Third International Conference on Ethnomathematics (ICEm-3

							Third International Conference on
   Ethnomathematics (ICEm-3)
     Auckland, New Zealand
       12-16 February, 2006.
 THE SCENARIO 30 YEARS AFTER

       Ubiratan D’Ambrosio
          ubi@pucsp.br
1976: ICME 3 , Karlsruhe
“WHY TEACH MATHEMATICS”
           or
“OBJECTIVES AND GOALS OF
 MATHEMATICS EDUCATION”

MATHEMATICS AS A WESTERN
 BODY OF KNOWLEDGE AND
 CONCEPT (15th-16th Century)
         Ubiratan D'Ambrosio ICEm 3   2
A broader historiography [including the
   mathematics of non-mathematicians].
    – Mathematics and society [PEACE].
    – Mathematics and culture.
•   A holistic concept of curriculum.
•   Mathematics acquired by societies which
    are not in the main stream [consumers, not
    producers, of Mathematics] ≈ the cultural
    strangeness of Mathematics.
      [reference to Claudia Zaslavsky’s Africa
    Counts]

                   Ubiratan D'Ambrosio ICEm 3   3
1977-78: The name Ethnomathematics [by
  analogy with ethnobiology,
  ethnomusicology, ethnography].
ICM 1978, Helsinky:
  The etymological exercise:
          alustapasivistykselitys,
  and the option for something more
  acceptable:
     ethno [culture]
     + mathema [explaining,
  understanding]
     + tics [techné, arts, techniques].
              Ubiratan D'Ambrosio ICEm 3   4
1980: ICME 4, Berkeley.
  The holistic concept of curriculum:
         methods
                                 • (O,C,M)
                                      contents
     objectives
and the cycle of knowledge [learning and
 teaching]: FROM REALITY TO ACTION.
     THE GROUND WAS PREPARED!

                Ubiratan D'Ambrosio ICEm 3       5
1984: ICME 5, Adelaide
 My talk:
   SOCIO-CULTURAL BASES OF
     MATHEMATICS EDUCATION.

 theory and examples leading to the
 concept of
     ETHNO+MATHEMA+TICS

            Ubiratan D'Ambrosio ICEm 3   6
THEORY:
The Cycle of Knowledge:
• generation,
• intellectual and social organization,
• transmission and diffusion.
     ⇒ CULTURAL DYNAMICS
              [the Basin Metaphor]


              Ubiratan D'Ambrosio ICEm 3   7
    MAIN ISSUES RAISED
• A broad historiography [which
  includes the mathematics by non-
  mathematicians ≈ the people].
• Cultural Dynamics of the Encounters,
  throughout history.
• The Political Dimension [the
  expansion of the Empires since the
  15th century and the STATE OF THE
  WORLD]

             Ubiratan D'Ambrosio ICEm 3   8
      THE STATE OF THE WORLD: MAIN
     ISSUES AFFECTING MATHEMATICS
               EDUCATION

    national security, personal security,
•    government/politics,
•    economics: social and environmental impact,
•    relations among nations,
•    relations among social classes,
•    people’s welfare,
•   the preservation of natural and cultural
    resources.

                   Ubiratan D'Ambrosio ICEm 3   9
MATHEMATICS, MATHEMATICIANS
 AND MATHEMATICS EDUCATORS
 ARE DEEPLY INVOLVED WITH ALL
          THESE ISSUES.
AND THESE ISSUES ARE INTRINSIC
    TO THE PHENOMENON LIFE,
      AFFECTING HUMANS AS
   INDIVIDUALS, THE RELATIONS
       BETWEEN INDIVIDUAL,
    INDIVIDUALS ORGANIZED IN
 SOCIETIES AND THEIR RELATIONS
           WITH NATURE.
          Ubiratan D'Ambrosio ICEm 3   10
THE MOST INTRIGUING QUESTION
WHY DO PEOPLE INTERRUPT LIFE,
 THEIR OWN [suicides] and OF
 OTHERS [bombings, poisoning,
 executions, etc.]?
and
DESTROY THE ENVIRONMENT?
    WHY ARROGANCE, INIQUITY,
           BIGOTRY?


