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Desenvolvimento do raciocínio proporcional em alunos de 6º ano
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Orientador(es)
Resumo(s)
Este estudo foi realizado com alunos de uma turma de 6° ano, tendo como
principal objectivo analisar o modo como se desenvolve o raciocínio proporcional e
identificar as principais dificuldades que os alunos manifestam em conceitos ligados à
proporcionalidade directa. Foi elaborada uma proposta pedagógica em que se
privilegiou a resolução de problemas e se procurou confrontar os alunos com uma
diversidade de situações envolvendo o raciocínio proporcional.
Trata-se de um estudo empírico de natureza qualitativa, em que foram recolhidos
dados relativamente à globalidade da turma e dados mais aprofundados de um grupo
mais restrito de alunos, através de entrevistas.
A análise realizada indica-nos que existem elementos comuns a um conjunto
alargado de investigação nacional e internacional sobre esta temática, nomeadamente a
aplicação do raciocínio aditivo no inicio do estudo, a aplicação do raciocínio
multiplicativo à medida que os alunos reconhecem similaridades estruturais em
problemas de proporcionalidade directa, as dificuldades em estabelecer relações de
primeira-ordem e na conversão de percentagens em número racional.
No entanto, este estudo permite-nos também reflectir sobre a especificidade do
nosso currículo do ensino básico, no que diz respeito a este tema, e das consequências
que as opções programáticas poderão ter na possibilidade de desenvolvimento do
raciocínio proporcional nos alunos deste nível de escolaridade.
This study was done with a 6th grade mathematics class, and aimed to analyse the development of students' proportional reasoning and the main difficulties that they express in this domain. The mathematical theme "Direct Proportional" was developed mainly through problem solving and intended to have students experiencing a diversity of situations involving proportional reasoning. This is an empirical study, framed by a qualitative approach. There were constructed three case studies, using mainly the interview and the students' classroom productions as data collection process. The analysis produced shows us that there exist many common elements to a large number of results being produced by national and international research. For instance, students use mainly additive reasoning in the beginning of the study, they start using the multiplicative reasoning as they begin to recognize the structural similitude in problems involving proportion, and some of them express some difficulties in establishing first order relations and in converting percentage in a rational number. The study permit us to reflect on the specificity of the national curriculum in this theme, and of the consequences that the options being made by the cycle of basic education's syllabus might have on the development of students' proportional reasoning
This study was done with a 6th grade mathematics class, and aimed to analyse the development of students' proportional reasoning and the main difficulties that they express in this domain. The mathematical theme "Direct Proportional" was developed mainly through problem solving and intended to have students experiencing a diversity of situations involving proportional reasoning. This is an empirical study, framed by a qualitative approach. There were constructed three case studies, using mainly the interview and the students' classroom productions as data collection process. The analysis produced shows us that there exist many common elements to a large number of results being produced by national and international research. For instance, students use mainly additive reasoning in the beginning of the study, they start using the multiplicative reasoning as they begin to recognize the structural similitude in problems involving proportion, and some of them express some difficulties in establishing first order relations and in converting percentage in a rational number. The study permit us to reflect on the specificity of the national curriculum in this theme, and of the consequences that the options being made by the cycle of basic education's syllabus might have on the development of students' proportional reasoning
Descrição
Tese de mestrado em Educação (Didáctica da Matemática), apresentada à Universidade de Lisboa através da Faculdade de Ciências, 2007
Palavras-chave
Raciocínio Resolução de problemas Proporcionalidade Aprendizagem da matemática Teses de mestrado - 2007