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O pensamento dos alunos sobre sequências de crescimento do 1.º ao 2.º Ciclo
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O presente relatório de estágio resulta do trabalho desenvolvido na Prática de Ensino Supervisionada do Mestrado em Ensino do 1.º Ciclo do Ensino Básico (CEB) e de Matemática e Ciências Naturais no 2.º CEB. O relatório apresenta duas partes principais a que se segue uma reflexão global do percurso realizado. A primeira é relativa às práticas de ensino desenvolvida em quatro estágios, no qual se inclui as caracterizações da instituição, da turma e da prática de ensino. A segunda relativa à componente investigativa desenvolvida em duas turmas com o tema “O pensamento dos alunos sobre sequências de crescimento do 1.º ao 2.º ciclo”. A pesquisa visa compreender o desenvolvimento de estratégias de generalização por alunos do 1.º e do 2.º ciclos, em sequências pictóricas de crescimento. Os participantes do estudo foram duas turmas, uma de 4.º ano do 1.º CEB, com 24 alunos, e outra do 6.º ano do 2.º CEB, com 12 alunos, selecionados por conveniência por coincidirem com turmas onde os estágios decorreram. A recolha de dados foi documental das produções escritas dos alunos a tarefas matemáticas que integraram um pré-questionário, fichas de trabalho realizadas durante a intervenção com uma abordagem exploratória em sala de aula e de um pós- questionário. As tarefas foram aplicadas individualmente, a pares e em pequenos grupos, e permitiram observar a evolução do pensamento algébrico dos alunos. Os resultados evidenciaram que os alunos de ambos os ciclo utilizam variadas estratégias, sendo que no 1.º ciclo se destaca o uso de estratégias recursivas e covariação na exploração de sequências crescentes, com números naturais. No 2.º ciclo, na exploração de sequências crescentes com números naturais, os alunos recorreram maioritariamente a estratégias recursivas, inclusive na exploração de sequências decrescentes, com números racionais, sendo que alguns demonstraram já serem capazes de expressar as generalizações por meio de expressões algébricas. No trabalho com sequências decrescentes, com número racionais, a maioria dos alunos recorre também à estratégia recursiva.
This report was carried as part of the Research in Supervised Teaching Practice curricular unit of the Master's Degree in Teaching the 1st Cycle of Basic Education (CBE) and Mathematics and Natural Sciences in the 2nd CBE. The report is divided into three parts: the first concerns the teaching practices developed during four internships, which include descriptions of the institution, the class, and the teaching practice itself; the second focuses on the research component developed in two classes within the field of Mathematics, specifically on the topic of “Students’ thinking about growth patterns from the 1st to the 2nd cycle”, presenting the objectives, guiding questions, participants, data collection instruments and techniques, as well as the presentation and discussion of the results obtained; and the third consists of a final reflection on the entire process undertaken. The participants selected for this study were two classes, one from the 4th year of the 1st CBE, with 24 students, and another from the 6th year of the 2nd CBE, with 12 students, chosen for convenience as they coincided with the internship locations. Data collection was carried out through the application of a pre-questionnaire, intervention worksheets with an exploratory approach in the classroom, and a post- questionnaire. The tasks were carried out individually, in pairs, and in small groups, allowing for the observation of the development of students’ algebraic thinking. The results showed that students from both cycles use a variety of strategies. In the 1st cycle, the use of recursive strategies and covariation stands out in the exploration of increasing sequences with natural numbers. In the 2nd cycle, when exploring increasing sequences with natural numbers, students mainly relied on recursive strategies, including in the exploration of decreasing sequences with rational numbers, with some already demonstrating the ability to express generalizations through algebraic expressions. In working with decreasing sequences with rational numbers, most students also resorted to the recursive strategy.
This report was carried as part of the Research in Supervised Teaching Practice curricular unit of the Master's Degree in Teaching the 1st Cycle of Basic Education (CBE) and Mathematics and Natural Sciences in the 2nd CBE. The report is divided into three parts: the first concerns the teaching practices developed during four internships, which include descriptions of the institution, the class, and the teaching practice itself; the second focuses on the research component developed in two classes within the field of Mathematics, specifically on the topic of “Students’ thinking about growth patterns from the 1st to the 2nd cycle”, presenting the objectives, guiding questions, participants, data collection instruments and techniques, as well as the presentation and discussion of the results obtained; and the third consists of a final reflection on the entire process undertaken. The participants selected for this study were two classes, one from the 4th year of the 1st CBE, with 24 students, and another from the 6th year of the 2nd CBE, with 12 students, chosen for convenience as they coincided with the internship locations. Data collection was carried out through the application of a pre-questionnaire, intervention worksheets with an exploratory approach in the classroom, and a post- questionnaire. The tasks were carried out individually, in pairs, and in small groups, allowing for the observation of the development of students’ algebraic thinking. The results showed that students from both cycles use a variety of strategies. In the 1st cycle, the use of recursive strategies and covariation stands out in the exploration of increasing sequences with natural numbers. In the 2nd cycle, when exploring increasing sequences with natural numbers, students mainly relied on recursive strategies, including in the exploration of decreasing sequences with rational numbers, with some already demonstrating the ability to express generalizations through algebraic expressions. In working with decreasing sequences with rational numbers, most students also resorted to the recursive strategy.
Descrição
Mestrado em Ensino do 1º ciclo e de Matemática e Ciências da Naturais no 2º ciclo do Ensino Básico
Palavras-chave
ensino básico estratégias de generalização matemática pensamento algébrico sequências de crescimento algebraic thinking basic education generalization strategies growth sequences mathematics
Contexto Educativo
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Licença CC
Sem licença CC