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Aprendizagem do conceito de limite : um estudo envolvendo alunos do 11º ano do ensino secundário
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Resumo(s)
O presente estudo foi realizado no âmbito da prática de ensino supervisionado e
teve por base a lecionação de seis aulas de 90 minutos, numa turma de 11.º ano do ensino
secundário da Escola Secundária Padre Alberto Neto (ESPAN), integrada no
Agrupamento de Escolas Queluz-Belas, abrangendo o tema Limites de Funções Reais
de Variável Real, no domínio Funções Reais de Variável Real.
O estudo teve como objetivo fundamental compreender como alunos do 11.º ano
do Ensino Secundário aprendem e aplicam o conceito de limite, bem como as principais
dificuldades que denotam em termos de ensino-aprendizagem. Para tal, foram
formuladas as seguintes questões a que se procuraram dar resposta: Qual o significado
do conceito de limite que os alunos apresentam ao longo do estudo? Com que conflitos
cognitivos inibidores ou perturbadores da correta apreensão do conceito se confrontam
alguns alunos? Como mobilizam os alunos o conceito de limite na resolução de tarefas?
Quais as principais dificuldades evidenciadas pelos alunos?
As conclusões do trabalho estão suportadas numa análise qualitativa dos dados
recolhidos. Para o acervo de informação, recorreu-se à recolha de documentos escritos
produzidos pelos alunos, à observação do trabalho dos alunos durante a resolução das
tarefas propostas, com recurso a notas de campo, e à realização de algumas entrevistas,
sendo estas duas últimas acompanhadas com registo áudio.
O estudo confirma as dificuldades descritas na literatura sobre a aprendizagem
do conceito de limite e a tendência dos alunos para se apropriarem de uma interpretação
procedimental do conceito, sem previamente terem alcançado e consolidado a sua
compreensão formal. Esta compreensão procedimental é suficiente para responder com
sucesso a muitos exercícios de aplicação, ficando aquém da compreensão relacional,
estruturação essencial ao entrosamento do conceito com outros domínios, seja da
Matemática ou de outras ciências. Para o professor, o principal desafio é selecionar e
preparar tarefas que promovam a comunicação sobre o tema, permitindo desse modo
identificar obstáculos cognitivos à correta apreensão do conceito de limite pelos alunos
e, ao mesmo tempo, sejam desafiantes e motivadoras para a turma, ilustrando sempre
que possível a utilidade do conceito na resolução de problemas do mundo real.
The current study was carried out within the scope of a supervised teaching practice. It was based on the work developed while teaching six lessons of 90 minutes, in a 11th grade class of high school education at Escola Secundária Padre Alberto Neto (ESPAN) and it encompassed the subject Limits of Real Functions of Real Variable, in the realm of Real Functions of Real Variable. The main objective of this study was to understand how 11th grade students learn and use the concept of limit as well as the problems they reveal in terms of the teaching learning process. Therefore, answers were sought for the following questions: Which meaning of concept of limit do students reveal throughout the teaching unit? Which cognitive conflicts that inhibit or hinder the correct apprehension of the concept do some students face? How do the students use the concept of limit in task-solving situations? How do students use the notion of limit in solving tasks that involve it? What are the main difficulties shown by the students? The results presented are based on a qualitative analysis of the data collected throughout the teaching unit. This information collection resulted from the students’ written productions in the tasks proposed in class, supported by direct observation and field notes complemented with audio recordings of some interviews done. The study corroborates the difficulties described in papers about learning the concept of limit as well as students’ tendency to seize a procedural interpretation of the concept without having first reached and mastered its formal understanding. This procedural understanding is enough to solve many application exercises successfully, but it is far less than enough for the relational understanding, which is essential when relating the concept to other areas of Maths or science. Finally, the main challenge for the teacher is to select and prepare tasks that not only promote communication on the topic (thus enabling the identification of cognitive obstacles to a correct apprehension of the concept of limit by the students), but are simultaneously challenging and motivating for the class and point out the usefulness of the concept to solve real world problems.
The current study was carried out within the scope of a supervised teaching practice. It was based on the work developed while teaching six lessons of 90 minutes, in a 11th grade class of high school education at Escola Secundária Padre Alberto Neto (ESPAN) and it encompassed the subject Limits of Real Functions of Real Variable, in the realm of Real Functions of Real Variable. The main objective of this study was to understand how 11th grade students learn and use the concept of limit as well as the problems they reveal in terms of the teaching learning process. Therefore, answers were sought for the following questions: Which meaning of concept of limit do students reveal throughout the teaching unit? Which cognitive conflicts that inhibit or hinder the correct apprehension of the concept do some students face? How do the students use the concept of limit in task-solving situations? How do students use the notion of limit in solving tasks that involve it? What are the main difficulties shown by the students? The results presented are based on a qualitative analysis of the data collected throughout the teaching unit. This information collection resulted from the students’ written productions in the tasks proposed in class, supported by direct observation and field notes complemented with audio recordings of some interviews done. The study corroborates the difficulties described in papers about learning the concept of limit as well as students’ tendency to seize a procedural interpretation of the concept without having first reached and mastered its formal understanding. This procedural understanding is enough to solve many application exercises successfully, but it is far less than enough for the relational understanding, which is essential when relating the concept to other areas of Maths or science. Finally, the main challenge for the teacher is to select and prepare tasks that not only promote communication on the topic (thus enabling the identification of cognitive obstacles to a correct apprehension of the concept of limit by the students), but are simultaneously challenging and motivating for the class and point out the usefulness of the concept to solve real world problems.
Descrição
Relatório da Prática de Ensino Supervisionada, Mestrado em Ensino de Matemática, Universidade de Lisboa, Instituto de Educação, 2021
Palavras-chave
Limite (Matemática) Ensino-aprendizagem Dificuldades Ensino secundário (11º ano) Relatórios da prática de ensino supervisionada - 2021