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O Poder de Ensinar Matemática

Abstract

Dissertação de Mestrado em Ensino de Matemática no 3.º ciclo do Ensino Básico e no Secundário apresentada à Faculdade de Ciências e Tecnologia

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O Poder de Ensinar Matemática

Author: Almeida, Bibiana Vultão
Year: 2022
Source: https://estudogeral.uc.pt/bitstream/10316/103156/1/Bibiana_Relato%cc%81rio.pdf
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Bibiana Vultão Almeida

O Poder de Ensi nar Mate mática

VOLUME 1

Relatório de Estágio no âmbito do Mestrado em Ensino da
Matemática no 3.º ciclo do Ensino Básico e no Secundário,
orientado pela Professora Doutora Helena Albuquerque e
apresentada ao Departamento de Matemática da Faculdade de
Ciências e Tecnologia.

Ju nho de 20 22

O P oder de Ensinar Matemática
Bibiana V ultão Almeida
Mestrado em Ensino da Matemática no 3. º ciclo do Ensino Básico e no Secundá rio
Master in Mathematics T eaching in the 3rd Cycle of Basic and Seconda ry Education
Relató rio de Estágio | Rep o rt of Stage
Junho 2022

iii
Ninguém é tão gr ande que não possa apr ender ,
Nem tão pequeno que não possa ensinar .
ÉSOPO

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Agradecimentos
A Deus acima de tudo.
Ao meu pai e aos meus irmãos, Ângelo e Nilton, por todo o carinho, atenção e apoio que me
deram dur ante toda a minha vida.
À minha mãe que, mesmo ausente , sempr e esteve tão pr esente.
Aos meus queridos avós, por todas as palavras sábias e de conforto, por me acarinhar em e
aconselhar em.
Ao meu David, pelo seu amor , pela imensa paciência e compr eensão, por nunca me ter deixado ir
abaixo, por me incentivar e acr editar que eu seria capaz de superar qualquer obstáculo.
Às minhas cole gas de estágio e amigas para a vida, Ana Rita e Diana, por todo o incentivo,
entr eajuda e suporte que me pr opor cionaram ao longo deste ano.
Aos meus grandes amigos de cur so, Afonso, Car olina, David, Diana, Duarte, Hugo e Marta, pela
sua amizade infinita, pelo apoio que me deram em todos os momentos, por acr editar em e me ajudar em
a che gar onde c he guei.
À minha Catarina, amiga de longa data, por todos os desabafos, pela sua amizade e atenção
dedicadas sempr e que pr ecisei.
A todos os Pr ofessor es que contrib uíram par a a minha formação durante toda a minha vida, em
especial ao Pr ofessor César , que num certo momento afirmou "Um dia serás minha cole ga". Hoje
sou.
À dir eção da Escola Secundária José F alcão, a toda a comunidade docente e não docente da
mesma, pelo acolhecimento, assistência e simpatia.
Aos meus alunos, que jamais esquecer ei, pela forma como me acolheram e r espeitar am e por tudo
o que me ensinaram.
À minha Pr ofessora e Orientador a Científica, Pr ofessora Doutor a Helena Albuquer que, por não
só me transmitir o seu saber com muito pr ofissionalismo, mas também por todas as palavras amigas e
conselhos para a vida.
À minha Orientadora C ooperante, Pr ofessor a Natividade Corr eia, por toda a dedicação e paciên-
cia, por estar sempr e pr eocupada em indicar o caminho certo, pelas e xperiências, apr endizagens e
valor es transmitidos.
A Coimbra, par a que te lembr es de mim.

