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Authors
Abstract(s)
Este estudo foi realizado no âmbito da prática de ensino supervisionada e teve
por base a lecionação de dez aulas de 50 minutos a uma turma do 8º ano de
escolaridade da Escola Básica e Secundária Padre Alberto Neto no ano letivo 2016-
2017, que abrangeu o tema “Dízimas infinitas não periódicas e números reais” do
domínio Números e Operações (MEC, 2013).
O objetivo do estudo é compreender como os alunos se apropriam da noção
de número irracional, como a utilizam e as dificuldades que manifestam quando
resolvem tarefas que envolvem estes números. Sendo assim, procurei responder a
quatro questões: (1) Como é que os alunos identificam números irracionais sob
várias representações? (2) Como é que os alunos representam números irracionais na
reta real? (3) Como é que os alunos operam com números irracionais? (4) Como é
que os alunos comparam números irracionais sob várias representações?
Os resultados apresentados têm por base uma análise qualitativa dos dados
recolhidos a partir da observação participante, apoiada em notas de campo e em
gravações áudio e vídeo, bem como recolha documental, constituída pelas produções
escritas dos alunos nas tarefas propostas ao longo da unidade de ensino e de
minitestes. Os resultados obtidos sugerem que os alunos têm uma tendência para
recorrer a representações alternativas de um número para classificá-lo quanto à
irracionalidade: se o número está escrito na forma de fração, recorrem à sua
representação decimal, e se consiste na raiz quadrada de um número natural,
calculam a raiz desse número. Os alunos representam números irracionais na reta real
recorrendo a um processo de construção geométrica, envolvendo o Teorema de
Pitágoras e uma circunferência. Os alunos mobilizam conhecimentos que já possuem
de regras operatórias envolvendo números racionais e aplicam-nos consoante o
permitido com os números irracionais. Quando os números irracionais estão na
forma de dízima, os alunos estabelecem relações de ordem entre eles comparando os
algarismos das respetivas ordens, e quando estão na forma de raiz quadrada,
comparam os radicandos. As dificuldades concetuais foram as mais difíceis de
ultrapassar, e nalguns casos, mantiveram-se até ao final da intervenção letiva.
This study was carried out as a supervised teaching practice and it was based on the teaching of ten lessons of 50 minutes to an 8th grade class of the Escola Básica e Secundária Padre Alberto Neto during the school year of 2016-2017, covering the topic “Non-periodical infinite decimals and real numbers” of the curriculum unit Numbers and Operations (MEC, 2013). The objective of this study was to understand how students learn the notion of irrational number, how they use it and the difficulties they reveal when solving tasks that involve these numbers. For that, I sought to answer four questions: (1) How do students identify irrational numbers in different representations? (2) How do students represent irrational numbers in the number line? (3) How do students operate with irrational numbers? (4) How do students compare irrational numbers in different representations? The results presented are based on a qualitative analysis of the data collected from participant observation, supported on field notes and on video and audio recording of the classes, as well as the students’ written solutions of the tasks proposed during the teaching unit and the written assessment tests. The results suggest that the students tend to use alternative representations of a number to classify them according to their irrationality: when the number is a fraction, they turn to their decimal representation, and when it is a square root of a natural number, they calculate it using a calculator. The students represent irrational numbers in the number line through a process of geometrical construction, involving the Pythagorean Theorem and a circumference. The students mobilize their knowledge of calculating rational numbers and apply it to irrational numbers as possible. When the irrational numbers are in their decimal representations, students establish order relations between them by comparing the digits of the same orders, and when they are square roots of a natural number, they compare the radicands. The conceptual difficulties were the hardest to overcome, which in some cases, remained until the end of the teaching unit.
This study was carried out as a supervised teaching practice and it was based on the teaching of ten lessons of 50 minutes to an 8th grade class of the Escola Básica e Secundária Padre Alberto Neto during the school year of 2016-2017, covering the topic “Non-periodical infinite decimals and real numbers” of the curriculum unit Numbers and Operations (MEC, 2013). The objective of this study was to understand how students learn the notion of irrational number, how they use it and the difficulties they reveal when solving tasks that involve these numbers. For that, I sought to answer four questions: (1) How do students identify irrational numbers in different representations? (2) How do students represent irrational numbers in the number line? (3) How do students operate with irrational numbers? (4) How do students compare irrational numbers in different representations? The results presented are based on a qualitative analysis of the data collected from participant observation, supported on field notes and on video and audio recording of the classes, as well as the students’ written solutions of the tasks proposed during the teaching unit and the written assessment tests. The results suggest that the students tend to use alternative representations of a number to classify them according to their irrationality: when the number is a fraction, they turn to their decimal representation, and when it is a square root of a natural number, they calculate it using a calculator. The students represent irrational numbers in the number line through a process of geometrical construction, involving the Pythagorean Theorem and a circumference. The students mobilize their knowledge of calculating rational numbers and apply it to irrational numbers as possible. When the irrational numbers are in their decimal representations, students establish order relations between them by comparing the digits of the same orders, and when they are square roots of a natural number, they compare the radicands. The conceptual difficulties were the hardest to overcome, which in some cases, remained until the end of the teaching unit.
Description
Relatório da Prática de Ensino Supervisionada, Mestrado em Ensino de Matemática, Universidade de Lisboa, Instituto de Educação, 2018
Keywords
Números irracionais Representações Alunos Dificuldades Relatórios da prática de ensino supervisionada - 2018