Creativity and Modeling: Inquiry-Based Learning

??
Motivação do Aluno
The process
O tema das Funções
Analisamos a produção dos estudantes
Criatividade na Matemática
Creative mathematical thinking
MathMagic: Computational and
Mathematical Thinking
A fundação da ciência
O nascimento de uma ideia
Estes são com um c maiúsculo!
o que fazer com c minúsculo?
what happens in mathematics?
Function Hero!
A combination of theories
Divergent thinking - guilford
Fluency
Flexibility
elaboration
originality

creative process - wallas
Preparation
incubation
illumination
verification
Préparation
Incubation
Illumination
Traduction
Vérification
Préparation
Incubation
Illumination
Traduction
Vérification
Préparation
Incubation
Illumination
Traduction
Vérification
Divergence
Convergence
Henri de Toulouse-Lautrec, Au lit (huile sur carton, 1892, Musée d'Orsay, Paris)
Publication
réflexion
Motivation
action
formulation
validation
formulation
validation?
phase pragmatique -> phase empirique ->
phase théorique
aplicaCiÓn
BEFORE IT STARTS
GET BORING...
this is an empty circle (not so empty), just because i wanted it here.

are you not happy?

Deal with it....


thank you very much!
Perseverance
Tolerance
1. Plantear la pregunta correcta
2. Mundo real →formulación matemática
3. Cálculo
4. De vuelta a la realidad, verificación
Christian Mercat
IREM de Lyon
Pedro Lealdino Filho
nstitut
de
echerche
sur l'
nseignement
des
athématiques
Université Claude Bernard
1
Institut Camille Jordan
mc
Squared
¿Qué es la matemática?
http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers
matemática >> computación
*
Mathematics are better left to experts and initiated people

Mathematics can not be the subject of a conversation (contrarily to literature or philosophy)

Mathematics are only an abstraction, they don’t deal with reality

There is no room for uncertainty in mathematics

There is no room for creativity and imagination in mathematics

In mathematics, there is nothing left to discover

The mathematic courses are not pratical enough

Courses haven’t changed in the last decades when the world is evolving greatly and fast

With new means available to students, learning is no longer required, one just has to quickly find solutions to problems that are encountered

The structure of math courses doesn’t allow learning autonomy

A teacher only purpose is to bring knowledge to students

Mathematics weight too much in engineer training

There is almost no connection between math teaching and the engineer job reality

In engineer school, theory are taught without taking into account their applications

In engineer school, mathematics are mostly pure and abstract

Aprender matemáticas en las clases de primeros sirve sobre todo con el propósito de ayudar a los niños moverse en la vida
Natural phenomena are too complex to be apprehended by mathematics

Only applied mathematics are interesting

Mathematics are used mostly in technical domains

Mathematics have an interest, especially for solving concrete problems

Mathematics are a human construction

A mathematical theory can not be refuted

A mathematical model is necessarily limited

Only math can approach truth

Mathematics raised from concrete needs

Mathematics are only a tool for science

The mathematic courses are extremely pratical

The mathematics courses are not theoretical enough

The mathematic courses are extremely theoric

Mathematics can not be avoided in engineer training

Math teaching doesn’t try to establish links with other sciences

We need more applied mathematics in engineer training

Las matemáticas pueden aplicarse a los objetos artificiales elaborados y mucho menos a los objetos encontrados en la naturaleza
Mathematics serve no purpose in human sciences

Mathematics are useles in everyday life

Модуль 1 - Для чего нужна математика?

Objectif 1 – A quoi servent les mathématiques?

