1. 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

2. Ubiratan D'Ambrosio ICEm 32 1976: ICME 3, Karlsruhe “WHY TEACH MATHEMATICS” or “OBJECTIVES AND GOALS OF MATHEMATICS EDUCATION” MATHEMATICS AS A WESTERN BODY OF KNOWLEDGE AND CONCEPT (15 th -16 th Century)

3. Ubiratan D'Ambrosio ICEm 33 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 ]

4. Ubiratan D'Ambrosio ICEm 34 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].

5. Ubiratan D'Ambrosio ICEm 35 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!

6. Ubiratan D'Ambrosio ICEm 36 1984: ICME 5, Adelaide My talk: SOCIO-CULTURAL BASES OF MATHEMATICS EDUCATION. theory and examples leading to the concept of ETHNO+MATHEMA+TICS

7. Ubiratan D'Ambrosio ICEm 37 THEORY: The Cycle of Knowledge: generation, intellectual and social organization, transmission and diffusion. ⇒ CULTURAL DYNAMICS [the Basin Metaphor]

8. Ubiratan D'Ambrosio ICEm 38 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 15 th century and the STATE OF THE WORLD]

9. Ubiratan D'Ambrosio ICEm 39 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.

10. Ubiratan D'Ambrosio ICEm 310 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.

11. Ubiratan D'Ambrosio ICEm 311 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?

12. Ubiratan D'Ambrosio ICEm 312 THESE ARE THE DENIAL OF THE ESSENCE OF THE PHENOMENON LIFE and HISTORY SHOWS THAT MATHEMATICS IS INTRINSICALLY INVOLVED WITH ALL THIS.

13. Ubiratan D'Ambrosio ICEm 313 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.

14. Ubiratan D'Ambrosio ICEm 314 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

15. Ubiratan D'Ambrosio ICEm 315 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.

16. Ubiratan D'Ambrosio ICEm 316 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.

17. Ubiratan D'Ambrosio ICEm 317 These strategies are modes of behavior and individual and collective knowledge, which include communication, and language in the species homo, and instruments.

18. Ubiratan D'Ambrosio ICEm 318 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.

19. Ubiratan D'Ambrosio ICEm 319 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.

20. Ubiratan D'Ambrosio ICEm 320 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.

21. Ubiratan D'Ambrosio ICEm 321 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.

22. Ubiratan D'Ambrosio ICEm 322 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!

23. Ubiratan D'Ambrosio ICEm 323 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.

24. Ubiratan D'Ambrosio ICEm 324 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.

25. Ubiratan D'Ambrosio ICEm 325 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.

26. Ubiratan D'Ambrosio ICEm 326 OUR MISSION: TO REFLECT ON THE RESPONSIBILITY OF MATHEMATICIANS AND MATHEMATICS EDUCATORS IN OFFERING THE ELEMENTS TO RESPOND TO THIS PRIORITY. OUR PROPOSAL: ETHNOMATHEMATICS

27. Ubiratan D'Ambrosio ICEm 327 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].

28. Ubiratan D'Ambrosio ICEm 328 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.

29. Ubiratan D'Ambrosio ICEm 329 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].

30. Ubiratan D'Ambrosio ICEm 330 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”]

31. Ubiratan D'Ambrosio ICEm 331 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.