z } ~ } ~ z ¡ z z ¡ ® ~ } ~ ~ { z ~ z (648(0$6 '( '(021675$d2 3$5$ … ·...
TRANSCRIPT
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- Demostración en matemáticas- Esquemas de demostración- Razonamiento matemático- Representaciones- Álgebra Lineal
- Proof in mathematics- Proof schemes- Mathematical reasoning- Representations- Linear Algebra
Revista Latinoamericana de Investigación en Matemática Educativa 23 -
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- Démonstration en mathématiques
- Schémas de démonstration- Raisonnement mathématique- Représentations- Algèbre Linéaire
- Demonstração em matemática- Esquemas de demonstração- Raciocínio matemático- Representações- Álgebra Linear
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Demonstração e suas Funções
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aquilo porque
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Esquemas de Demonstração
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Categorias Subcategorias Descrição
ED de convicção externa
As conjeturas são validadas por recurso a fatores externos, como:
ED empíricos As conjeturas são validadas com recurso à experiência.
ED dedutivos As conjeturas são validadas para todos os casos (generalidade). A argumentação é organizada em etapas apropriadas para alcançar o objetivo final (pensamento operacional) e é baseada em regras lógicas (inferência lógica)
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Nível Características Descrição
1
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3
Representação e significação em processos de raciocínio matemático
sense making
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Figura 1.
Significar(“Sense making”)
RepresentarLinguagem natural, pictórica, algébrica, geométrica, estatística...
DeduçãoInduçãoAbdução
Formular conjeturasespecíficas
Formular questões- Específicas
- Gerais
Formular conjeturasgerais
Generalizar Justificar- Informalmentes
- Formalmente
Testare usar
propriedadesmatemáticas
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background
Opções metodológicas
design
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Alice Maria Pedro
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Moodle
Características das aulas
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Figura 2.
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[0 1 0 0 0]
100
0
0
10
0
351
0
4
318
1
2 0 00 0 0
010
0
Figura 3.
Características das tarefas
Figura 4.
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,=
× ( ) × ( )=
,
= (1 ) +
= =
Figura 5.
=
× × 1 =
Figura 6.
Figura 7.
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Alice
+ = +
3 × 1
Figura 8.
{1,2,3}
+ +
+
+
+
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Figura 9.
Figura 10.
3 = 6
=
= (1 ) + =
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× 1 =
Figura 11.
=
10 0
=00
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= 0 0
= 1 = 0
{0, 1}
= =
=
=
=
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Figura 12.
Maria
Figura 13.
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Figura 14.
= ==
1
1
X
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Figura 15.
=
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= =
=
= =
= ( ) = ( )
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Figura 16.
,
Pedro
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Figura 17.
+ = +
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Figura 18.
=
Figura 19.
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=
=
Figura 20.
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Figura 21.
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×
Comparação de resultados
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{( , , 0): , }
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Alic
eM
aria
Pedr
oTC
AVTS
PITA
PLTC
AVTS
PITA
PLTC
AVTS
PITA
PLED R TR
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sense making
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modus ponens
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sense-making;
Explanation and Proof in Mathematics: Philosophical and Educational Perspectives
The Qualitative Report 13
Educação e MatemáticaEducação e
MatemáticaAtas do
CIEMeLP2015
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Programa e MetasCurriculares de Matemática para o Ensino Básico
Programa e Metas Curriculares de Matemática para o Ensino Secundário
Investigação qualitativa em educação
Educação & Sociedade
Education and Culture 29
Bolema 28Revista de Educação
18
Teaching and LearningProof Across the Grades: A K-16 perspective
Quadrante
Atas do EIEM 2006American
Journal of PhysicsAnálise de erros
Educação e Matemática
Democracy and education
Revista Latinoamericana de Investigación en Matemática Educativa 19
Educational Studies in Mathematics 61
Actes du XXXIIe Colloque COPIRELEM
—
Educational Studies in Mathematics
Handbook of International Research in Mathematics Education
Educational Studies in Mathematics
Proof and Proving in Mathematics Education
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For the Learning of Mathematics 7
Research on Collegiate Mathematics Education
Second handbook of research on mathematics teaching and learning
Journal for Research in Mathematics Education 31
Mathematical Thinking and Learning 20
Education and Culture 28
Mathematical Thinking and Learning 7
The Journal of Mathematical BehaviorRevista do Professor de Matemática
Combinatorics and reasoningThinking mathematically
Actas do Encontro de Investigação em Educação Matemática EIEM 2011 - Ensino e Aprendizagem da Álgebra
Boletim GEPEM
Quadrante 20
Procedia Social and Behavioral Sciences
Handbook of research on the psychology of mathematics education
The origins of intelligence in children
O professor e o desenvolvimentocurricular
A demonstração na prática social da aula de matemática
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Da Investigação às PráticasII
Educational Studies in MathematicsUm curso de Geometria Analítica e Álgebra Linear
Mathematical Thinking and Learning
Compendium for research in mathematics education
Educational Studies in Mathematics 96
Educational Studies in Mathematics 12Aprender de los errores
Case study research: design and methods
Autores
Patrícia Damas Beites
Maria Luísa Frazão Rodrigues Branco
Maria Cecília Rosas Pereira Peixoto da Costa