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Aprender frações a partir de diferentes contextos: um estudo no 3.º ano
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O presente projeto investigativo tem como objetivo principal compreender como é que diferentes contextos contribuem para a compreensão do conceito de fração nos alunos de 3.º ano de escolaridade. A investigação desenvolveu-se em contexto de estágio pedagógico ao longo de sete semanas, inserindo-se numa abordagem qualitativa e no âmbito da investigação sobre a prática e com o intuito de conseguir responder às questões de investigação: “Que significados de fração os alunos utilizam nos diferentes contextos?” e “Que representações os alunos usam no diferentes contextos explorados?”. Ao longo da realização deste projeto investigativo foram implementadas quatro tarefas cuidadosamente selecionadas e desenhadas com contextos diversos, de modo a explorar diferentes significados de fração e de tipos de representações (físicas, visuais, verbais, simbólicas e contextuais). A recolha dos dados foi feita através da observação participante, com registos áudio das discussões matemáticas, e da recolha documental das produções dos alunos.
Os resultados evidenciam que o contexto desempenha um papel determinante na forma como os alunos interpretam e utilizam os significados de fração, tendo utilizado sobretudo o significado parte–todo em contextos com unidades contínuas ou visuais claramente identificáveis, como alimentos, figuras geométricas ou pizas. Já o significado de fração como quociente emergiu de forma mais marcada nas tarefas de partilha equitativa, onde a própria natureza do contexto favorecia a interpretação da fração enquanto resultado de uma divisão. Os resultados revelam ainda que os alunos recorreram a um conjunto diversificado de representações, com predominância das representações verbais, utilizadas para justificar decisões e descrever procedimentos, e das representações simbólicas, ativadas sempre que o objetivo da tarefa exigia o registo formal das frações. As representações visuais foram particularmente eficazes na clarificação da unidade e as representações contextuais permitiram atribuir significado às ações matemáticas, sobretudo em situações de partilha ou nas narrativas provenientes da literatura infantil. Desta forma, o estudo conclui que a aprendizagem das frações é fortemente influenciada pela qualidade dos contextos propostos, pela clareza das tarefas e pela diversidade de representações que os alunos podem mobilizar. A inclusão de materiais manipuláveis, de narrativas significativas e de cenários do quotidiano facilita a construção conceptual e aproxima os alunos de um entendimento mais flexível e profundo do número racional. Contudo, evidencia-se igualmente a necessidade de um trabalho continuado e sistemático, capaz de apoiar os alunos na transição gradual entre diferentes significados e formas de representação, promovendo uma compreensão mais integrada e duradoura do conceito de fração.
The present research project aims primarily to understand how different contexts contribute to third-grade students’ understanding of the concept of fractions. The study was conducted within the context of a teaching practicum over a seven-week period, following a qualitative approach and framed within research on practice, with the purpose of addressing the following research questions: “Which meanings of fractions do students use in different contexts?” and “Which representations do students use in the different contexts explored?”. Throughout the development of this research project, four carefully selected and designed tasks were implemented in diverse contexts in order to explore different meanings of fractions and different types of representations (physical, visual, verbal, symbolic, and contextual). Data were collected through participant observation, including audio recordings of mathematical discussions, as well as through the documentary collection of students’ work. The results show that context plays a decisive role in how students interpret and use fraction meanings. Students predominantly used the part–whole meaning in contexts involving continuous units or clearly identifiable visual representations, such as food, geometric figures, or pizzas. In contrast, the meaning of fraction as a quotient emerged more strongly in tasks involving equitable sharing, where the nature of the context itself supported the interpretation of fractions as the result of a division. The findings also reveal that students made use of a wide range of representations, with a predominance of verbal representations, used to justify decisions and describe procedures, and symbolic representations, activated whenever the task required the formal recording of fractions. Visual representations proved particularly effective in clarifying the unit, while contextual representations helped attribute meaning to mathematical actions, especially in sharing situations or narratives drawn from children’s literature. In conclusion, the study highlights that learning fractions is strongly influenced by the quality of the proposed contexts, the clarity of the tasks, and the diversity of representations that students are able to mobilize. The inclusion of manipulatives, meaningful narratives, and everyday-life scenarios facilitates conceptual construction and brings students closer to a more flexible and deeper understanding of rational numbers. Nevertheless, the study also points to the need for sustained and systematic work to support students in the gradual transition between different meanings and forms of representation, promoting a more integrated and long-lasting understanding of the concept of fractions.
The present research project aims primarily to understand how different contexts contribute to third-grade students’ understanding of the concept of fractions. The study was conducted within the context of a teaching practicum over a seven-week period, following a qualitative approach and framed within research on practice, with the purpose of addressing the following research questions: “Which meanings of fractions do students use in different contexts?” and “Which representations do students use in the different contexts explored?”. Throughout the development of this research project, four carefully selected and designed tasks were implemented in diverse contexts in order to explore different meanings of fractions and different types of representations (physical, visual, verbal, symbolic, and contextual). Data were collected through participant observation, including audio recordings of mathematical discussions, as well as through the documentary collection of students’ work. The results show that context plays a decisive role in how students interpret and use fraction meanings. Students predominantly used the part–whole meaning in contexts involving continuous units or clearly identifiable visual representations, such as food, geometric figures, or pizzas. In contrast, the meaning of fraction as a quotient emerged more strongly in tasks involving equitable sharing, where the nature of the context itself supported the interpretation of fractions as the result of a division. The findings also reveal that students made use of a wide range of representations, with a predominance of verbal representations, used to justify decisions and describe procedures, and symbolic representations, activated whenever the task required the formal recording of fractions. Visual representations proved particularly effective in clarifying the unit, while contextual representations helped attribute meaning to mathematical actions, especially in sharing situations or narratives drawn from children’s literature. In conclusion, the study highlights that learning fractions is strongly influenced by the quality of the proposed contexts, the clarity of the tasks, and the diversity of representations that students are able to mobilize. The inclusion of manipulatives, meaningful narratives, and everyday-life scenarios facilitates conceptual construction and brings students closer to a more flexible and deeper understanding of rational numbers. Nevertheless, the study also points to the need for sustained and systematic work to support students in the gradual transition between different meanings and forms of representation, promoting a more integrated and long-lasting understanding of the concept of fractions.
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Palavras-chave
Contextos Tipos de Representações Significados das Frações Contexts Representations Meanings of Fractions