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Representações matemáticas na resolução de problemas no 1.º ano de escolaridade
| Name: | Description: | Size: | Format: | |
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| 1.75 MB | Adobe PDF |
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Abstract(s)
Pressupõe-se que a resolução de problemas, capacidade matemática englobante, envolva a utilização de conhecimentos e técnicas matemáticas formais. Contudo, os alunos nem sempre conseguem solucioná-los da forma pretendida, não conseguindo explicar o seu pensamento. Para resolver problemas matemáticos, podemos recorrer a várias representações que, por sua vez, são uma forma de expressar ideias e conceitos matemáticos através de múltiplas formas, sejam elas operações numéricas ou desenhos. A questão surge ao pensar que se abrirmos o leque de possibilidades de representação, os alunos conseguirão mais facilmente explicar e representar o seu pensamento. Neste seguimento, indagou-se quais seriam as representações utilizadas por alunos de 1.º ano de escolaridade que ainda estão no começo do seu percurso escolar e que ainda não têm um aprofundado conhecimento da matemática formal.
A presente investigação foi realizada com uma turma de 1.º ano de escolaridade, pertencente a uma escola em contexto rural, em Loulé – Algarve, no ano letivo 2023/2024. Foram apresentados aos participantes, oito problemas matemáticos, os quais foram resolvidos recorrendo a várias tipologias de representação. De forma a estudar quais as representações que surgiriam, foi deixado ao critério dos alunos que representação utilizar e posteriormente, foram solicitados três alunos em cada aula para apresentar o seu trabalho. As apresentações foram gravadas em vídeo e em áudio e as produções dos alunos recolhidas, servindo estes meios de suporte à apresentação e análise dos dados.
Ao analisar os dados conclui-se que a tipologia de representação mais utilizada foi a representação gráfica, recorrendo a desenhos, enquanto a representação algébrica, relacionada com variáveis que misturam números e letras, demarcou-se como ausente. Por outro lado, a representação verbal teve alguma expressão no início da intervenção educativa, porém foi a representação numérica ou aritmética, relacionada com o uso de operações numéricas, que obteve um maior crescimento no seu aparecimento, começando a ganhar expressão entre as resoluções, à medida que os alunos iam apresentando os seus trabalhos.
It is assumed that problem solving, an all-encompassing mathematical skill, involves the use of formal mathematical knowledge and techniques. However, students don't always manage to solve them in the way they intended and are unable to explain their thinking. To solve mathematical problems, we can use various representations which, in turn, are a way of expressing mathematical ideas and concepts in multiple ways, be they numerical operations or drawings. The question arises when we think that if we open up the range of representation possibilities, students will be able to explain and represent their thinking more easily. In this context, we wondered what representations are used by first-year students who are still at the beginning of their school career and who do not yet have a deep knowledge of formal maths. This research was carried out with a 1st year class from a rural school in Loulé - Algarve, in the 2023/2024 school year. The participants were presented with eight mathematical problems, which were solved using various types of representation. In order to study which representations would emerge, it was left to the students' discretion which representation to use and then three students were asked in each class to present their work. The presentations were video and audio recorded, and the students' productions were collected to support the presentation and analysis of the data. Analysing the data shows that the most used type of representation was graphical, using drawings, while algebraic representation, related to variables that mix numbers and letters, was absent. On the other hand, verbal representation had some expression at the start of the educational intervention, but it was numerical or arithmetical representation, related to the use of numerical operations, that saw the greatest growth in its appearance, beginning to gain expression among the resolutions as the students presented their work.
It is assumed that problem solving, an all-encompassing mathematical skill, involves the use of formal mathematical knowledge and techniques. However, students don't always manage to solve them in the way they intended and are unable to explain their thinking. To solve mathematical problems, we can use various representations which, in turn, are a way of expressing mathematical ideas and concepts in multiple ways, be they numerical operations or drawings. The question arises when we think that if we open up the range of representation possibilities, students will be able to explain and represent their thinking more easily. In this context, we wondered what representations are used by first-year students who are still at the beginning of their school career and who do not yet have a deep knowledge of formal maths. This research was carried out with a 1st year class from a rural school in Loulé - Algarve, in the 2023/2024 school year. The participants were presented with eight mathematical problems, which were solved using various types of representation. In order to study which representations would emerge, it was left to the students' discretion which representation to use and then three students were asked in each class to present their work. The presentations were video and audio recorded, and the students' productions were collected to support the presentation and analysis of the data. Analysing the data shows that the most used type of representation was graphical, using drawings, while algebraic representation, related to variables that mix numbers and letters, was absent. On the other hand, verbal representation had some expression at the start of the educational intervention, but it was numerical or arithmetical representation, related to the use of numerical operations, that saw the greatest growth in its appearance, beginning to gain expression among the resolutions as the students presented their work.
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Keywords
1.º ciclo do ensino básico Matemática Representações matemáticas Resolução de problemas