ethnomathematics in the global world: a …ncm.gu.se/media/ncm/dokument/dambrosio.pdfubiratan...

Ubiratan D'Ambrosio ubi@usp.br Stockholm

ROYAL INSTITUTE OF TECHNOLOGYStockholm, Sweden

26 January 2007

ETHNOMATHEMATICS IN THE GLOBAL WORLD: A STRATEGY

FOR SOCIAL JUSTICE.Ubiratan D’Ambrosio

ubi@usp.br

Globalization implies great changes in demography, with undesirable consequences for social justice.

In this talk I will discuss the apparent contradiction of a contextualized approach to mathematics in a World characterized by globalization and why the pedagogical strand of the Program Ethnomathematics may be a good strategy for achieving social justice.

AS AN EDUCATOR, I MUST ADDRESS THE GLOBAL ISSUES IN THE WORLD TODAY:

• ENVIRONMENTAL CRISIS• GOVERNANCE AND PEOPLE’S ROLE• DISRUPTION OF THE ECONOMIC SYSTEM• RELATIONS AMONG SOCIAL CLASSES and

NATIONS• INSTITUTIONAL EROSION• INDIVIDUAL AND NATIONAL SECURITY• MOUNTING SOCIAL CRISES• PEOPLE’S WELFARE• FEAR OF THE OTHER.

MY MAIN CONCERN AS A MATHEMATICIAN

Mathematics is regarded as the dorsal spine of Modern Civilization. It is the basis upon which Science, Technology and Human Behavior relies. On the other hand, no one disagrees that Science and Technology have controversial effects on the quality of life, threatening the basic conditions for sustainable life. And that Human Behavior is, frequently, despicable.

Bigotry, arrogance and inequity are sofrequent, in violation of human dignity.

SOCIETIES, ALL OVER THE WORLD, BELIEVE THAT EDUCATION IS IMPORTANT, FOR TWO MAIN REASONS:

1) TO ENHANCE CREATIVITY OF CHILDREN AND ADULTS, WHICH ALLOW FOR INVENTING THE NEW;

2) TO PROMOTE CITIZENSHIP, UNDERSTANDING RIGHTS AND DUTIES OF EVERY INDIVIDUAL.

BUT, WE WANTRESPONSIBLE CREATIVITY, NOT TO CREAT

NEW INSTRUMENTS WHICH REINFORCE BIGOTRY, ARROGANCE AND INEQUITY;

and ETHICAL [WORLD] CITIZENSHIP, WITH

• RESPECT for the OTHER/DIFFERENT • SOLIDARITY with the OTHER/DIFFERENT• COOPERATION with the OTHER/DIFFERENT.

WE ALL BELIEVE THAT MATHEMATICS CAN HELP TO ACHIEVE THE MAJOR GOALS OF EDUCATION, i.e., RESPONSIBLE CREATIVITY and an ETHICAL [WORLD] CITIZENSHIP.

BUT, WHAT KIND OF MATHEMATICS?

Bertrand Russell and Albert Einstein stated, in the Pugwash Manifesto (1955), that to achieve equilibrium and safety in a world menaced by war and fear, a New Thinking is needed.

IS IT FEASIBLE A NEW THINKING INMATHEMATICS AND MATHEMATICS

EDUCATION?

A VERY AMBITIOUS GOAL!

I address the possibilities ofMathematics, which is the dorsalspine of Modern Civilization, leadingHumanity, through MathematicsEducation, to an era ofPEACE and DIGNITY FOR ALL.

THE PATTERN OF MOST CURRICULUM PROPOSALS:

• contents ⇒ methods • objectives: largely ignore socio-cultural

context. ONE CHARACTERISTIC OF MOST PROPOSALS

IS A STRONG EMPHASIS ON THE QUANTITATIVE (COMPILATION AND CONTROL OF DATA AND ASSESSMENT) IN DETRIMENT OF THE QUALITATIVE (WHERE SOCIO-CULTURAL ISSUES ARE FUNDAMENTAL)

A REFLECTION COMING FROM THE HISTORY OF KNOWLEDGE,

IN PARTICULAR OF MATHEMATICS.