Resumo
O presente Relatório de Estágio, redigido no âmbito do Mestrado em Ensino da Matemática no 3º
Ciclo do Ensino Básico e no Secundário, da Faculdade de Ciências e T ecnologia da Uni versidade de
Coimbra, descre ve as ati vidades desen v olvidas durante o Estágio Curricular , no ano leti v o 2021/2022,
na Escola Secundária José Falcão em Coimbra.
Sob a Orientação Científica da Professora Doutora Helena Alb uquerque e sob Orientação
Pedagógica da Professora Nati vidade Correia, o Núcleo de Estágio de Matemática foi, ainda, consti-
tuído pelas estagiárias Ana Rita Carv alho, Bibiana Almeida e Diana Batista.
O Núcleo de Estágio desen volv eu a sua prática leti va no Ensino Secundário em duas turmas do
10º ano de Matemática A e numa turma do 12º ano de Matemática A.
Este relatório, organizado por capítulos, descre ve e e videncia os trabalhos desen v olvidos rela-
cionados com a prática leti v a supervisionada, a participação nas estruturas de orientação pedagógica e
educati v a e as atividades e xtracurriculares dinamizadas.
Como conclusão, será apresentada uma reflexão sobre o percurso realizado ao longo deste ano
leti vo, destacando a importância que este te ve na preparação da vida profissional da autora deste
relatório.
Pala vras-Chav e : Estágio; Matemática; Prática Letiv a; Pedagogia; Professora.

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Abstract
This Internship Report, de veloped under the Master’ s in Mathematics T eaching in the 3rd Cycle
of Basic and Secondary Education, at the Faculty of Sciences and T echnology of the Uni versity of
Coimbra, describes all the acti vities conducted under the Curricular Internship during the academic
year of 2021/2022 at the José Falcão High School in Coimbra.
Under the scientific supervision of Professor Dr . Helena Alb uquerque and the pedagogic super-
vision of Professor Nati vidade Correia, the Mathematics Internship Group was, yet, comprised by
interns Ana Rita Carv alho, Bibiana Almeida, and Diana Batista.
The Internship Group de v eloped its High School teaching practices across two classes of the 10 th
Grade of Mathematics A and one class of the 12 th Grade of Mathematics A.
This report, or ganised by chapters, describes and demonstrates, in a detailed manner , all the
conducted assignments relating to the supervised teaching practice, the participation in the pedagogic
and educational frame work, as well as all the e xtracurricular acti vities carried out.
The conclusion of this report presents a reflection reg arding the academic year as a whole,
underlining its importance preparing, the author of this report, for future professional career as a
teacher .
K ey-W ords : Internship; Mathematics; T eaching Practices ; Pedagogic; T eacher .

Conteúdo
Lista de Figuras xv
1 Intr odução 1
2 Enquadramento do Estágio Curricular 3
2.1 Escola Secundária José Falcão [ 7 ] ........................... 3
2 . 1 . 1 H i s t ó r i a d a E s c o l a ............................... 3
2 . 1 . 2 O f e r t a F o r m a t i v a ................................ 4
2.2 Núcleo de Estágio de Matemática . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Caracterização das turmas de estágio . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 . 3 . 1 T u r m a 5 d o 1 0 º a n o ............................... 5
2 . 3 . 2 T u r m a 7 d o 1 0 º a n o ............................... 8
2 . 3 . 3 T u r m a 3 d o 1 2 º a n o ............................... 8
3 Prática P edagógica 9
3 . 1 P l a n i fi c a ç õ e s ...................................... 9
3 . 1 . 1 P l a n i fi c a ç ã o A n u a l ............................... 9
3.1.2 Planificações por Período . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1.3 Planificações por Unidade . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 . 1 . 4 P l a n o s d e A u l a ................................. 10
3 . 2 A u l a s .......................................... 10
3.2.1 Aulas Observ adas Pela Professora Estagiária . . . . . . . . . . . . . . . . . 10
3 . 2 . 2 A u l a s L e c i o n a d a s ................................ 11
3.2.3 Aula de Cidadania e Desen volvimento . . . . . . . . . . . . . . . . . . . . . 20
3 . 3 A p o i o a o E s t u d o ..................................... 20
3 . 4 F i c h a s d e T r a b a l h o ................................... 21
3 . 5 A v a l i a ç ã o ........................................ 21
3.5.1 Momentos Formais de A valiação . . . . . . . . . . . . . . . . . . . . . . . . 22
3.5.1.1 Prov as Parcelares . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3 . 5 . 1 . 2 P r o v a s G l o b a i s ............................ 22
3.5.1.3 T rabalhos de Grupo em Sala de Aula . . . . . . . . . . . . . . . . 22
3 . 5 . 2 P r o j e t o M A I A ................................. 23
3.5.3 A v aliação na Disciplina de Matemática A . . . . . . . . . . . . . . . . . . . 24

