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Representações matemáticas na aprendizagem das funções : um estudo com alunos do 7º ano de escolaridade
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Orientador(es)
Resumo(s)
Este
trabalho
de
projeto
tem
como
objetivo
compreender
como
uma
metodologia
de
ensino
focada
em
tarefas
que
promovem
a
transição
entre
diferentes
representações
matemáticas
contribui
para
a
aprendizagem
das
funções.
De
forma
a
analisar
como
é
desenvolvida
esta
aprendizagem
foram
definidas
as
seguintes
questões
de
investigação:
1)
Que
aprendizagens
revelam
os
alunos
no
que
diz
respeito
à
definição
de
função
e
à
determinação
de
imagens
a
partir
de
objetos
e
vice-‐versa?,
2)
De
que
forma
os
alunos
interpretam
e
relacionam
as
variáveis
envolvidas
a
partir
de
diferentes
representações
de
uma
função?
e
3)
Que
dificuldades
manifestam
os
alunos
na
transição
entre
os
diferentes
modos
de
representar
uma
função?.
O
trabalho
foi
desenvolvido
com
uma
turma
de
7.º
ano,
no
âmbito
da
unidade
temática
Funções,
lecionada
nos
2.º
e
3.º
períodos
do
ano
letivo
2017/2018
numa
escola
secundária
do
concelho
de
Oeiras.
O
estudo
seguiu
uma
metodologia
de
natureza
qualitativa
assente
num
paradigma
interpretativo
e
a
recolha
de
dados
foi
realizada
através
de
observação
participante
e
por
recolha
documental.
Os
documentos
recolhidos
foram:
registos
áudio
e
vídeo
das
aulas,
resoluções
de
alunos
e
registos
escritos
da
professora.
Da
implementação
da
unidade
de
ensino
verificou-‐se
que
a
maioria
dos
alunos
evidenciou
compreender
a
definição
de
função
e
que,
no
geral,
estes
não
revelaram
dificuldades
significativas
na
transição
entre
diferentes
representações.
Em
situações
contextualizadas,
partindo
de
diferentes
representações
de
uma
função,
os
alunos
mostraram
ser
capazes
de
interpretar
e
relacionar
corretamente
as
variáveis
envolvidas.
Ainda
assim,
verificou-‐se
que
é
na
transição
da
representação
algébrica
para
a
gráfica
que
são
cometidos
mais
erros
e
que
é
a
partir
da
representação
gráfica
que
surgem
mais
dificuldades
relativamente
à
forma
como
os
alunos
relacionam
as
variáveis.
Ao
longo
do
estudo
foram
diagnosticadas
dificuldades
ao
nível
da
utilização
e
da
compreensão
do
significado
da
simbologia
própria
das
funções
e
observadas
incorreções
na
construção
de
gráficos.
This study aims to understand how a teaching methodology focused on tasks that promote the transition between different mathematical representations contributes to the learning of the functions. In order to analyze how this learning is developed, the following research questions were defined: 1) What do students learn about the definition of function, and determination of images from objects and vice-‐versa?, 2) How do students interpret and relate the variables involved from different representations of a function? and 3) What difficulties students manifest in the transition between the different ways of representing a function?. The work was developed with a group of 7th grade students, within the scope of the thematic unit Functions, taught in the 2nd and 3rd terms of the 2017/2018 school year in a secondary school in the county of Oeiras. The study followed a methodology of qualitative nature based on an interpretative paradigm and the data collection was accomplished by participant observation and by documentary collection. The documents collected were: audio and video records of the classes, student resolutions and written records of the teacher. From the implementation of the teaching unit it was observed that the majority of the students evidenced to understand the definition of function and that, in general, the students did not reveal significant difficulties in the transition between different representations. In contextualized situations, starting from different representations of a function, the students showed they were able to interpret and relate correctly the variables involved. It was observed, however, that it is in the transition from the algebraic representation to the graphical representation that more errors are committed and that it is from the graphical representation that more difficulties arise regarding the way the students relate the variables. Throughout the study difficulties in the use and understanding of the meaning of the symbology proper to the functions were diagnosed as well as some inaccuracies in the construction of graphs were observed.
This study aims to understand how a teaching methodology focused on tasks that promote the transition between different mathematical representations contributes to the learning of the functions. In order to analyze how this learning is developed, the following research questions were defined: 1) What do students learn about the definition of function, and determination of images from objects and vice-‐versa?, 2) How do students interpret and relate the variables involved from different representations of a function? and 3) What difficulties students manifest in the transition between the different ways of representing a function?. The work was developed with a group of 7th grade students, within the scope of the thematic unit Functions, taught in the 2nd and 3rd terms of the 2017/2018 school year in a secondary school in the county of Oeiras. The study followed a methodology of qualitative nature based on an interpretative paradigm and the data collection was accomplished by participant observation and by documentary collection. The documents collected were: audio and video records of the classes, student resolutions and written records of the teacher. From the implementation of the teaching unit it was observed that the majority of the students evidenced to understand the definition of function and that, in general, the students did not reveal significant difficulties in the transition between different representations. In contextualized situations, starting from different representations of a function, the students showed they were able to interpret and relate correctly the variables involved. It was observed, however, that it is in the transition from the algebraic representation to the graphical representation that more errors are committed and that it is from the graphical representation that more difficulties arise regarding the way the students relate the variables. Throughout the study difficulties in the use and understanding of the meaning of the symbology proper to the functions were diagnosed as well as some inaccuracies in the construction of graphs were observed.
Descrição
Trabalho de projeto de mestrado, Educação (Área de especialidade Didática da Matemática), Universidade de Lisboa, Instituto de Educação, 2018
Palavras-chave
Funções (Matemática) Variáveis Dificuldades escolares Ensino básico (3º Ciclo) Trabalhos de projeto de mestrado - 2018