Third International Conference on Ethnomathematics

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Third International Conference on
Ethnomathematics (ICEm-3) Auckland, New
Zealand12-16 February, 2006.

• THE SCENARIO 30 YEARS AFTER
• Ubiratan DAmbrosio
• ubi_at_pucsp.br

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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)

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• 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 Zaslavskys Africa Counts

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• 1977-78 The name Ethnomathematics by analogy
  with ethnobiology, ethnomusicology, ethnography.
• ICM 1978, Helsinky
• The etymological exercise alustapasivistyks
  elitys,
• and the option for something more acceptable
• ethno culture
• mathema explaining, understanding
• tics techné, arts, techniques.

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• 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!

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• 1984 ICME 5, Adelaide
• My talk
• SOCIO-CULTURAL BASES OF MATHEMATICS EDUCATION.
• theory and examples leading to the concept of
• ETHNOMATHEMATICS

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• THEORY
• The Cycle of Knowledge
• generation,
• intellectual and social organization,
• transmission and diffusion.
• ? CULTURAL DYNAMICS
• the Basin Metaphor

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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

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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,
• peoples welfare,
• the preservation of natural and cultural
  resources.
•   

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• 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.

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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?

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• THESE ARE THE DENIAL OF
• THE ESSENCE OF
• THE PHENOMENON LIFE
• and
• HISTORY SHOWS THAT MATHEMATICS IS INTRINSICALLY
  INVOLVED WITH ALL THIS.

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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.

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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

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• 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.

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• 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.

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• These strategies are
• modes of behavior and individual and collective
  knowledge,
• which include communication, and language in the
  species homo, and instruments.

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• 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.

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• 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.

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• 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.

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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.

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• 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!

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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.

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• 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.

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• 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.

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• OUR MISSION TO REFLECT ON THE RESPONSIBILITY OF
  MATHEMATICIANS AND MATHEMATICS EDUCATORS IN
  OFFERING THE ELEMENTS TO RESPOND TO THIS
  PRIORITY.
•  OUR PROPOSAL ETHNOMATHEMATICS

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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.

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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.

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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.

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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

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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.