaram de acordo com o nível de complexidade das tarefas. Alguns desafios e dificuldades comuns que encontraram foram: a compreensão conceptual; a aplicação de propriedades geométricas de maneira eficaz; a visualização espacial; as conexões geométricas; a construção de argumentos lógicos para justificar as respostas; a conexão da Geometria com as aplicações ao mundo real; e a ansiedade provocada pelo tempo limitado que tiveram para resolver as provas. Em muitos casos, estas dificuldades tornaram-se impeditivas de processos cognitivos necessários para desencadear a escolha de estratégias adequadas para a resolução das tarefas.
In Mathematics learning, tasks are a determining aspect of students' work, directing their attention to particular content and specific forms of information processing. In the particular case of teaching and learning Geometry, they constitute a natural context for the development of reasoning culminating in demonstration work. In this study my objectives were to analyze the concepts necessary to solve tasks, the representations and cognitive processes requested and used by students, within the scope of Geometry, in external assessment tests in Mathematics. For this purpose, the assessment tests (2010 and 2011) and the final tests of the 2nd cycle (2013 and 2014), from the first phase, were considered. Given the defined objectives and the questions formulated, the study followed a research methodology of a descriptive and interpretative nature. Data collection used documentary compilation (student productions) and semi-structured interviews following the external tests, recorded in audio and video, based on an intentional sample. The data were analyzed based on categories, based on the literature gathered on the topic. The analysis and understanding of geometric thinking required, among other aspects, taking into account the constraints inherent to the environment in which the tests took place, including the fact that there was a limited time for their resolution and also that the results obtained in the final exams be considered when calculating the final classification of a given academic year. In general, the results obtained showed that the students faced several difficulties and, as expected, these varied according to the level of complexity of the tasks. Some common challenges and difficulties they encountered were: conceptual understanding; the application of geometric properties effectively; spatial visualization; geometric connections; the construction of logical arguments to justify the answers; the connection of Geometry with applications to the real world; and the anxiety caused by the limited time they had to solve the tests. In many cases, these difficulties became impediments to the cognitive processes necessary to trigger the choice of appropriate strategies for solving tasks.
In Mathematics learning, tasks are a determining aspect of students' work, directing their attention to particular content and specific forms of information processing. In the particular case of teaching and learning Geometry, they constitute a natural context for the development of reasoning culminating in demonstration work. In this study my objectives were to analyze the concepts necessary to solve tasks, the representations and cognitive processes requested and used by students, within the scope of Geometry, in external assessment tests in Mathematics. For this purpose, the assessment tests (2010 and 2011) and the final tests of the 2nd cycle (2013 and 2014), from the first phase, were considered. Given the defined objectives and the questions formulated, the study followed a research methodology of a descriptive and interpretative nature. Data collection used documentary compilation (student productions) and semi-structured interviews following the external tests, recorded in audio and video, based on an intentional sample. The data were analyzed based on categories, based on the literature gathered on the topic. The analysis and understanding of geometric thinking required, among other aspects, taking into account the constraints inherent to the environment in which the tests took place, including the fact that there was a limited time for their resolution and also that the results obtained in the final exams be considered when calculating the final classification of a given academic year. In general, the results obtained showed that the students faced several difficulties and, as expected, these varied according to the level of complexity of the tasks. Some common challenges and difficulties they encountered were: conceptual understanding; the application of geometric properties effectively; spatial visualization; geometric connections; the construction of logical arguments to justify the answers; the connection of Geometry with applications to the real world; and the anxiety caused by the limited time they had to solve the tests. In many cases, these difficulties became impediments to the cognitive processes necessary to trigger the choice of appropriate strategies for solving tasks.
Descrição
Palavras-chave
Pensamento geométrico avaliação externa tarefas de geometria Geometric thinking external evaluation Geometry tasks