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Funciónes y creatividad

MEM 2017 Bogotá
by

Christian Mercat

on 12 February 2017

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Transcript of Funciónes y creatividad

Creatividad en el aula
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/
Technologia
¿valor añadida?
¿o impedimento?
affordance
J. Gibson
vs. creatividad
Pierre Gallais
http://www.institutdemathologie.fr
http://www.mathcitymap.de
Pr. Dr. Matthias Ludwig
http://www.math.uni-frankfurt.de/~ludwig/
Originalidad
Flexibilidad
Fluidez
Elaboración
poco frecuente, ingeniosas mas que correctas, imprectibilidad, unicidad, sorpresa
sin rigidez, receptiva, tolerenta, versatil, capaz de cambios, libre, rica en argumentación, ve desde distintos angulos
muchas alternativas, analogías, semejanzas, relaciones...
Henri Poincaré
La ciencia y la hipótesis
Jacques Hadamard
Essai sur la psychologie de l'invention dans le domaine mathématique
Théorème vivant
Cédric Villani
Guilford, Lowenfeld, Torrance
cuidadosa, con detalles, minuciosa, ve los pasos siguientes
+
Análisis
Síntesis
Comunicación
Apertura mental
Marín, de la Torre
Jos Leys
Étienne Ghys
Aurélien Alvarez
http://www.chaos-math.org/
http://www.dimensions-math.org/
preparación
incubación
Iluminación
traducción
verificación
Preparación
Incubación
Iluminación
traducción
verificación
Preparación
Incubación
Iluminación
traducción
verificación
Divergencia
Convergencia
Henri de Toulouse-Lautrec, Au lit (huile sur carton, 1892, Musée d'Orsay, Paris)
publicación
Aprender no a estimular creatividad pero a no castrarla
© Régis Goiffon
Preparación
Incubación
Iluminación
traducción
verificación
CONGRESO!
Julio Le Parc
Victor Vasarely
mc
Squared
Individual
Producto
Proceso
Ambiente
rasgos
acción de clase
logros
tareas colectivas
reflexión
de matemática
fuera d
Funciónes y
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!
Acción, formulación, validación
cambios del medio ambiente
http://mathenjeans.fr
Benoit Ray, Lycée de Tunis
Benoit Ray, Lycée de Tunis
http://www.ert.tn/pmf/spip.php?article336
Action Pédagogique Pilote
Tous chercheurs
https://www.geogebra.org/m/fY7Wstbr
https://www.facebook.com/pedro.lealdinofilho/videos/1548290168814433/?l=6819618236367935652
http://bit.ly/webcamconf
Briget Riley
http://observer.com/2012/09/bridget-riley-wins-2012-sikkens-prize-for-contribution-to-color/
(Evening Standard/Getty Images)
http://bit.ly/StrasbourgIREM2016
http://bit.ly/GeogebraBookOpArt
https://imaginary.org/program/surfer
http://www.nctm.org/Publications/Mathematics-Teacher/2016/Vol110/Issue5/Mathematical-Modeling-in-the-High-School-Curriculum/
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