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As justificações matemáticas de alunos do 8º ano no estudo do Teorema de Pitágoras
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Este estudo decorreu durante a minha prática letiva, no Colégio Militar, no ano letivo
2020/2021, numa turma de 8.º ano, no âmbito da unidade didática “Teorema de
Pitágoras” que contemplou 18 aulas de 50 minutos. O seu objetivo é compreender as
justificações matemáticas, enquanto processo de raciocínio matemático, numa turma
de 8.º ano, através das questões: como se caracterizam as justificações matemáticas
dos alunos na resolução de tarefas sobre o Teorema de Pitágoras? e Quais os
conhecimentos que evidenciam nessas justificações e quais as suas dificuldades?
A lecionação das aulas assentou na diversificação de tarefas: exercícios,
problemas e numa tarefa de exploração com o software GeoGebra. Adotei uma
abordagem de caráter exploratório, centrada no aluno. A metodologia de trabalho
desenvolvia-se em três momentos: introdução da tarefa, trabalho autónomo dos alunos
e discussão e sistematização dos resultados e aprendizagens em grande grupo. Recorri
ainda ao uso de PowerPoints para introduzir conteúdos ou como fator motivacional.
A investigação baseia-se na observação participante das aulas, seguindo uma
metodologia interpretativa e qualitativa. Os métodos e procedimentos de recolha de
dados foram a observação participante (notas de campo e gravação áudio e vídeo) e a
recolha documental das produções escritas dos alunos. Para a análise de dados, segui
um quadro concetual relativo aos vários níveis de complexidade e tipos de formalidade
das justificações. Também averiguei quais os conhecimentos matemáticos que os
alunos mobilizam nas suas justificações e as dificuldades evidenciadas.
Como principais resultados verifica-se que, inicialmente, os alunos tinham uma
grande resistência nas questões em que eram solicitadas justificações por não saberem
como o fazer; a partir da ficha 2 essa dificuldade foi diminuindo. As justificações, a
nível de complexidade, foram maioritariamente baseadas em propriedades ou
procedimentos matemáticos, definições, hipóteses ou teoremas; já na tarefa de
exploração, basearam-se em exemplos particulares. O tipo de formalidade variou entre
uma justificação incompleta e formal completa. As dificuldades dos alunos incidem
sobretudo nos conhecimentos prévios e na notação matemática.
This study took place during my teaching intervention, at Colégio Militar, in the academic year 2020/2021, in an 8th grade class, in the Didatic Unit “Pythagorean theorem”, which included 18 lessons of 50 minutes each. Its aim is to understand the mathematical justifications, as mathematical reasoning process, in an 8th grade class, through the questions: how are the students mathematical justifications characterized in solving tasks about the Pythagorean Theorem? and What knowledge and difficulties are evidenced in these justifications? The teaching method was based on task diversification: exercises, problems, and an exploratory task, with the software GeoGebra. I used an exploratory, student centered approach. The work methodology was based on three moments: introduction of the task, autonomous work of the students and discussion and systematization of results and learning in a big group. I also used PowerPoints for introduction of the content or as a motivational factor. The investigation is based on classroom observation, following an interpretive and qualitative methodology. The methods and procedures for collecting data were participant observation (field notes and audio and video recording) and students' written productions. For data analysis, I followed a conceptual framework related to the various levels of complexity and types of formality of justifications. I also explored which mathematical knowledge the students mobilized in their justifications and their main difficulties. As main results, I concluded that, in the first tasks, the students had a huge resistance in justifying their answers, because they did not know how to do it. From worksheet 2 onwards, this difficulty has reduced. The justifications, in terms of complexity level, were mostly based on mathematical properties or procedures, definitions, hypothesis or theorems; in the exploratory task, they were based on particular examples. The formality varied between incomplete and complete formal. The students’ difficulties were mainly in prior knowledge and mathematical notation.
This study took place during my teaching intervention, at Colégio Militar, in the academic year 2020/2021, in an 8th grade class, in the Didatic Unit “Pythagorean theorem”, which included 18 lessons of 50 minutes each. Its aim is to understand the mathematical justifications, as mathematical reasoning process, in an 8th grade class, through the questions: how are the students mathematical justifications characterized in solving tasks about the Pythagorean Theorem? and What knowledge and difficulties are evidenced in these justifications? The teaching method was based on task diversification: exercises, problems, and an exploratory task, with the software GeoGebra. I used an exploratory, student centered approach. The work methodology was based on three moments: introduction of the task, autonomous work of the students and discussion and systematization of results and learning in a big group. I also used PowerPoints for introduction of the content or as a motivational factor. The investigation is based on classroom observation, following an interpretive and qualitative methodology. The methods and procedures for collecting data were participant observation (field notes and audio and video recording) and students' written productions. For data analysis, I followed a conceptual framework related to the various levels of complexity and types of formality of justifications. I also explored which mathematical knowledge the students mobilized in their justifications and their main difficulties. As main results, I concluded that, in the first tasks, the students had a huge resistance in justifying their answers, because they did not know how to do it. From worksheet 2 onwards, this difficulty has reduced. The justifications, in terms of complexity level, were mostly based on mathematical properties or procedures, definitions, hypothesis or theorems; in the exploratory task, they were based on particular examples. The formality varied between incomplete and complete formal. The students’ difficulties were mainly in prior knowledge and mathematical notation.
Descrição
Relatório da Prática de Ensino Supervisionada, Mestrado em Ensino de Matemática no 3º Ciclo do Ensino Básico e no Ensino Secundário, Universidade de Lisboa, Instituto de Educação, 2021
Palavras-chave
Raciocínio matemático Teorema de Pitágoras Matemática - Estudo e ensino Ensino básico (3º Ciclo) Relatórios da prática de ensino supervisionada - 2021