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O uso das estratégias de cálculo mental por alunos do 3º ano de escolaridade
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| 3.59 MB | Adobe PDF |
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Abstract(s)
O cálculo mental, essencial ao longo da vida, deve ser desenvolvido desde os primeiros anos de escolaridade, através do contacto com diversas experiências. A matemática é para todos e, tal como o NCTM defende, aqueles que compreendem e são capazes de fazer matemática terão oportunidades e opções significativamente maiores para construir os seus futuros (NCTM, 2007, p. 5). Para que tal seja possível, o cálculo mental deve ser devidamente desenvolvido e estimulado desde cedo, permitindo um aumento da eficácia de utilização ao longo do tempo. A implementação de rotinas de cálculo mental permite aos alunos o desenvolvimento de estratégias de cálculo flexíveis entre os números, utilizando as propriedades das operações.
O estudo desenvolvido baseia-se na utilização e na evolução das estratégias usadas pelos alunos durante a exploração de tiras de cálculo mental e cadeias numéricas. Para a concretização do mesmo, foram colocadas duas questões: Quais as estratégias de cálculo mental que os alunos usam? Como evoluem as escolhas das estratégias de cálculo mental?
Este estudo foi realizado numa turma com 20 alunos com idades entre os 7 e os 8 anos de idade e seguiu uma metodologia qualitativa de investigação-ação.
Os resultados obtidos permitem afirmar que no final do estudo os alunos se mostram mais à-vontade com algumas estratégias, que parecem ter facilitado o desenvolvimento do raciocínio e da comunicação matemática. Nas diferentes operações apresentadas no estudo os alunos mostraram a sua preferência por algumas estratégias específicas. No que diz respeito às operações de adição os alunos usam mais estratégias de decomposição; na subtração os alunos preferem a estratégia de saltos e, na multiplicação os alunos dividem-se em procedimentos aditivos e procedimentos multiplicativos. Em todas as operações existe sempre um grande número de alunos que apresenta apenas o resultado, não evidenciando o tipo de estratégia utilizada. Com a exploração das cadeias numéricas os alunos usaram algumas estratégias que não tinham sido aplicadas na resolução das tiras, mostrando alguma evolução no desenvolvimento do seu raciocínio, bem como na comunicação.
Mental calculation, essential throughout life, should be developed from the early years of schooling, through contact with diverse experiences. Math is for everyone and, as the NCTM argues, those who understand and are able to do mathematics will have significantly greater opportunities and options to build their future (NCTM, 2007, p. 5). For this to be possible, mental calculation must be properly developed and nurtured from an early age, allowing an efficiency of use increase over time. The implementation of mental calculation routines allows students to develop flexible calculation strategies between the numbers, using the properties of the numerical operations. The present study is based on the use and development of strategies used by students during the exploration of mental calculation strips and numeric strings. To achieve it, two questions were placed: What are the mental calculation strategies that students use? How does the choices of mental calculation strategies develop? This study was conducted in a class with 20 students between the ages of 7 and 8 years old and followed a qualitative methodology of action research. The results indicate that at the end of the study the students were more comfortable with some strategies that seem to have facilitated the development of reasoning and mathematical communication. In different operations presented in the study, the students showed their preference for some specific strategies. With regard to the operations of adding, students used more strategies of decomposition; in the subtraction, students preferred the strategy of jumps and, in multiplication, the students were divided between additive and multiplicative procedures. In all operations there were always a large number of students that only presented the result, not showing the kind of strategy used. With the operation of numeric strings, students used some strategies that had not been applied in the resolution of the strips, showing some evolution in the development of their reasoning, as well as in the communication.
Mental calculation, essential throughout life, should be developed from the early years of schooling, through contact with diverse experiences. Math is for everyone and, as the NCTM argues, those who understand and are able to do mathematics will have significantly greater opportunities and options to build their future (NCTM, 2007, p. 5). For this to be possible, mental calculation must be properly developed and nurtured from an early age, allowing an efficiency of use increase over time. The implementation of mental calculation routines allows students to develop flexible calculation strategies between the numbers, using the properties of the numerical operations. The present study is based on the use and development of strategies used by students during the exploration of mental calculation strips and numeric strings. To achieve it, two questions were placed: What are the mental calculation strategies that students use? How does the choices of mental calculation strategies develop? This study was conducted in a class with 20 students between the ages of 7 and 8 years old and followed a qualitative methodology of action research. The results indicate that at the end of the study the students were more comfortable with some strategies that seem to have facilitated the development of reasoning and mathematical communication. In different operations presented in the study, the students showed their preference for some specific strategies. With regard to the operations of adding, students used more strategies of decomposition; in the subtraction, students preferred the strategy of jumps and, in multiplication, the students were divided between additive and multiplicative procedures. In all operations there were always a large number of students that only presented the result, not showing the kind of strategy used. With the operation of numeric strings, students used some strategies that had not been applied in the resolution of the strips, showing some evolution in the development of their reasoning, as well as in the communication.
Description
Keywords
Cálculo mental Estratégias de cálculo mental Cadeias numéricas Mental calculation Mental calculation strategies Numeric strings Relatório de projeto de investigação Relatório de estágio