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Publication
Representações usadas na resolução de problemas
| Name: | Description: | Size: | Format: | |
|---|---|---|---|---|
| 1.74 MB | Adobe PDF |
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Abstract(s)
O estudo que apresento tem como propósito analisar e compreender as representações matemáticas que os alunos utilizam para resolver problemas e o seu papel no processo de resolução. Para tal efeito, formulei duas questões: 1. Que representações usam os alunos para resolver problemas? 2. Que funções têm as representações usadas pelos alunos e como se relacionam? No enquadramento teórico debruço-me sobre a importância da resolução de problemas, o significado de problema, tipologias de classificação de problemas de um ponto de vista educativo e aspetos importantes do processo de ensinar a resolver problemas. Além disso, refiro o significado e o papel das representações matemáticas, tipos de representações e a relevância de se estabelecer conexões entre elas.
Em termos metodológicos, este estudo enquadra-se numa abordagem qualitativa de investigação e constitui uma investigação sobre a prática. Como métodos de recolha de dados, usei a observação participante, a recolha documental e entrevistas clínicas. Os participantes deste estudo foram alunos de uma turma do 3.º ano de escolaridade, de uma escola de Setúbal. Durante o tempo dedicado à intervenção pedagógica explorei seis problemas, integrados no domínio Números e Operações, em contexto de sala aula. No
final do estágio, selecionei dois alunos, a quem realizei entrevistas clínicas, tendo por ponto de partida a proposta de resolução de problemas.
Os resultados deste estudo relevam que as representações ativas não tiveram grande destaque enquanto meio de apoio à resolução de problemas. Os alunos recorreram, na grande maioria, a dois tipos de representações: icónicas e simbólicas. No que se refere ao primeiro tipo, usaram esquemas ou diagramas para organizar visualmente as informações de que dispunham e para resolver os problemas. Além disso, utilizaram desenhos com a mesma função que se caracterizavam por serem pouco pormenorizados.
As representações simbólicas eram usadas para resolver o problema e para verificar o resultado. A maioria das representações icónicas tinham, também, elementos simbólicos, nomeadamente números ou operações. Saliento que, habitualmente, partiam das representações menos abstratas para as mais simbólicas, estabelecendo relações entre si.
The purpose of this study is to analyze and understand the mathematical representations that students use to solve problems and their role in the resolution process. To that end, I posed two questions: 1. What representations do students use to solve problems? 2. What functions do the representations used by the students have and how do they relate? In the theoretical framework I dwell on the importance of problem solving, the meaning of problem, types of problems from an educational point of view and important aspects of the process of teaching to solve problems. In addition, I refer to the meaning and role of mathematical representations, types of representations, and the relevance of establishing connections between them. In methodological terms, this study is part of a qualitative research approach and is an investigation of the practice. As methods of data collection, I used participant observation, documentary collection, and clinical interviews. The participants of this study were 3rd grade students, from a school in Setúbal. During the time dedicated to the pedagogical intervention I explored six problems, integrated in the domain “Numbers and Operations”, in a classroom context. At the end of the internship, I selected two students, to whom I conducted clinical interviews, using a problem solving proposition as a starting point. The results of this study show that the active representations did not stand out as a means of supporting problem solving. The majority of students used two types of representations: iconic and symbolic. For the first type, they used schemes or diagrams to visually organize the information they had and to solve the problems. In addition, they used drawings with the same function that were characterized by being less detailed. Symbolic representations were used to solve the problem and to verify the result. Most iconic representations also had symbolic elements, namely numbers or operations. I emphasize that they usually went from less abstract representations to more symbolic ones, establishing relations between them.
The purpose of this study is to analyze and understand the mathematical representations that students use to solve problems and their role in the resolution process. To that end, I posed two questions: 1. What representations do students use to solve problems? 2. What functions do the representations used by the students have and how do they relate? In the theoretical framework I dwell on the importance of problem solving, the meaning of problem, types of problems from an educational point of view and important aspects of the process of teaching to solve problems. In addition, I refer to the meaning and role of mathematical representations, types of representations, and the relevance of establishing connections between them. In methodological terms, this study is part of a qualitative research approach and is an investigation of the practice. As methods of data collection, I used participant observation, documentary collection, and clinical interviews. The participants of this study were 3rd grade students, from a school in Setúbal. During the time dedicated to the pedagogical intervention I explored six problems, integrated in the domain “Numbers and Operations”, in a classroom context. At the end of the internship, I selected two students, to whom I conducted clinical interviews, using a problem solving proposition as a starting point. The results of this study show that the active representations did not stand out as a means of supporting problem solving. The majority of students used two types of representations: iconic and symbolic. For the first type, they used schemes or diagrams to visually organize the information they had and to solve the problems. In addition, they used drawings with the same function that were characterized by being less detailed. Symbolic representations were used to solve the problem and to verify the result. Most iconic representations also had symbolic elements, namely numbers or operations. I emphasize that they usually went from less abstract representations to more symbolic ones, establishing relations between them.
Description
Keywords
Aprendizagem da matemática Resolução de problemas Representações matemáticas Funções das representações Mathematical representations Function of representations Relatório de projeto de investigação Relatório de estágio Problem solving Mathematical representations