TO ACHIEVE RESPONSES TO THEIR MATERIAL AND SPIRITUAL NEEDS, HUMANS GENERATE

• WAYS, STYLES, ARTS and TECHNICS [techné → tics]

• of DOING/KNOWING, that is, OF LEARNING, OF EXPLAINING and OF COPING WITH [mathema]

• THE NATURAL, SOCIAL and CULTURAL ENVIRONMENT [ethno].

ethno + mathema + tics

thus,ETHNOMATHEMATICS EMERGES AS A

TRANSDISCIPLINARIAN AND TRANSCULTURAL

RESEARCH PROGRAM IN THE HISTORY AND PHILOSOPHY OF MATHEMATICS, WITH PEDAGOGICAL IMPLICATIONS.

ETHNOMATHEMATICS RESEARCH IS BASED IN THREE MAIN QUESTIONS:

1. How are ad hoc practices and solution of problems developed into methods?

2. How are methods developed into theories?

3. How are theories developed into scientific invention?

IMPLICATIONS FOR THE HISTORY OF MATHEMATICS

SINCE ACADEMICS MATHEMATICS [≈SCHOOL MATHEMATICS]

IS THE ETHNOMATHEMATICS OF THE WESTERN TRADITIONS, THE THREE QUESTIONS PROVIDE A BROADER HISTORIOGRAPHY OF ACADEMICS MATHEMATICS.

IT IS IMPORTANT TO SHOW THE STUDENTS THE PRESENCE OF MATHEMATICS IN A WORLD DOMINATED BY TECHNO-SCIENCE,

BUT ALSO : TO REASSURE THE STUDENTS OF

THEIR CULTURAL ROOTS

AN IMPORTANT REASON TO TEACH HISTORY OF MATHEMATICS IS TO SHOW THAT THERE IS A DYNAMICS IN THE EVOLUTION OF MATHEMATICAL KNOWLEDGE, TO WHICH ALL THE PEOPLES MADE THEIR CONTRIBUTION, NOT ONLY THE “HEROES” RECOGNIZED IN THE TRADITIONAL HISTORIES OF MATHEMATICS.

IT IS IMPORTANT TO RECALL THE CONTRIBUTION OF THE COMMON MAN.

THE CONCERN WITH THE COMMONMAN, THE MAN IN THE STREET, THENON-MATHEMATICIAN. “An old French mathematician said: ‘A

mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street.’”

David Hilbert ICM Paris 1900

THE PEDAGOGICAL IMPLICATIONS• Felix Klein (1849-1925): Elementary

Mathematics from an Advanced Standpoint (1908; 3rd edition 1924): “The presentation in the schools, however, should be psychological and not systematic. The teacher so to speak, must be a diplomat. He must take account of the psychic processes in the boy in order to grip his interest; and he will succeed only if he presents things in a form intuitively comprehensible.“

• his interest : depends on time [when] and space [where] and on the socio-cultural environment, i.e., on ethno.

THE LOCALIZATION OF TIMEAND SPACE, HENCE THE RECOGNITIONOF DIFFERENT SOCIO-CULTURAL

ENVIRONMENTS IS MADE POSSIBLE THANKS TOGLOBALIZATION.

THE INTENSE CULTURAL DYNAMICSCAUSED BY GLOBALIZATION GIVES RISETO A NEW THINKING. HILBERT’S “MAN WHOM YOU MEET ON

THE STREET” MAY BE UNDERSTOOD AS “PERIPHERAL CULTURES” WHICH WE ENCOUNTER IN THE

GLOBALIZATION PROCESS.

PARAPHRASING A POPULAR LEMMAOF THE EARLY 70’S, WHENTECHNOLOGY OF INFORMATION ANDCOMMUNICATION WAS INCIPIENT, WEMAY CHARACTERIZE THE NEWTHINKING AS

“THINK LOCALLY, ACT GLOBALLY”.

