A carregar...
Publicação
A aprendizagem da derivada de funções no 12º ano : uma análise dos erros e dificuldades dos alunos
| Nome: | Descrição: | Tamanho: | Formato: | |
|---|---|---|---|---|
| 3.18 MB | Adobe PDF |
Resumo(s)
Este estudo tem por base o trabalho desenvolvido na lecionação de cinco aulas
de 90 minutos que decorreram no 2.º período do ano letivo de 2015/2016, numa turma
do 12.º ano de escolaridade, da Escola Secundária da Ramada, em Odivelas. A unidade
de ensino lecionada foi subordinada ao tema “Cálculo Diferencial”, nos tópicos da função
derivada (regras de derivação) e da função composta e sua derivada. O objetivo deste
estudo, de cariz investigativo, foi compreender, através de um estudo sobre os seus erros
e dificuldades, como é que alunos do 12.º ano aprendem a derivada de funções, dando
particular atenção à derivada da função composta. Para o atingir, procurei responder às
seguintes questões: (1) Como procedem os alunos na determinação de derivadas de
funções? Em particular, que estratégias adotam na determinação dessas derivadas? (2)
Que erros cometem e que dificuldades manifestam os alunos quando determinam a
derivada de uma função?
As tarefas propostas aos alunos, envolvendo derivadas de funções, foram
pensadas de modo a que estes tivessem uma efetiva experiência matemática,
proporcionando-lhes o desenvolvimento de várias capacidades, como a autonomia e a
capacidade de lidar com situações complexas (Ponte, 2005). Destaque ainda para a
formulação de conjeturas, a capacidade de generalização e o discurso matemático, que
foram trabalhados ao longo das várias tarefas.
O estudo desenvolvido assenta numa abordagem qualitativa e interpretativa,
tendo os dados sido recolhidos através de observação participante e recolha documental
das resoluções escritas dos alunos das tarefas propostas na unidade de ensino.
Os resultados obtidos sugerem que os alunos adquiriram os conhecimentos
necessários à determinação de derivadas de funções. Nas estratégias que utilizaram
privilegiaram a representação algébrica, revelando serem capazes de manipular
expressões algébricas e funções de forma a reconhecer a regra de derivação a aplicar. No
entanto, cometeram vários erros, quer processuais (simplificação de expressões) quer
concetuais (definição de derivada num ponto, por exemplo), frequentemente por
incompreensão de tópicos matemáticos lecionados em anos anteriores, como por
exemplo, as regras operatórias das potências ou funções envolvendo radicais.
This study is based on the work developed under the teaching of five lessons of 90 minutes that occurred during the 2nd term in the school year 2015/2016, with a 12th grade class of the Escola Secundária da Ramada, in Odivelas. The unit taught was “Differential Calculus”, in the topics of derivative function (derivation rules) and the composite function and its derivative. The objective of this investigation work was to understand, through the study of their errors and difficulties, how students of 12th grade learn the derivative of functions, giving special attention at the derivative of composite function. In order to achieve this goal, I tried to answer the following questions: (1) How do students proceed in determining the derivative of functions? In particular, what strategies do they use in determining those derivatives, (2) What errors do students commit and what difficulties do students manifest when determine the derivative of a function? The tasks suggested to the high school students, involving the derivative of functions, were created with the purpose of providing an effective mathematical experience, giving them the opportunity of developing several capacities, such as their autonomy and the capacity of dealing with complex situations (Ponte, 2005). Highlight yet the formulation of conjectures, the capacity of generalization and the mathematical speech, that were worked during the several tasks. This study is built upon a qualitative and interpretative approach, having the data been collected through the participant observation and through the documental gathering of students' written answers of the tasks proposed during the teaching unit. The results obtained suggest that students had acquired the necessary knowledge for the determination of the derivative of functions. In the strategies that they presented, the students privileged the algebraic representation, revealing being able to manipulate algebraic expressions and functions in order to recognize the derivative rule to apply. However, they committed several mistakes, such as procedural (simplification of expressions) and conceptual (definition of derivative on a point, for example), often because of the incomprehension of mathematical topics lectured during previous years, such as, the derivation rule of powers or the functions involving radicals.
This study is based on the work developed under the teaching of five lessons of 90 minutes that occurred during the 2nd term in the school year 2015/2016, with a 12th grade class of the Escola Secundária da Ramada, in Odivelas. The unit taught was “Differential Calculus”, in the topics of derivative function (derivation rules) and the composite function and its derivative. The objective of this investigation work was to understand, through the study of their errors and difficulties, how students of 12th grade learn the derivative of functions, giving special attention at the derivative of composite function. In order to achieve this goal, I tried to answer the following questions: (1) How do students proceed in determining the derivative of functions? In particular, what strategies do they use in determining those derivatives, (2) What errors do students commit and what difficulties do students manifest when determine the derivative of a function? The tasks suggested to the high school students, involving the derivative of functions, were created with the purpose of providing an effective mathematical experience, giving them the opportunity of developing several capacities, such as their autonomy and the capacity of dealing with complex situations (Ponte, 2005). Highlight yet the formulation of conjectures, the capacity of generalization and the mathematical speech, that were worked during the several tasks. This study is built upon a qualitative and interpretative approach, having the data been collected through the participant observation and through the documental gathering of students' written answers of the tasks proposed during the teaching unit. The results obtained suggest that students had acquired the necessary knowledge for the determination of the derivative of functions. In the strategies that they presented, the students privileged the algebraic representation, revealing being able to manipulate algebraic expressions and functions in order to recognize the derivative rule to apply. However, they committed several mistakes, such as procedural (simplification of expressions) and conceptual (definition of derivative on a point, for example), often because of the incomprehension of mathematical topics lectured during previous years, such as, the derivation rule of powers or the functions involving radicals.
Descrição
Relatório da Prática de Ensino Supervisionada, Mestrado em Ensino de Matemática, Universidade de Lisboa, Instituto de Educação, 2016
Palavras-chave
Derivadas Dificuldades escolares Ensino secundário Relatórios da prática de ensino supervisionada - 2016