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O pensamento algébrico na resolução de problemas com sistemas de duas equações do 1º grau com duas incógnitas em alunos do 8º ano de escolaridade
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Orientador(es)
Resumo(s)
O presente estudo pretendeu compreender o pensamento algébrico de alunos do 8.º
ano de escolaridade na resolução de problemas com sistemas de duas equações do 1.º grau
com duas incógnitas. Com este intuito, procurei compreender os significados que
atribuíram à simbologia matemática e quais as principais dificuldades que revelaram,
apurar qual(is) a(s) estratégia(s) mais utilizada(s) na resolução de problemas e perceber as
razões dessa escolha e, por fim, compreender as principais dificuldades associadas à
tradução e à resolução de situações contextualizadas ou não.
O estudo assenta num paradigma interpretativo, seguindo uma abordagem mista,
usando dados quantitativos e qualitativos. Posicionei-me como observadora participante e
os principais métodos de recolha de dados foram a observação direta, a recolha das
produções escritas dos alunos, as entrevistas e um questionário anónimo. A turma esteve
envolvida na realização das tarefas, no entanto, selecionei quatro pares de alunos para
aprofundamento do estudo, aos quais realizei entrevistas em dois momentos da intervenção
letiva. A análise dos dados seguiu a análise de conteúdo. As questões de natureza ética
foram consideradas neste estudo.
Os resultados obtidos evidenciam que os alunos desenvolveram o pensamento
algébrico. A maioria revelou ter sentido de símbolo, estando a principal dificuldade ligada
ao formalismo do método de substituição. O sentido de variável estava bem desenvolvido,
mas os alunos apresentaram dificuldades na atribuição de significado à incógnita quando
esta não era explicitada no enunciado. A representação algébrica foi a mais escolhida pelos
alunos e a principal razão apontada para esta escolha foi o saber/controlar o que estavam a
fazer. Os alunos demonstraram maior facilidade na interpretação e resolução de problemas
de índole geométrica e nas situações descontextualizadas. A interpretação das situações
dos problemas verbais que traduzem situações próximas ao quotidiano foram dificuldades
acrescidas, não pelo contexto, mas sim pela definição das variáveis.
This study aimed to understand the algebraic thinking of students of the 8th grade in solving problems with systems of two equations of 1st degree with two unknowns. To this end, I sought to understand the meanings they attributed to the mathematical symbols and the main difficulties they revealed, in order to determine and understand which strategy(s) is/are most used to solve problems and the reasons for that choice and finally to recognize the main difficulties associated with the translation and resolution of contextualized situations or not. The study is based on an interpretative paradigm, following a mixed approach, using quantitative and qualitative data. I positioned myself as a participant observer and the main data collection methods were direct observation, collection of written productions of the students, interviews and an anonymous questionnaire. The class was involved in the tasks; however, I selected four pairs of students for further study, to whom I conducted interviews in two moments of the teaching intervention. Data analysis followed the content analysis. Ethical issues were considered in this study. The results obtained show that the students developed algebraic thinking. Most of them have revealed knowing the sense of symbol and the main difficulty shown is linked to the formalism of the replacement method. The sense of variable was well developed, but the students had difficulties in assigning meaning to the unknown when it was not made explicit in the statement. The algebraic representation was the most chosen by the students and the main reason given for this choice was the knowledge/control of knowing what they were doing. Students demonstrated greater competence in interpretation and resolution of geometric problems and decontextualized situations. The interpretation of the situations of verbal problems which translate situations close to everyday life were added difficulties, not due to the context, but due to the definition of the variables.
This study aimed to understand the algebraic thinking of students of the 8th grade in solving problems with systems of two equations of 1st degree with two unknowns. To this end, I sought to understand the meanings they attributed to the mathematical symbols and the main difficulties they revealed, in order to determine and understand which strategy(s) is/are most used to solve problems and the reasons for that choice and finally to recognize the main difficulties associated with the translation and resolution of contextualized situations or not. The study is based on an interpretative paradigm, following a mixed approach, using quantitative and qualitative data. I positioned myself as a participant observer and the main data collection methods were direct observation, collection of written productions of the students, interviews and an anonymous questionnaire. The class was involved in the tasks; however, I selected four pairs of students for further study, to whom I conducted interviews in two moments of the teaching intervention. Data analysis followed the content analysis. Ethical issues were considered in this study. The results obtained show that the students developed algebraic thinking. Most of them have revealed knowing the sense of symbol and the main difficulty shown is linked to the formalism of the replacement method. The sense of variable was well developed, but the students had difficulties in assigning meaning to the unknown when it was not made explicit in the statement. The algebraic representation was the most chosen by the students and the main reason given for this choice was the knowledge/control of knowing what they were doing. Students demonstrated greater competence in interpretation and resolution of geometric problems and decontextualized situations. The interpretation of the situations of verbal problems which translate situations close to everyday life were added difficulties, not due to the context, but due to the definition of the variables.
Descrição
Relatório da Prática de Ensino Supervisionada, Mestrado em Ensino de Matemática, Universidade de Lisboa, Instituto de Educação, 2016
Palavras-chave
Pensamento matemático Equações Símbolo Representações Relatórios da prática de ensino supervisionada - 2016