            Ubiratan D'Ambrosio ICEm 3   11
  THESE ARE THE DENIAL OF
       THE ESSENCE OF
   THE PHENOMENON LIFE
             and
    HISTORY SHOWS THAT
        MATHEMATICS IS
INTRINSICALLY INVOLVED WITH
           ALL THIS.


         Ubiratan D'Ambrosio ICEm 3   12
   THE PHENOMENON LIFE
     INDIVIDUAL                 NATURE/REALITY


         OTHERS/SOCIETY
EVERY INDIVIDUAL NEEDS NATURE FOR
 INDIVIDUAL SURVIVAL
and
OTHERS FOR CREATING, INCLUDING THE
 CONTINUITY OF THE SPECIES.
            Ubiratan D'Ambrosio ICEm 3     13
INTERMEDIACIES CREATED BY THE
       HUMAN SPECIES
             instruments
INDIVIDUAL                           NATURE/REALITY

      language                production
        emotions            labor

         OTHERS/SOCIETY
 THUS ENHANCING THE POSSIBILITIES OF
SURVIVAL AND CREATING THE QUEST FOR
           TRANSCENDENCE
               Ubiratan D'Ambrosio ICEm 3         14
THE PULSIONS OF SURVIVAL
 AND TRANSCENDENCE ARE
 THE CHARACTERISTICS OF
   THE HUMAN SPECIES.

 THE ADVENTURE OF THE
  HUMAN SPECIES IS THE
 SEARCH OF SURVIVAL AND
    TRANSCENDENCE.
       Ubiratan D'Ambrosio ICEm 3   15
Every animal species develop, in the
 search of survival, the means to work
 with the most immediate environment,
 which supplies air, water, food, the
 other individual necessary for
 procreation, and everything that is
 necessary for the survival of the
 individuals and of the species.



              Ubiratan D'Ambrosio ICEm 3   16
These strategies are
modes of behavior and individual
   and collective knowledge,
which include communication,
 and language in the species
 homo, and instruments.


            Ubiratan D'Ambrosio ICEm 3   17
In the search of transcendence,
  the species homo develop the
  perception of past, present and
  future, and their linkage, and the
  explanations of facts and
  phenomena encountered in their
  natural and imaginary
  environment.


             Ubiratan D'Ambrosio ICEm 3   18
These are incorporated to the memory,
 individual and collective, and
 organized as arts, technics, which
 evolve as representations of the real
 [MODELS], the elaboration about
 these representations [artifacts], the
 organization of systems about
 explanations of the origins and the
 creation of myths and mysteries, and
      attempts to know the future.

               Ubiratan D'Ambrosio ICEm 3   19
The attempts to know the future
 [divinatory arts] encounter
 support in the memory, where
 we find the myths, the mysteries,
 history and the traditions, which
 include religions and value
 systems.



            Ubiratan D'Ambrosio ICEm 3   20
     SYSTEMS OF KNOWLEDGE
Through these MODELS humans learn how
 to survive [now ≈ time and here ≈ space]
 and how to transcend time and space, and
 as consequence generate systems of
 explanations for myths and mysteries, for
 facts and phenomena and how to deal and
 cope with them. These systems of
 knowledge, organized as arts, techniques,
 theories, are the essence of the
          ETHNOMATHEMATICS.
                Ubiratan D'Ambrosio ICEm 3   21
Other systems of knowledge, ALL
 BASED ON THESE CONCEPTS and
 IDEAS [generally called
 MATHEMATICAL CONCEPTS and
 IDEAS] are the divination arts,
 astrology, the oracles, logic, the I
 Ching, numerology and the
 SCIENCES, in general, through
 which we may know what will
 happen – before it happens!

             Ubiratan D'Ambrosio ICEm 3   22
MATHEMATICAL CONCEPTS and
        IDEAS, particularly
 observing, classifying, ordering,
comparing, measuring, quatifying,
       inferring, inventing,

when organized in a specificic way
[Western] constitute what is called
        MATHEMATICS.

