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Relatório de Estágio - Representações e Comunicação Matemática na aprendizagem de sucessões
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Resumo(s)
A presente dissertação encontra-se organizada em duas partes. A primeira parte corres-
ponde ao relatório de estágio desenvolvido no ano letivo 2024/2025, no âmbito do qual foram
acompanhadas duas turmas: uma principal do 11.º ano e uma secundária do 9.º ano. Nesta
parte apresentam-se a caracterização das turmas, a planificação das aulas lecionadas, a des-
crição das atividades realizadas e uma reflexão sobre a prática pedagógica desenvolvida.
A segunda parte da dissertação é dedicada ao projeto de investigação realizado com um
grupo de alunos do 11.º ano. Este estudo teve como objetivo compreender o processo de
tradução entre as diferentes representações das sucessões e analisar o papel da comunicação
matemática usada para expressar estes conceitos. Para tal, procurou-se responder às seguintes
questões de investigação:
1. Como se caracteriza a aprendizagem do conceito de sucessão nomeadamente na
tradução entre as representações numérica, gráfica e algébrica das sucessões?
2. Quais são os critérios adotados pelos alunos na escolha de uma representação das
sucessões em diferentes situações?
3. De que forma os alunos comunicam matematicamente os seus raciocínios ao efe-
tuarem a tradução entre as diferentes representações?
A investigação seguiu uma abordagem qualitativa, recorrendo a quatro estudos de caso.
A recolha de dados foi realizada através de técnicas de observação, entrevistas, notas de
campo e análise documental.
Os resultados permitiram concluir que a tradução entre representações assume um papel
fundamental na aprendizagem das sucessões, embora se tenham evidenciado dificuldades
nessa tradução. Verificou-se que a escolha de uma representação dependeu da natureza da
tarefa, das dificuldades sentidas e das preferências individuais do aluno. Constatou-se ainda
que a comunicação matemática foi mais clara na oralidade, enquanto que nos registos escritos
se evidenciaram fragilidades no rigor formal.
The present dissertation is organized into two parts. The first part corresponds to the report of the pedagogical internship carried out during the 2024/2025 school year, under which context two classes were accompanied: a main class from the 11th grade and a secondary class from the 9th grade. This section presents the characterization of the classes, the planification of the taught lessons, the description of the performed activities and a reflection on the devel- oped pedagogical practice. The second part of this dissertation is dedicated to the research project conducted with a group of 11th grade students. The aim was to understand the process of translation among different representations of sequences and to analyse the role of mathematical communication used to express these concepts. To this end, the study sought to answer the following research questions: 1. How is the learning of the concept of sequence characterized, specifically in the translation between the numerical, graphical and algebraic representations of se- quences? 2. What criteria do students adopt in choosing a representation of sequences in differ- ent situations? 3. How do students communicate their reasoning mathematically when translating be- tween different representations? The research followed a qualitative approach, based on four case studies. The data was collected through observation techniques, interviews, field notes and documents analysis. The results allowed to conclude that the translation between representations plays a fun- damental role in the learning of sequences, although there are evidences of difficulties in trans- lating between the different representations. It was observed that the choice of representation depended on the nature of the task, the difficulties and the individual preferences of the stu- dent. It was also verified that mathematical communication was clearer in oral expression, while in written records there were evidence of weaknesses in formal accuracy.
The present dissertation is organized into two parts. The first part corresponds to the report of the pedagogical internship carried out during the 2024/2025 school year, under which context two classes were accompanied: a main class from the 11th grade and a secondary class from the 9th grade. This section presents the characterization of the classes, the planification of the taught lessons, the description of the performed activities and a reflection on the devel- oped pedagogical practice. The second part of this dissertation is dedicated to the research project conducted with a group of 11th grade students. The aim was to understand the process of translation among different representations of sequences and to analyse the role of mathematical communication used to express these concepts. To this end, the study sought to answer the following research questions: 1. How is the learning of the concept of sequence characterized, specifically in the translation between the numerical, graphical and algebraic representations of se- quences? 2. What criteria do students adopt in choosing a representation of sequences in differ- ent situations? 3. How do students communicate their reasoning mathematically when translating be- tween different representations? The research followed a qualitative approach, based on four case studies. The data was collected through observation techniques, interviews, field notes and documents analysis. The results allowed to conclude that the translation between representations plays a fun- damental role in the learning of sequences, although there are evidences of difficulties in trans- lating between the different representations. It was observed that the choice of representation depended on the nature of the task, the difficulties and the individual preferences of the stu- dent. It was also verified that mathematical communication was clearer in oral expression, while in written records there were evidence of weaknesses in formal accuracy.
Descrição
Palavras-chave
Sucessões Representações Comunicação Matemática