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Resolução de tarefas de divisão: um estudo com alunos do 4º ano de escolaridade
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O presente estudo tem como objetivo compreender o modo como os alunos do 4.º ano resolvem tarefas matemáticas, associadas à operação divisão. Neste âmbito, foram definidas as seguintes questões: (i) Quais são as estratégias usadas pelos alunos na resolução de tarefas de divisão? e (ii) Que dificuldades manifestam os alunos na resolução de tarefas de divisão?.
O quadro teórico integra três temáticas fundamentais para este estudo: aprender matemática com compreensão; o papel do professor na aprendizagem da Matemática e a aprendizagem da divisão.
O estudo segue uma metodologia qualitativa e interpretativa, e tem como participantes quatro alunos de uma turma de 4.º ano.
Foi organizada uma intervenção na turma de 4.º ano que consistiu num conjunto de quatro sequências de tarefas propostas aos alunos num contexto de sala de aula. De modo a caracterizar as suas estratégias de resolução e as suas dificuldades foram selecionados quatro alunos.
A análise das estratégias usadas pelos quatro alunos selecionados e as dificuldades que manifestaram quando resolvem tarefas, associadas à operação da divisão evidenciam que: (i) a resolução das tarefas propostas dependem do conhecimento que cada aluno tem das quatro operações; (ii) utilizam uma variedade de estratégias; (iii) há alunos que usam mais do que uma estratégia na mesma tarefa. Os resultados mostram, ainda que as dificuldades manifestadas pelos alunos resultam de não estarem consciencializados para a relação inversa entre a divisão e a multiplicação e o uso de subtrações sucessivas para resolverem tarefas associadas à divisão.
The present study aims at understanding how students from the fourth grade solve mathematical tasks associated with the division operation. In this context, I defined the following questions: (i) What are the strategies used by students in solving division problems? and ( ii ) What difficulties affect students in solving division problems? The theoretical framework integrates three key themes for this study: to learn mathematics with understanding, the teacher's role in learning mathematics and learning division. The study follows a qualitative and interpretive methodology, and has four students from a class of fourth grade as participants. An intervention was organized in a class of fourth grade, and it consisted in a set of four sequences of tasks proposed to students in the context of the classroom. In order to characterize their resolution strategies and their difficulties, four students were selected. The analysis of the strategies used by the four selected students and the difficulties they manifested when they solve tasks related to the division operation show that: (i) the resolution of the proposed tasks depends on the knowledge that every student has of the four operations, (ii) the students use a variety of strategies; (iii) there are students who use more than one strategy in the same task. The results show also that the difficulties manifested by students exist because they are unaware of the inverse relationship between multiplication and division and using successive subtraction to solve tasks associated with the division.
The present study aims at understanding how students from the fourth grade solve mathematical tasks associated with the division operation. In this context, I defined the following questions: (i) What are the strategies used by students in solving division problems? and ( ii ) What difficulties affect students in solving division problems? The theoretical framework integrates three key themes for this study: to learn mathematics with understanding, the teacher's role in learning mathematics and learning division. The study follows a qualitative and interpretive methodology, and has four students from a class of fourth grade as participants. An intervention was organized in a class of fourth grade, and it consisted in a set of four sequences of tasks proposed to students in the context of the classroom. In order to characterize their resolution strategies and their difficulties, four students were selected. The analysis of the strategies used by the four selected students and the difficulties they manifested when they solve tasks related to the division operation show that: (i) the resolution of the proposed tasks depends on the knowledge that every student has of the four operations, (ii) the students use a variety of strategies; (iii) there are students who use more than one strategy in the same task. The results show also that the difficulties manifested by students exist because they are unaware of the inverse relationship between multiplication and division and using successive subtraction to solve tasks associated with the division.
Descrição
Mestrado em Educação Pré-Escolar e Ensino do 1º Ciclo do Ensino Básico
Palavras-chave
Aprendizagem da divisão Estratégicas usadas pelos alunos Tarefas matemáticas Alunos do 1º ciclo do ensino básico Division learning Strategies used by pupils Mathematics tasks Pupils of basic primary school Relatório de projeto de investigação Relatório de estágio
Contexto Educativo
Citação
Editora
Escola Superior de Educação, Instituto Politécnico de Setúbal