- as the Guarani did in their iconic representation of numerals 1 to 10 in Table 4.2.
Tradition, in this way, becomes the coming together of ideas and living knowledges
created and recreated by individuals that share the same social group and historical
situation. Starting with this proposal, the Guarani, Krenak, Pankararu, Kaingang
and Terena peoples continue reasserting their constitutional and human rights by
developing their own numerical systems and mathematical ideas at their villages and
in their local schools. Map-making today has enabled a growing body of Indigenous
multimedia literature informing the culturally specific curricula of each one of
Brazil's 900-plus Indigenous schools. Mathematics educators welcome the fact that
Indigenous Peoples are organizing themselves for political, economic, social, and
cultural enhancement, in order to bring to an end all forms of discrimination and
oppression wherever they occur.
ACKNOWLEDGEMENTS FOR CHAPTER 4
This essay was written with the support of MARI-Indigenous Education Group of
the University of São Paulo, through the FAPESP sponsored project “Anthropology,
History and Education: The Indigenous Question and Schooling” (grant number
94/3292-9). An early version was originally published in Portuguese as “A
construção de conhecimentos matemáticos de povos indígenas em São Paulo”
in: Lopes da Silva, A. and Ferreira, M. L. (Eds.) 2000 Práticas Pedagógicas na
Escola Indígena . São Paulo: FAPESP/MARI-USP/Global Editora, Pp. 211-235.
This expanded version includes essays and maps in Ferreira, M. L. (Ed.) (2000).
O Livro de Mapas de São Paulo (The Topic of Maps of São Paulo). São Paulo,
SP: Instituto Cajamar.
An abbreviated version of this chapter was published as Ferreira, M. L. (2012).
Map-making in São Paulo, Southern Brazil. Colonial History, Social Diversity, and
Indigenous Peoples' Rights. In: Alternative Forms of Knowing (in) Mathematics.
Celebrations of Diversity of Mathematical Practices. Swapna Mukhopadhyay &
Wolff-Michael Roth (Eds.) New Directions in Science and Mathematics Education,
Vol. 24. Rotterdam, The Netherlands: Sense Publishers, pp. 115-158.
All illustrations, photos, and translations are by the author, unless otherwise noted.
Topics and documents that played a major role in the crafting of the Book of Maps included: 1)
Madikauku - Os Dez Dedos Das Mãos. Matemática e Povos Indígenas no Brasil (Ferreira 1998a);
2) Povos Indígenas no Brasil 1991-1995 (Ricardo 1995b); 3) The Estatuto do Índio of 1973, a
presidential decree which defines the rights of Indigenous communities in Brazil; 4) The International
Labour Organization - ILO 169, which deals specifically with the rights of Indigenous and Tribal
Peoples; 5) The 1988 Constitution of the Federative Republic of Brazil; and 6) The United Nations
Universal Declaration of Human Rights.
First recorded in the opening pages of the topic Madikauku (Ferreira 1998a:3). Jaime Lllulu Manchinere
is a mathematics teacher on the Mamoadate Indigenous Area in the state of Acre, northwestern Brazil.
For a full discussion of the economy of gift exchange and mathematics, see Chapter 1.