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A aprendizagem da adição e subtração através da resolução de problemas
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| 3.12 MB | Adobe PDF |
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Abstract(s)
O presente estudo foca-se na resolução de problemas de adição e subtração no contexto do 2.º ano de escolaridade, tendo como objetivo compreender o modo como os alunos resolvem esses problemas. Mais concretamente, pretende identificar as estratégias utilizadas pelos alunos, compreender as dificuldades que manifestam e perceber se, no final do estudo, houve mudanças nas estratégias utilizadas. A fundamentação teórica inclui, essencialmente, os seguintes tópicos: o sentido de número e cálculo mental; a aprendizagem das operações de adição e subtração e a resolução de problemas destas operações; as estratégias de adição e subtração; as dificuldades na resolução de problemas de adição e subtração; e, finalmente, a resolução de problemas destas operações nas orientações curriculares. Do ponto de vista metodológico, esta investigação caracteriza-se como qualitativa e enquadra-se num paradigma interpretativo. Nela participaram 17 alunos pertencentes a uma turma do 2.º ano de escolaridade, tendo sido escolhidos 2 desses alunos para uma análise aprofundada das suas resoluções. A recolha de dados ocorreu ao longo de quatro semanas e meia através da observação participante, de entrevistas clínicas e da análise documental. A análise dos catorze problemas, construídos ou adaptados por mim, teve por base as produções escritas de dois alunos permitindo obter conclusões desta investigação. Os resultados deste estudo evidenciam que: (1) os alunos recorrem a três tipos de representação do cálculo para resolver os problemas: horizontal, vertical e através da reta numérica; (2) as estratégias mais utilizadas são a 1010, uma próxima ao algoritmo e a N10; (3) nos problemas de subtração com sentido completar e comparar os alunos tendem a utilizar estratégias aditivas, enquanto que nos problemas com sentido retirar não se verifica qualquer preferência; (4) as principais dificuldades relacionam-se com a interpretação de enunciados, a seleção e utilização correta das estratégias, a interpretação dos resultados e a justificação dos raciocínios; (5) os alunos tiveram oportunidade de conhecer e manipular um modelo de apoio ao cálculo, a reta numérica, que os conduziu à utilização de novas estratégias.
The present study focuses on solving addition and subtraction problems in the context of the second grade, aiming at how students solve these problems. More specifically, it intends to identify the strategies used by the students, to understand the difficulties they manifest and to perceive if, at the end of the study, there were changes in the strategies used. The theoretical framework includes, essentially, the following topics: number sense and mental calculation; learning the operations of addition and subtraction and problems solving with these operations; addition and subtraction strategies; difficulties in solving addition and subtraction problems; and, finally, the resolution of problems with these operations in the curricular guidelines. From the methodological point of view, this research is characterized as qualitative and fits into an interpretative paradigm. The study involves seventeen students belonging to a second grade, and two of these students were chosen for an in-depth analysis of their resolutions. Data collection took place over four and a half weeks through participant observation, clinical interviews, and documental analysis. The analysis of the fourteen problems, constructed or adapted by me, was based on the written productions of two students, allowing to obtain the conclusions of this investigation. The results of this study show that: (1) students use three types of calculus representation to solve the problems: horizontal, vertical and across the number line; (2) the most commonly used strategies are 1010, close to the algorithm, and N10; (3) in the subtraction problems with meaning to complete and compare the students tend to use additive strategies, while in the problems with withdraw sense there is no preference; (4) the main difficulties are related to the interpretation of the problems statements, selection and correct use of strategies, interpretation of results and justification of reasoning; (5) the students had the opportunity to know and manipulate a model of support to the calculation, the numerical line, that led them to use new strategies.
The present study focuses on solving addition and subtraction problems in the context of the second grade, aiming at how students solve these problems. More specifically, it intends to identify the strategies used by the students, to understand the difficulties they manifest and to perceive if, at the end of the study, there were changes in the strategies used. The theoretical framework includes, essentially, the following topics: number sense and mental calculation; learning the operations of addition and subtraction and problems solving with these operations; addition and subtraction strategies; difficulties in solving addition and subtraction problems; and, finally, the resolution of problems with these operations in the curricular guidelines. From the methodological point of view, this research is characterized as qualitative and fits into an interpretative paradigm. The study involves seventeen students belonging to a second grade, and two of these students were chosen for an in-depth analysis of their resolutions. Data collection took place over four and a half weeks through participant observation, clinical interviews, and documental analysis. The analysis of the fourteen problems, constructed or adapted by me, was based on the written productions of two students, allowing to obtain the conclusions of this investigation. The results of this study show that: (1) students use three types of calculus representation to solve the problems: horizontal, vertical and across the number line; (2) the most commonly used strategies are 1010, close to the algorithm, and N10; (3) in the subtraction problems with meaning to complete and compare the students tend to use additive strategies, while in the problems with withdraw sense there is no preference; (4) the main difficulties are related to the interpretation of the problems statements, selection and correct use of strategies, interpretation of results and justification of reasoning; (5) the students had the opportunity to know and manipulate a model of support to the calculation, the numerical line, that led them to use new strategies.
Description
Keywords
Aprendizagem da adição e subtração Estratégias de adição e subtração Resolução de problemas Dificuldades dos alunos Learning of addition and subtraction Addition and subtraction strategies Problem solving Difficulties of students Relatório de projeto de investigação Relatório de estágio