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Aprendizagem das equações do 1.º grau : um estudo com alunos do 7.º ano de escolaridade
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Este trabalho pretende identificar, analisar e categorizar os métodos e os erros
cometidos na resolução de equações de 1º grau por alunos de uma turma do 7º ano de
escolaridade numa escola EB 2,3, em Lisboa.
Para este estudo foram escolhidos quatro alunos com diferentes níveis de
desempenho, recorrendo ao aproveitamento escolar em Matemática nos 1.º e 2º.
períodos letivos. A recolha de dados baseou-se numa entrevista semi-estruturada,
gravada em áudio e transcrita na íntegra; e na recolha documental (produções escritas
dos alunos, cadernos diários e testes de avaliação, e documentos vários da escola); e na
observação e gravação vídeo de aulas.
Os resultados obtidos evidenciam que os métodos mais frequentemente usados
pelos alunos do 7.º ano de escolaridade na resolução de equações de 1.º grau foram: o
método de substituição por tentativa e erro, e o método formal que inclui transpor ou
efetuar a mesma operação em ambos os lados da equação.
Os erros mais frequentemente cometidos foram: erros por eliminação, erros por
redistribuição, os erros de divisão,e a ausência de estrutura. Foi também identificado um
erro com origem em atitudes afetivas e emocionais face à Matemática.
Verificou-se que os alunos na resolução de equações de 1º. grau, numa primeira fase
recorreram à representação pictórica e, posteriormente passaram a usar esta
representação conjuntamente com a representação algébrica.
This work aimed to identify, analyse and categorise the methods, as well as the mistakes committed by students belonging to a 7th-form class, attending an intermediate school in Lisbon, while solving simple equations. To the present survey, four students, with different levels of achievement, have been selected, having the school marks at Mathematic attained by the end of the first and second terms provided a valuable asset. Data gathering was supplied by a semi-structured, audiorecorded interview and fully transcribed; and the documental collecting (the pupils’ written productions, namely in their exercise-books and assessment tests; the observation, the video recording of classes themselves. The results show that the methods seventh-formers more frequently applied in finding a solution for simple equations, were the replacement strategy by trial and error or the formal method which includes to reversing or accomplishing the same operation on both sides of equation. The mistakes that were most frequently commited by the students were: elimination errors, redistribution mistakes, division error and structure absence. One error was also identified, matching stem from affectionate and emotional attitudes facing mathematics. It was verified that the pupils, when finding a solution for simple equations, in a first phase had appealed to pictorial representation and, later began to use this representation together with the algebraic representation.
This work aimed to identify, analyse and categorise the methods, as well as the mistakes committed by students belonging to a 7th-form class, attending an intermediate school in Lisbon, while solving simple equations. To the present survey, four students, with different levels of achievement, have been selected, having the school marks at Mathematic attained by the end of the first and second terms provided a valuable asset. Data gathering was supplied by a semi-structured, audiorecorded interview and fully transcribed; and the documental collecting (the pupils’ written productions, namely in their exercise-books and assessment tests; the observation, the video recording of classes themselves. The results show that the methods seventh-formers more frequently applied in finding a solution for simple equations, were the replacement strategy by trial and error or the formal method which includes to reversing or accomplishing the same operation on both sides of equation. The mistakes that were most frequently commited by the students were: elimination errors, redistribution mistakes, division error and structure absence. One error was also identified, matching stem from affectionate and emotional attitudes facing mathematics. It was verified that the pupils, when finding a solution for simple equations, in a first phase had appealed to pictorial representation and, later began to use this representation together with the algebraic representation.
Descrição
Relatório da prática de ensino supervisionada, Ensino da Matemática, Universidade de Lisboa, 2012
Palavras-chave
Equações Aprendizagem da matemática Relatórios da prática de ensino supervisionada - 2012