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Processos de raciocínio matemático e representações de alunos do 8º ano no tópico das funções
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Orientador(es)
Resumo(s)
Este relatório resulta da intervenção letiva realizada com uma turma do 8.º ano do
ensino básico, ocorrida durante a subunidade didática – Gráficos de Funções Afins, no final
do 2.º Período do ano letivo 2019/2020.
O objetivo deste trabalho reside em compreender os processos de raciocínio
matemático e as representações usadas por alunos do 8.˚ ano na resolução de tarefas sobre
funções.
Para dar resposta a esta problemática formulei três questões orientadoras que se
prendem com as características dos processos de raciocínio e as dificuldades sentidas na
resolução das tarefas, com as representações privilegiadas pelos alunos e com a noção que
revelam de função e ainda com a relação entre os processos de raciocínio e as representações
usadas.
A lecionação da unidade de ensino seguiu uma abordagem maioritariamente
exploratória, tendo como objetivo a aprendizagem dos alunos. Foram utilizadas tarefas
diversificadas com características predominantemente exploratórias e privilegiado o trabalho
autónomo a pares, bem como os momentos de discussão e a síntese de conteúdos. Os alunos
foram avaliados recorrendo à observação e questionamento, à análise das produções escritas
dentro e fora da sala de aula e através de uma Questão de Aula.
A metodologia de investigação seguiu um paradigma interpretativo e uma abordagem
qualitativa, onde fui simultaneamente professora e investigadora. Os principais métodos de
recolha de dados foram a observação, com registo áudio e vídeo e as produções escritas dos
alunos. A análise de dados focou-se nos processos de raciocínio dos alunos, nas
representações utilizadas e nas principais dificuldades observadas.
Os resultados evidenciaram a intuição dos alunos na interpretação da relação funcional
envolvida na representação gráfica de uma função. No entanto, verificam-se dificuldades na
transição do concreto para o abstrato e na atribuição de significado à simbologia utilizada.
Estas dificuldades são evidentes sobretudo na capacidade de generalização e na conversão
para a representação algébrica de uma função.
Ainda assim, apesar das dificuldades identificadas, verificou-se que as tarefas
exploratórias focadas em correspondências quantitativas contextualizadas foram facilitadoras
do processo de generalização, promovendo a compreensão de conceitos abstratos.
As dificuldades observadas na justificação residem essencialmente na capacidade de
os alunos comunicarem matematicamente, evidenciando a necessidade de continuar a
trabalhar estas capacidades transversais.
This report is the result of the teaching intervention carried out with a class of grade 8, which took place during the didactic sub-unit – Affine Function Charts, at the end of the 2nd period of the 2019/2020 school year. The aim of this report resides on the understanding of the processes of mathematical reasoning and the representations used by grade 8 students in solving tasks about functions. In order to achieve this aim, I formulated three guiding questions related to the characteristics of the reasoning processes and the difficulties felt in solving tasks, with the representations privileged by the students and with the notion that they reveal of function and also with the relationship between the reasoning processes and the representations used. The teaching of the didactic unit followed a mostly exploratory approach, aiming for students’ learning. A diversity of tasks were used, with predominantly exploratory characteristics, and the teaching approach privileged autonomous work in pairs, as well as moments of discussion and the synthesis of contents. The students were evaluated using observation and questioning, the analysis of written productions inside and outside the classroom and through a Class Question. The research methodology followed an interpretive paradigm and a qualitative approach, where I was both a teacher and a researcher. Data was collected by observation, with audio and video recording and collection of students' written productions. Data analysis focused on the students' reasoning processes, the representations they used and their main difficulties. The results evidenced the students' intuition in the interpretation of the functional relationship involved in the graphical representation of a function. However, there are difficulties in the transition from the concrete to the abstract and in the attribution of meaning to the symbology used. These difficulties are evident above all in the ability to generalize and convert to the algebraic representation of a function. Even so, despite the difficulties identified, the exploratory tasks focused on contextualized quantitative correspondences facilitated the generalization process, promoting the understanding of abstract concepts. The difficulties observed in the justification essentially reside in the students' ability to communicate mathematically, highlighting the need to continue working on these transversal skills.
This report is the result of the teaching intervention carried out with a class of grade 8, which took place during the didactic sub-unit – Affine Function Charts, at the end of the 2nd period of the 2019/2020 school year. The aim of this report resides on the understanding of the processes of mathematical reasoning and the representations used by grade 8 students in solving tasks about functions. In order to achieve this aim, I formulated three guiding questions related to the characteristics of the reasoning processes and the difficulties felt in solving tasks, with the representations privileged by the students and with the notion that they reveal of function and also with the relationship between the reasoning processes and the representations used. The teaching of the didactic unit followed a mostly exploratory approach, aiming for students’ learning. A diversity of tasks were used, with predominantly exploratory characteristics, and the teaching approach privileged autonomous work in pairs, as well as moments of discussion and the synthesis of contents. The students were evaluated using observation and questioning, the analysis of written productions inside and outside the classroom and through a Class Question. The research methodology followed an interpretive paradigm and a qualitative approach, where I was both a teacher and a researcher. Data was collected by observation, with audio and video recording and collection of students' written productions. Data analysis focused on the students' reasoning processes, the representations they used and their main difficulties. The results evidenced the students' intuition in the interpretation of the functional relationship involved in the graphical representation of a function. However, there are difficulties in the transition from the concrete to the abstract and in the attribution of meaning to the symbology used. These difficulties are evident above all in the ability to generalize and convert to the algebraic representation of a function. Even so, despite the difficulties identified, the exploratory tasks focused on contextualized quantitative correspondences facilitated the generalization process, promoting the understanding of abstract concepts. The difficulties observed in the justification essentially reside in the students' ability to communicate mathematically, highlighting the need to continue working on these transversal skills.
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, 2022
Palavras-chave
Raciocínio matemático Funções (Matemática) Representações dos alunos Dificuldades Resolução de problemas Relatórios da prática de ensino supervisionada - 2022