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

Third International Conference on Ethnomathematics (ICEm-3)

Auckland, New Zealand12-16 February, 2006.

THE SCENARIO 30 YEARS AFTER

Ubiratan D’Ambrosio

[email protected]

Ubiratan D'Ambrosio ICEm 3 2

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)


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]


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].


1980: ICME 4, Berkeley.The holistic concept of curriculum:

methods • (O,C,M)

contents objectivesand the cycle of knowledge [learning and

teaching]: FROM REALITY TO ACTION.

THE GROUND WAS PREPARED!


1984: ICME 5, Adelaide

My talk:

SOCIO-CULTURAL BASES OF MATHEMATICS EDUCATION.

theory and examples leading to the concept of

ETHNO+MATHEMA+TICS


THEORY:

The Cycle of Knowledge:

• generation,

• intellectual and social organization,

• transmission and diffusion.

⇒ CULTURAL DYNAMICS

[the Basin Metaphor]


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]


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.


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.


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?


THESE ARE THE DENIAL OF THE ESSENCE OF

THE PHENOMENON LIFE and

HISTORY SHOWS THAT MATHEMATICS IS

INTRINSICALLY INVOLVED WITH ALL THIS.


THE PHENOMENON LIFE

INDIVIDUAL NATURE/REALITY

OTHERS/SOCIETY

EVERY INDIVIDUAL NEEDS NATURE FOR INDIVIDUAL SURVIVAL

andOTHERS FOR CREATING, INCLUDING THE

CONTINUITY OF THE SPECIES.


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


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.


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.


These strategies are

modes of behavior and individual and collective knowledge,

which include communication, and language in the species homo, and instruments.


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.


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.


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.


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.


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!


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.


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.


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.


OUR MISSION: TO REFLECT ON THE RESPONSIBILITY OF

MATHEMATICIANS AND MATHEMATICS EDUCATORS IN OFFERING THE ELEMENTS TO RESPOND TO THIS PRIORITY.

OUR PROPOSAL: ETHNOMATHEMATICS


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].


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.


THE SCENARIO NOW

CRITICAL VIEWS OF MATHEMATICS EDUCATION as THE RESULT OF STRESSING THE POLITICAL DIMENSION

BUTwhich meets the resistance of A

NOSTALGIC and OBSOLETE PERCEPTION OF WHAT IS MATHEMATICS [the malignous efeects of STANDIZED EVALUATION].


THE SCEPTICISM ABOUT ETHNOMATHEMATICS

which results of a DAMAGING CONFUSION OF ETHNOMATHEMATICS WITHETHNIC-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”]


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.

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

Documents

ubiratan dambrosio icem

mathematics educators

ethnomathematics icem

world slide

th century slide

basin metaphor slide

main issues

cultural dynamics