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O desenvolvimento da estruturação espacial nos primeiros anos de escolaridade
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Este estudo tem como objetivo compreender como é que os alunos do 1.º ano do ensino básico progridem na compreensão das estruturas de figuras bidimensionais e tridimensionais, e que papel tem o raciocínio espacial nessa estruturação, no contexto de uma investigação baseada em design.
O enquadramento teórico centra-se no desenvolvimento da estruturação espacial enquanto forma de construção de representações mentais. Assumindo que estas representações são criadas a partir de relações que são estabelecidas e que emergem da interação entre concreto e abstrato, é mobilizada a noção de raciocínio espacial, enquanto conjunto de processos que permitem compreender e transformar o espaço. Os materiais manipuláveis e os desenhos das construções assumem um papel de destaque no processo de abstração.
Este estudo segue a modalidade de investigação baseada em design, tendo sido realizada uma experiência de ensino, constituída por micro-ciclos de design, numa turma de 1.º ano com 24 alunos e respetiva professora, onde foram implementadas 19 tarefas de caráter exploratório, ao longo de vinte sessões com cerca de 60 minutos cada sessão. Dos 24 alunos, foram selecionados 4 para uma análise mais aprofundada, embora fosse considerada e analisada a participação de todos os alunos, em momentos de discussão coletiva. Foram utilizadas a observação participante, com registo áudio e vídeo, a recolha documental e notas de campo, como técnicas de recolha de dados. A análise dos dados assenta em três níveis hierárquicos de estruturação espacial: um nível pré-estrutural, um nível em que a estruturação é local e um nível mais sofisticado de estruturação global.
Os resultados sugerem que os alunos começam por estabelecer relações locais antes de estabelecerem relações globais, quer seja na composição ou na decomposição de figuras. Na estruturação espacial, estão envolvidos processos de raciocínio espacial que parecem facilitar o aprofundamento de relações, quer seja nas figuras bidimensionais, tridimensionais ou na articulação entre bidimensionalidade e tridimensionalidade. A composição e decomposição de figuras emergem como dois processos de raciocínio espacial que permitem analisar e compreender a estrutura das figuras, enquanto outros processos mais dinâmicos como rodar, inverter ou dobrar permitem aprofundar o tipo de relações intrínsecas às figuras e estabelecer relações entre a bidimensionalidade e tridimensionalidade. A complexidade dos processos de raciocínio espacial usados pelos alunos também parece estar dependente do nível de estruturação espacial dos alunos. A estruturação espacial e os processos de raciocínio espacial parecem ser influenciados pela manipulação dos materiais e pelos desenhos que os alunos fazem das suas construções.
Desta investigação, emerge um conjunto de princípios de design que suportam a conjetura sobre como promover a estruturação espacial, nos primeiros anos de escolaridade.
This study aims to understand how first grade students develop their understanding of two and three-dimensional shapes’ structures, and what role spatial reasoning plays in that structuring, in the context of a design-based research. The theoretical framework is focused on spatial structuring as a form of creating mental representations. Assuming that these representations are based on relationships that are established and that emerge from the interaction between concrete and abstract, spatial reasoning is mobilized as a set of processes that allow understanding and transforming space. Manipulatives and drawings assume a prominent role in the process of abstraction. The study follows a design-based research method, where a teaching experiment, with design micro-cycles, has been conducted, in a 1st grade class, with 24 students and their teacher. 19 tasks where implemented, through 20 lessons with about 60 minutes each. From the 24 students, 4 were selected for an in-dept analysis. It also has been collected and analysed the contributes of all 24 students, during whole-class discussions. Data was collected through participant observation, with audio and video recording, document collection and fieldnotes. Data analysis was based on three hierarchical levels of spatial structuring, comprising a pre-structural level, a local structuring level and a, more sophisticated, global structuring level. Results suggest that students start by establishing local relationships before establishing global relationships, either in composing or decomposing shapes. Hence, spatial reasoning processes are involved with spatial structuring and seem to contribute to deepen students’ understanding of shapes structures, in two-dimensional and three-dimensional shapes and in the relationship between two and three-dimensionality. Composing and decomposing shapes emerge as two spatial reasoning processes that allow analysing and understanding shapes’ structures, while other processes such as rotating, flipping and folding allow deepening shapes’ intrinsic relationships and establishing relationships between two and three dimensionality. Also, the complexity of spatial reasoning processes students use seems to depend on their spatial structuring level. Both spatial structuring and spatial reasoning seem to be influenced by the use of manipulatives and by the drawings students make of the shapes. A set of principles emerged from this research that support a conjecture about how to enhance spatial structuring, in early grades.
This study aims to understand how first grade students develop their understanding of two and three-dimensional shapes’ structures, and what role spatial reasoning plays in that structuring, in the context of a design-based research. The theoretical framework is focused on spatial structuring as a form of creating mental representations. Assuming that these representations are based on relationships that are established and that emerge from the interaction between concrete and abstract, spatial reasoning is mobilized as a set of processes that allow understanding and transforming space. Manipulatives and drawings assume a prominent role in the process of abstraction. The study follows a design-based research method, where a teaching experiment, with design micro-cycles, has been conducted, in a 1st grade class, with 24 students and their teacher. 19 tasks where implemented, through 20 lessons with about 60 minutes each. From the 24 students, 4 were selected for an in-dept analysis. It also has been collected and analysed the contributes of all 24 students, during whole-class discussions. Data was collected through participant observation, with audio and video recording, document collection and fieldnotes. Data analysis was based on three hierarchical levels of spatial structuring, comprising a pre-structural level, a local structuring level and a, more sophisticated, global structuring level. Results suggest that students start by establishing local relationships before establishing global relationships, either in composing or decomposing shapes. Hence, spatial reasoning processes are involved with spatial structuring and seem to contribute to deepen students’ understanding of shapes structures, in two-dimensional and three-dimensional shapes and in the relationship between two and three-dimensionality. Composing and decomposing shapes emerge as two spatial reasoning processes that allow analysing and understanding shapes’ structures, while other processes such as rotating, flipping and folding allow deepening shapes’ intrinsic relationships and establishing relationships between two and three dimensionality. Also, the complexity of spatial reasoning processes students use seems to depend on their spatial structuring level. Both spatial structuring and spatial reasoning seem to be influenced by the use of manipulatives and by the drawings students make of the shapes. A set of principles emerged from this research that support a conjecture about how to enhance spatial structuring, in early grades.
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Palavras-chave
Estruturação espacial raciocínio espacial articulação 2D/3D desenhos materiais manipuláveis primeiros anos Spatial structuring spatial reasoning integration 2D/3D drawings manipulatives early grades