xii Conteúdo
3 . 5 . 4 A u t o a v a l i a ç ã o .................................. 25
3 . 6 A ç õ e s d e F o r m a ç ã o ................................... 25
3.6.1 Jornadas Pedagógicas: Desafios da Educação no Séc.XXI . . . . . . . . . . 25
3 . 6 . 2 A v a l i a ç ã o P e d a g ó g i c a ............................. 26
3.6.3
IX Encontro Nacional de F ormadores: Como aprende quem aprende? As
idiossincrasias da aprendizagem. . . . . . . . . . . . . . . . . . . . . . . . . 26
3.6.4 De Aluno a Professor: Futuros Pre vistos para o Ensino na Escola Pública . . 26
4 Estruturas de Orientação P edagógica e Educativa 27
4.1 Or gãos da Escola [ 7 ] .................................. 27
4 . 2 D i r e ç ã o d e T u r m a................................. ... 27
4 . 3 R e u n i õ e s ........................................ 28
4 . 3 . 1 R e u n i ã o G e r a l ................................. 28
4.3.2 Reuniões de Departamento de Matemática e Ciências Experimentais . . . . . 28
4.3.3 Reuniões de Grupo Disciplinar . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.3.4 Reuniões de Conselho de T urma . . . . . . . . . . . . . . . . . . . . . . . . 29
4.3.5 Reuniões de Núcleo de Estágio . . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Atividades na Escola 31
5.1 Atividades Desen v olvidas pelo Núcleo de Estágio de Matemática . . . . . . . . . . . 31
5.1.1 Quem Quer Ser Matemático? ......................... 31
5.1.2 Concurso A Matemática e os Afetos ...................... 34
5 . 1 . 3 S e m a n a d a M a t e m á t i c a ............................. 35
5.1.3.1 Exposição: A Matemática e os Afetos ................ 36
5.1.3.2 MathCityMap na ESJF . . . . . . . . . . . . . . . . . . . . . . . 37
5.1.3.3
Palestras - Alice do outr o lado do espelho e De Pitágor as aos
Nossos Dias: A Matemática e a Música ............... 38
5.2 Atividades Desen v olvidas pela Professora Estagiária . . . . . . . . . . . . . . . . . 39
5.3 Colaboração em Outras Ati vidades . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6 Conclusão 43
Bibliografia 45
Anexo A Planificação Anual de Matemática A do 10º ano 47
Anexo B Planificação do 3º P eríodo de Matemática A para o 10º ano 49
Anexo C Planificação Semanal do 3º P eríodo 53
Anexo D Planificação por Unidade - P olinómios 55
Anexo E Plano de A ula 59
Anexo F Ficha Inf ormativ a - Lógica e T eoria de Conjuntos 63

