The role of language in ethnomathematics

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The role of language in ethnomathematics

• Does the language make it ethnomathematics?

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• Tamsin Meaney
• University of Otago
• Uenuku Fairhall
• Te Kura o Te Koutu
• Tony Trinick
• University of Auckland

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Ethnomathematics

• Borba (1990) suggested that ethnomathematics is
  mathematical knowledge expressed in the
  language code of a given sociocultural group.

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Language and culture

• Levi-Strauss (1963, p296) stated that a society
  consists of individuals and groups which
  communicate with one another.
• Geertz (1975) suggested that when an experience
  is described in language, meaning is added. In
  analysing an experience in order to describe it,
  an individual is constrained by their linguistic
  repertoire.

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• In te reo Mäori, runga can mean up but in
  different situations can also mean above, top
  and south and are linked to life, standing
  and Sky Father (Salmond, 1976).

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• Changing the language which is used to describe
  the experience, whether it is a change in natural
  language or a change in register within a
  language will have an impact on how that
  experience is described and therefore what is
  valued within this experience.

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• The mathematics register is the words and
  grammatical expressions which are used
  consistently to describe mathematical ideas
• It is only when the mathematical ideas within an
  ethnomathematical activity are valued by
  discussants that the mathematics register will be
  deployed.

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Ethnomathematics in kura kaupapa

• In kura kaupapa Mäori, the pedagogy of these
  schools is based on, but not exclusively, Mäori
  preferred teaching and learning methods (Smith,
  1990 p147-148).

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• Children may only speak te reo Mäori at kura
• Most of their outside kura experiences would be
  similar to their Pakeha peers

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• Teachers at the kura value students outside kura
  experiences such as using money but also felt
  that traditional practices such as
• Tukutuku, whakairo, ranga harakeke and
  naviagational skills
• could be used.

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Land Division

• Land belongs to extended family groups
• Share is dependent on the number of generations
  since title was recognised.

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• At a family night in 2004, parents came as
  students to attend various classes and the
  children were assistant teachers. Describing land
  division using the language of fractions meant
  that for the first time many parents understood
  how their land share came about and understood
  how fractions operated.

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• It relates to students backgrounds
• It shows that mathematical concepts were
  incorporated into traditional activities
• It makes the concept of fractions more than just
  a set of abstract ideas,
• Discussing the activity using the mathematics
  register in te reo Mäori added another dimension
  which had not been apparent to the parents
  previously.

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Newness of te reo Tätaitai

• Only developed since the 1980s
• Few teachers use it with upper secondary students
• Most teachers werent taught in te reo
• Teachers in the earlier grades dont know the te
  reo terms for some mathematical ideas

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• If the class and its teacher were confident in
  discussing mathematics and had a sophisticated
  understanding of the mathematics then more
  culturally appropriate terms would develop.

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Like Terms in algebra

• The term used in the new dictionary of
  mathematical terms, Te Reo Pängarau, is röpü
  meaning grouping.
• Students in Uenukus senior classes coined the
  term, whakawhänau, meaning making families.

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• It was through discussion of what was happening
  when like terms were gathered together that the
  students felt that whakawhänau was more
  appropriate. This is because the connotations
  which this term invoked more readily fitted their
  understanding of what was happening.

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• Discussion of Western mathematics in te reo
  tätaitai needs to be done in a way which makes
  use of the cultural connotations of the Mäori
  words.

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Conclusion

• In discussing ethnomathematical activities
  thought needs to be given to the language used to
  discuss them.
• The language will situate the activity within a
  set of cultural connotations.
• The language should contribute to adding meaning
  rather than detracting from the meaning in the
  activity if described using another language or
  register.

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And does language make it ethnomathematics?