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A aprendizagem da multiplicação e divisão através do uso de tarefas paralelas
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Abstract(s)
O presente relatório de investigação integra a área da Matemática e tem como principal
objetivo compreender o modo como o uso de tarefas com diferentes graus de dificuldade (tarefas
paralelas) associadas à multiplicação e divisão numa turma de 3.º ano contribui para a
aprendizagem destas operações. Como questões orientadoras foram definidas as seguintes: (i)
‘Quais as estratégias usadas pelos alunos do 3.º ano quando resolvem tarefas com diferentes
graus de dificuldade associadas à multiplicação?’; (ii) ‘Quais as estratégias usadas pelos alunos
do 3.º ano quando resolvem tarefas com diferentes graus de dificuldade associadas à divisão,
recorrendo ou não, à multiplicação?’ e (iii) ‘Que dificuldades manifestam os alunos do 3.º ano
quando resolvem tarefas com diferentes graus de dificuldade associadas à multiplicação e à
divisão?”.
A fundamentação teórica inclui, essencialmente, os tópicos: a aprendizagem da
multiplicação e da divisão e a sua progressão, as dificuldades sentidas associadas a estas
operações, a relação entre as operações multiplicação e divisão, tarefas que promovem a
aprendizagem da multiplicação e divisão, cálculo mental associado à multiplicação e à divisão,
diferenciar no ensino de Matemática recorrendo a tarefas com diferentes níveis de dificuldades.
Relativamente à metodologia, este estudo segue uma abordagem qualitativa e está
associado ao paradigma interpretativo. Na investigação participaram vinte e um alunos de uma
turma de 3.º ano de escolaridade, tendo sido escolhidos dois deles para uma análise mais
profunda das suas produções nas tarefas propostas. Para além da análise destas, foram analisadas
as gravações vídeo das discussões coletivas, que complementam a observação participante
realizada.
As conclusões deste estudo evidenciam que: (1) os alunos quando resolvem tanto tarefas
de multiplicação como de divisão, recorrem maioritariamente ao uso de estratégias
multiplicativas, (2) nas primeiras tarefas de multiplicação, recorrem também a estratégias
aditivas, (3) a estratégia multiplicativa mais utilizada pelos alunos é o uso de um produto
conhecido, (4) na última tarefa de divisão, há alunos que mostram compreender a relação entre
multiplicação e divisão, (5) as principais dificuldades manifestadas pelos alunos relacionam-se
com a interpretação dos enunciados e justificação dos raciocínios.
Embora o estudo tenha sido limitado no tempo, o recurso ao uso de tarefas com diferentes
graus de dificuldade parece ter contribuído para a maior parte dos alunos da turma terem
progredido na aprendizagem da multiplicação e divisão.
This study on the field of Mathematics aims to understand the way parallel tasks of different degrees of difficulty, associated with multiplication and division in a 3rd year class contributes to their learning arithmetic operations. The main questions of this study are: (i) “Which strategies are used by 3rd year students when they solve tasks with different degrees of difficulty associated with multiplication”?; (ii) “Which strategies are used by 3rd year students when they solve division tasks with different degrees of difficulty, using or not multiplication?” and (iii) “What are the difficulties, 3rd year students face, when they solve tasks with different degrees of difficulty associated to multiplication and division?”. The theoretical framework includes essentially: the learning process of multiplication and division and their progression, the difficulties faced by the students, how multiplication and division calculi are related, strategies that help their learning process, mental calculus associated to these calculation operations, differentiating in the mathematics teaching using tasks of different degrees of difficulty. Regarding the methodology, this study follows qualitative and interpretative approaches. All 21 students participated in the classroom intervention and two of them were selected for a deepest analysis of their resolutions. I also analysed video recordings of the classes’ discussions, which complemented my own observations. The final results of this project suggest that: (1) when students solve multiplication and division tasks, they use mainly multiplication strategies, (2) in their first multiplication strategies they also used addition strategies, (3) the most used multiplication strategy is the use of a known product, (4) in their last division task, there are students showing their understanding about the relation between multiplication and division, (5) their main difficulties are related to the interpretation of the question and the justification of their thoughts. Although this study has its duration as a limitation, the use of tasks of different degrees of difficulty seems to have contributed for the learning of multiplication and division and its progression for the most part of the students.
This study on the field of Mathematics aims to understand the way parallel tasks of different degrees of difficulty, associated with multiplication and division in a 3rd year class contributes to their learning arithmetic operations. The main questions of this study are: (i) “Which strategies are used by 3rd year students when they solve tasks with different degrees of difficulty associated with multiplication”?; (ii) “Which strategies are used by 3rd year students when they solve division tasks with different degrees of difficulty, using or not multiplication?” and (iii) “What are the difficulties, 3rd year students face, when they solve tasks with different degrees of difficulty associated to multiplication and division?”. The theoretical framework includes essentially: the learning process of multiplication and division and their progression, the difficulties faced by the students, how multiplication and division calculi are related, strategies that help their learning process, mental calculus associated to these calculation operations, differentiating in the mathematics teaching using tasks of different degrees of difficulty. Regarding the methodology, this study follows qualitative and interpretative approaches. All 21 students participated in the classroom intervention and two of them were selected for a deepest analysis of their resolutions. I also analysed video recordings of the classes’ discussions, which complemented my own observations. The final results of this project suggest that: (1) when students solve multiplication and division tasks, they use mainly multiplication strategies, (2) in their first multiplication strategies they also used addition strategies, (3) the most used multiplication strategy is the use of a known product, (4) in their last division task, there are students showing their understanding about the relation between multiplication and division, (5) their main difficulties are related to the interpretation of the question and the justification of their thoughts. Although this study has its duration as a limitation, the use of tasks of different degrees of difficulty seems to have contributed for the learning of multiplication and division and its progression for the most part of the students.
Description
Keywords
Aprendizagem da multiplicação Aprendizagem da divisão Tarefas paralelas Diferenciação em matemática Multiplication learning Division learning Parallel strategies Differentation in mathematics