Conteúdo xiii
Anexo G A ula Assistida 1 - Plano de A ula 69
Anexo H A presentação em P o werP oint - Inequações de grau superior ao primeiro 75
Anexo I A ula Assistida 1 - Desafios do jogo 83
Anexo J A ula Assistida 1 - Regras do jogo 87
Anexo K A ula Assistida 2 - Plano de A ula 89
Anexo L A pr esentação em P o werP oint - Sinal de uma função quadrática 95
Anexo M A ula Assistida 2 - Pistas do Caça ao T esouro 105
Anexo N A ula Assistida 2 - A v aliação do desempenho e da atividade 111
Anexo O Cidadania e Desen v olvimento - Plano de aula 113
Anexo P Pr ova P ar celar 117
Anexo Q Matriz, Pr ova Global de A v aliação e Critérios de Classificação 119
Q.1 Matriz da Pro v a Global de A valiação . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Q . 2 P r o v a G l o b a l d e A v a l i a ç ã o ............................... 122
Q . 3 C r i t é r i o s d e C l a s s i fi c a ç ã o ................................ 126
Anexo R T rabalho de Grupo em Sala de A ula 131
Anexo S Ficha de T rabalho - Função Quadrática 135
Anexo T Fichas de A utoa valiação 139
T .1 Ficha de Autoav aliação proposta pelo NEM . . . . . . . . . . . . . . . . . . . . . . 139
T .2 Ficha de Autoav aliação aprov ada pelo Grupo Disciplinar . . . . . . . . . . . . . . . 142
Anexo U Roteir o MathCityMap na ESJF para o 9ºano 145
Anexo V Fichas de T rabalho - Projeto Educacional II 149
V .1 Matemática aplicada à Biologia: Deri v ação de funções . . . . . . . . . . . . . . . . 149
V .2 Matemática aplicada à Psicologia: Deri v ação de funções . . . . . . . . . . . . . . . 152

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Lista de Figuras
2.1 Escola Secundária José Falcão . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Idades dos alunos da turma 5 do 10º ano . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Distância da residência dos alunos à escola . . . . . . . . . . . . . . . . . . . . . . 6
2.4 Disciplinas preferidas dos alunos da turma 5 do 10º ano . . . . . . . . . . . . . . . . 6
2.5 Disciplinas com maior dificuldade dos alunos da turma 5 do 10º ano . . . . . . . . . 7
2 . 6 T u r m a 1 0 º 5 ....................................... 7
3.1 Construção do painel do jogo - Desenho do esboço . . . . . . . . . . . . . . . . . . 13
3.2 Construção do painel do jogo - Pinturas e pormenores . . . . . . . . . . . . . . . . . 13
3.3 Aula Assistida 1 - Preparação do se gundo tempo leti v o . . . . . . . . . . . . . . . . 14
3.4 Mapa do tesouro - Ilha de São Miguel . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.5 Impressão e plastificação do puzzle . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 . 6 R e c o r t e d o p u z z l e .................................... 17
3.7 Entrada e saída do portal virtual . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3 . 8 D e n t r o d o p o r t a l v i r t u a l ................................. 18
3.9 Exploração do portal virtual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.10 Equipa V encedora - Caça ao tesouro . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.11 Aula de Cidadania e Desen v olvimento . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 . 1 2A p o i o a o E s t u d o ..................................... 21
3.13 Ex emplos de instrumentos de recolha de informação . . . . . . . . . . . . . . . . . 23
3.14 Grelha de a v aliação de uma Prov a Global de A v aliação . . . . . . . . . . . . . . . . 24
3 . 1 5 G r e l h a d a A v a l i a ç ã o F i n a l ................................ 25
5 . 1 C a r t a z d o C o n c u r s o................................... 31
5.2 Folha de respostas do concurso Quem Quer Ser Matemático? ............. 32
5.3 Certificados de participação no concurso Quem Quer Ser Matemático? ........ 33
5.4 Dia do concurso Quem Quer Ser Matemático? ..................... 33
5.5 V encedores do concurso Quem Quer Ser Matemático? ................ 33
5.6 Cartaz do concurso A Matemática e os Afetos ..................... 34
5.7 Certificado de participação no concurso A Matemática e os Afetos .......... 35
5.8 Entreg a dos prémios aos v encedores do concurso A Matemática e os Afetos ..... 35
5.9 Horário proposto para as ati vidades da Semana da Matemática . . . . . . . . . . . . 36
5.10 Exposição A Matemática e os Afetos .......................... 36
xv

xvi Lista de Figuras
5.11 Medalhas entre gues aos alunos do 3º Ciclo . . . . . . . . . . . . . . . . . . . . . . . 37
5.12 Decorrer da ati vidade MathCityMap na ESJF ..................... 37
5 . 1 3 C a r t a z d a s P a l e s t r a s ................................... 38
5.14 P alestra Alice do outr o lado do espelho ......................... 39
5.15 P alestra De Pitágoras aos nossos dias: A Matemática e a Música ........... 39
5.16 Aulas de Matemática aplicada à Biologia e à Psicologia . . . . . . . . . . . . . . . . 40
5.17 Jogo Deriva ....................................... 41