Genre

Модуль 2 - Математика в инженерных курсах
(содержание и методы)

Objectif 2 - Perceptions de l’enseignement des
mathématiques dans des écoles d’ingénieur

Perceptions of mathematics in engineering
courses

Общая информация

Informations Démographiques

Модуль 3 - Общее восприятие математики

Objectif 3 - Perceptions des mathématiques

Perception of Mathematics

Comité científico
Comisiónes Inter IREM (CII)
Recherche-Action
Épistémologie et histoire
CII APMEP Publimath
Collège
COPIRELEM
CORFEM
Didactique
Lycée
Lycée professionnel
Pop’Math
Repères
Statistique et probabilités
TICE
Université
EPI
nseignement
ratique
nterdisciplinaire
http://research.meumesmo.com.br/pesquisa/limesurvey/index.php?r=survey/index/sid/137861/lang/es
https://drive.google.com/file/d/0B7DYMJTPXwBbZmd0MzBRSUVsYms/view?usp=sharing
https://drive.google.com/file/d/0B7DYMJTPXwBbYXV2eXNma2dsZFU/view?usp=sharing
http://www.m2real.org/
© Régis Goiffon
Lyon
no sufren
las matemáticas,
¡disfrutan las!

https://imaginary.org/program/surfer
http://www.fondationvasarely.fr/
¡Hay creatividad en una expresión algebraica!
¡Hermosas cosas detrás de las funciónes!
http://www.nctm.org/Publications/Mathematics-Teacher/2016/Vol110/Issue5/Mathematical-Modeling-in-the-High-School-Curriculum/
Csíkszentmihályi, Liljedahl
A ciência e a hipótese
Henri Poincaré
Jacques Hadamard
Essai sur la psychologie de l'invention dans le domaine mathématique
Teorema vivendo
Cédric Villani
http://bit.ly/magie1-31
Preparation
Incubation
Illumination
Translation
Verification
Preparação
Incubação
Iluminação
Tradução
Verificação
Preparación
Incubación
Iluminación
traducción
verificación
Divergence
Convergence
Henri de Toulouse-Lautrec, Au lit (huile sur carton, 1892, Musée d'Orsay, Paris)
Publication
Reflection
Ação, formulação, validação
Troca de meio ambiente
f(x)=x³-x
exemplo: time 1
Dê-me um número, multiplique-o por si mismo duas vezes e subtrai-se uma vez. O que você ganha?
Como?
E Após?!
Originalidade
Flexibilidade
Fluidez
Elaboração
pouco frequente, mais do correta, engenhosa, imprevisível, única, supreendente

sem rigidez, receptiva, tolerante, versátil, capaz de mudar, livre, rica em argumentação, olha por vários ângulos
Muitas alternativas, analogias, semelhanças, relações
Guilford, Lowenfeld, Torrance
cuidadosa, com detalhes, minuciosa, enxerga os passos seguintes

+
Análise
Síntese
Comunicação
Abertura mental
Marín, de la Torre
Pessoal
Produto
Processo
Ambiente
Características
Ações de Grupo
Conquistas
Tarefas Coletivas
Uma combinação de teorias
Re-Earth
Surfer
https://imaginary.org/event/expo-imaginary-in-bogota
https://imaginary.org/es/program/surfer
Exemplo: time 2
abs(sin(x))
cos(x) + 2
x^(-2)
log(x)
exp(2*log(x))
exp(-x)
3*x
-x^(10)
abs(x)
log(-x+4)
log(x+6)
cos(x)
tan(-x)
f(x) = 0
sin(x-2)
exp(x^2)
cos(x^1/2)
cos(-x)
Webcam conforme
(x-3)(x+5)
http://bit.ly/webcamconf
http://bit.ly/GeogebraBookOpArt
nstituto
Pesquisa
de
em
ducação
atemática
Ciência, sociedade, história, educação, práticas
Casa de matemática e ciência da computação
frustação - muito difícil
tédio - muito fácil
perseverança
tolerância
fluxo
Dificuldade
Tempo e habilidade necessários
sentido de propósito - criatividade - produtividade
informação
conhecimento
criatividade
Pollok
Julio Le Parc
Bridget Rilley

How to formalize the activity into an
Inquiry-Based Learning approach?