            Ubiratan D'Ambrosio ICEm 3   23
It is agreed by all that
MATHEMATICS [as a way of
 organizing MATHEMATICAL
 CONCEPTS AND IDEAS] is the most
 universal mode of thought
and
SURVIVAL WITH DIGNITY is the most
 universal problem facing mankind.

                  Ubiratan D'Ambrosio ICEm 3   24
PRIORITY: TO LOOK INTO THE
 RELATIONS BETWEEN THESE TWO
 UNIVERSALS, that is, INTO THE
 ROLE OF MATHEMATICIANS AND
 MATH EDUCATORS IN THE
 PURSUIT OF A CIVILIZATION WITH
 DIGNITY FOR ALL, IN WHICH
 INIQUITY, ARROGANCE AND
 BIGOTRY HAVE NO PLACE.
           Ubiratan D'Ambrosio ICEm 3   25
OUR MISSION: TO REFLECT ON THE
       RESPONSIBILITY OF
     MATHEMATICIANS AND
  MATHEMATICS EDUCATORS IN
  OFFERING THE ELEMENTS TO
   RESPOND TO THIS PRIORITY.
        OUR PROPOSAL:
      ETHNOMATHEMATICS


           Ubiratan D'Ambrosio ICEm 3   26
        AND WHAT IS
    ETHNOMATHEMATICS?
ETHNOMATHEMATICS IS A
 RESEARCH PROGRAM IN THE
 HISTORY AND PHILOSOPHY OF
 MATHEMATICS, WITH
 PEDAGOGICAL IMPLICATIONS,
FOCUSING the ARTS AND
 TECHNIQUES [TICS] of EXPLAING,
 UNDERSTANDING and COPING
 WITH [MATHEMA] DIFFERENT
 SOCIO-CULTURAL ENVIRONMENTS
 [ETHNO].   Ubiratan D'Ambrosio ICEm 3 27
   THE PEDAGOGICAL STRAND OF
       ETHNOMATHEMATICS
THE MAJOR GOALS OF EDUCATION:
• TO PROMOTE CREATIVITY, HELPING
  PEOPLE TO FULFILL THEIR POTENTIALS
  AND RAISE TO THE HIGHEST OF THEIR
  CAPABILITY;
• TO PROMOTE CITIZENSHIP,
  TRANSMITTING VALUES AND
  UNDERSTANDING RIGHTS AND
  RESPONSIBILITIES IN SOCIETY.
POSSIBLE METHODS:
       PROJECTS, MODELLING.
             Ubiratan D'Ambrosio ICEm 3   28
     THE SCENARIO NOW
CRITICAL VIEWS OF MATHEMATICS
 EDUCATION as THE RESULT OF
 STRESSING THE POLITICAL
 DIMENSION
BUT
which meets the resistance of A
 NOSTALGIC and OBSOLETE
 PERCEPTION OF WHAT IS
 MATHEMATICS [the malignous
 efeects of STANDIZED
 EVALUATION].
           Ubiratan D'Ambrosio ICEm 3   29
     THE SCEPTICISM ABOUT
      ETHNOMATHEMATICS
which results of a DAMAGING CONFUSION
  OF ETHNOMATHEMATICS WITH
  ETHNIC-MATHEMATICS, caused by a
  strong emphasis on ETHNOGRAPHIC
  studies, sometimes not supported by
  theoretical foundations.
THIS MAY LEAD TO A FOLKLORISTIC
  PERCEPTION OF ETHNOMATHEMATICS
(an example: the misleading title of the
  special issue of Pour la Science -
  “Mathématiques éxotiques”]
              Ubiratan D'Ambrosio ICEm 3   30
        MY PROPOSAL
TO GIVE MORE ATTENTION TO THE
 THEORETICAL STRAND OF THE
 PROGRAM ETHNOMATHEMATICS
 as A RESEARCH PROGRAM IN THE
 HISTORY AND PHILOSOPHY OF
 MATHEMATICS [Mediterranean,
 Western and non-Western], WITH
 PEDAGOGICAL IMPLICATIONS.

           Ubiratan D'Ambrosio ICEm 3   31