SOME CLASSROOM ACTIONS AS A RESULT OF THE THEORETICAL

REFLECTIONS

ad hoc practices ⇛ methods methods ⇛ theories theories ⇛ inventions

FROM EXPERIENCE TO EXPERIMENT⇛THE SCIENTIFIC METHOD

OBSERVATIONAL/EXPERIENTIAL GEOMETRY: OBSERVING SOLIDS IN WATER (ad hoc)

EXPERIMENTAL GEOMETRY: MEASURING THE LEVEL OF WATER (method)

EXPLAINING THE CHANGES OF THE LEVEL OF WATER THE CONCEPT OF VOLUME (theory)

CONSTRUCTING SOLIDS OF A GIVEN VOLUME (invention)

MODELLING MAQUETTES (SCALE MODELS). e.g. Da Vinci machines , Brunelleschi perspective) ⇛ HISTORYSPACE and TIME (SPEED) MAPS OF TRAJECTORIES (e.g., home →

school) ⇛ SPACE AND TIME ⇛ SPEEDBUIDINGS and ARTIFACTS as reported by

BUILDERS and ARTISANS (students as interviewers) ⇛ ETHNOMATHEMATICS OF PROFESSIONAL GROUPS.

ETHNOGRAPHIC RESEARCH conducted bystudents: INDIAN VILLAGES

⇛ a “DUAL” MODEL OF TEACHING. THE PRODUCTION OF THE

“QUILOMBOS” (= EXTANT COMMUNITIES OF ESCAPED SLAVES).

DAYLY LIFE OF COMMUNITIES OF IMMIGRANTS (e,g., home economics, games).

COMMUNITIES OF IMMIGRANTS

MILTON ROSA: A Project: Encina High School, San Juan Unified School District, Sacramento, CA milrosa@hotmail.com.STATHOPOULOU XARA: The Connection between Cultural Context and Teaching & Learning of Mathematics: Ethnographical Research of a Class of Romany Children and of Their Community of Origin. (Doctoral Thesis, Aegean University, Greece) stath@rhodes.aegean.gr. CLÁUDIO JOSÉ MONTEIRO CADEIA: Ethnomathematics: the mental arithmetic in the gipsy community (Master’s Dissertation, Universidade do Minho, Portugal) povcad@sapo.pt.

• Ubiratan D’Ambrosio: Uniting Reality and Action: A holistic approach to Mathematics Education, in Teaching Teachers, Teaching Students, eds. L.A.Steen & D.J.Albers, Birkhäuser, Boston, 1981, pp. 33-42.

• ---------------------------: Literacy, Matheracy, and Technoracy: A Trivium for Today, Mathematical Thinking and Learning, 1(2), 1999; pp.131-153.

• ---------------------------: Mathematics and Peace: A Reflection on the Basis of Western Civilization, LEONARDO, vol.34,nº4, 2001; pp.327-332.

• ---------------------------: Ethnomatematics. The Art or Technique of Explaining and Knowing, transl. of the orig. 1990 by Patrick B. Scott, ISGEm/NMSU, Las Cruces, 1998.

• ---------------------------: Stakes in Mathematics Education for the Societies of Today and Tomorrow, One Hundred Years of L’Enseignement Mathématique, Proceedings of the EM-ICMI Symposium, Geneva, 20-22 October 2000, L’Enseignement Mathématiques, Genève, 2003; pp.301-316.

• ---------------------------: Ethnomathematics and its Place in the History and Pedagogy of Mathematics, Classics in Mathematics Education Research, eds. Thomas P. Carpenter, John A. Dossey and Julie L. Koehler, National Council of Teachers of Mathematics, Reston, VA, 2004, pp.194-199

• Ubiratan D’Ambrosio: Talk in Plenary 5, in ICME-10, 2004, Denmark, available in DVD-CD (through ICMI).

• ----------------------------: Ethnomathematics. Link between Traditions and Modernity, Sense Publishers, Rotterdam/Taipei, 2006 (ISBN 90-77874-76-3).

• ----------------------------: Peace, Social Justice and Ethnomathematics, International Perspectives on Social Justice and Mathematics Education, The Montana Mathematics Enthusiast, Monograph no1, ed. Bharath Sriraman, The University of Montana Press, Missoula, 2007; pp.25-34 (ISSN 1551-3440).

• ----------------------------: The Program Ethnomathematics and the challenges of globalization, CIRCUMSCRIBERE, International Journal for the History of Science, vol.1, 2006, pp.74-82. http://circumscribere.incubadora.fapesp.br/portal

SITES:

• http://vello.sites.uol.com.br/ubi.htm

• http://www.kult.lu.se/latinam/UVLA/UVLA1.HTM

• http://www.geocities.com/pluriversu [link Convidados]

ethnomathematics in the global world: a …ncm.gu.se/media/ncm/dokument/dambrosio.pdfubiratan...

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