Capítulo 1
Intr odução
O Estágio Curricular é o culminar do esforço feito ao longo de cinco anos e, por isso, tem uma
grande importância.
É tão bonito sentir que a transição de aluno a professor é feita no decorrer do Estágio Curricular .
Durante este ano leti vo, para os meus alunos eu era a professora, porém, continuav a a ser , para os
meus professores, uma aluna.
A educação é responsável pela transformação e desen v olvimento social, por isso é necessário que
o futuro professor tenha consciência do desafio que é ex ercer esta profissão. O estágio é apenas o
ponto de partida, a b usca por e voluir de ve ser uma taref a constante.
Este relatório, redigido no âmbito da unidade curricular Estágio e Relatório , presente no plano de
estudos do segundo ano do Mestrado em Ensino da Matemática no 3.º Ciclo do Ensino Básico e no
Secundário do Departamento de Matemática da Faculdade de Ciências e T ecnologia da Uni versidade
de Coimbra, tem como principal objeti v o a descrição e refle xão sobre o trabalho desen volvido ao
longo do Estágio Curricular . A autora deste relatório realizou o seu estágio na Escola Secundária José
Falcão (ESJF), durante o ano leti vo 2021/2022.
O Núcleo de Estágio de Matemática foi constituído pela Orientadora Científica, Professora
Doutora Helena Alb uquerque, pela Orientadora Cooperante, Professora Nati vidade Correia, e pelas
três estagiárias, Ana Rita Carv alho, Bibiana Almeida e Diana Batista.
No início do ano leti vo, foi realizado um sorteio para se definir quais as turmas que cada uma das
estagiárias iria acompanhar . Ficou assim determinado que eu iria ex ercer a minha prática pedagógica
na turma 5 do 10.º ano do Curso Científico-Humanístico de Ciências e T ecnologias, na disciplina de
Matemática A. Para além disso, todas as estagiárias ti v eram a oportunidade de assistir às aulas umas
das outras, e às aulas lecionadas pela Orientadora Cooperante, em cada uma das turmas atrib uídas à
mesma, prestando auxílio sempre que necessário.
O presente documento encontra-se or ganizado em cinco capítulos, sendo o primeiro a Introdução.
No segundo capítulo, Enquadramento do Estágio Curricular , para além de ser apresentada uma bre ve
nota histórica sobre a Escola, é caracterizado o Núcleo de Estágio de Matemática e as respetiv as
turmas.
No terceiro capítulo é descrita a Prática Pedagógica e o trabalho desen v olvido durante a mesma,
desde a elaboração de planificações, à prática leti va, passando pelas aulas assistidas, aulas de apoio,
a v aliação efetuada e ações de formação realizadas.
1

2 Introdução
O quarto capítulo é dedicado às Estruturas de Orientação Pedagógica e Educati v a. Neste ponto é
feita a descrição das reuniões em que a Professora Estagiária este ve presente e a referência ao trabalho
realizado na Direção de T urma do 10º5.
No capítulo seguinte, Ati vidades na Escola, são apresentadas as ati vidades or ganizadas e di-
namizadas por mim, pelo Núcleo de Estágio de Matemática, bem como as que estão presentes no
Plano Anual de Ati vidades, ligadas à disciplina de Matemática onde ti v e a oportunidade de colaborar .
Por fim, na Conclusão deste relatório está presente uma refle xão sobre a e xperiência e as apren-
dizagens que adquiri no decorrer do ano leti vo.
Ao longo deste documento são também referidos alguns materiais, apresentados em anexo, que
e videnciam o trabalho desen volvido.

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