This paper discusses a new philosophical perspective for ethnomathematics which articulates Ludwig Wittgenstein’s and Michel Foucault’s theoretical notions. It is conceived as a theoretical toolbox which allows the analysis of, on the one hand, the mathematical language games of different forms of life and their family resemblances and, on the other hand, the Eurocentric discourses of academic and school mathematics and their effects of truth. Based on fieldwork done in rural forms of life in the south of Brazil, examples of the use of this perspective are presented. The paper analyzes language games of those different forms of life and the school mathematics discipline, highlighting the complex network of learning and powers that makes other mathematics than that known as the mathematics be positioned “in a void” in school curricula.
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The chapter “The coming of Will Adams to Japan” starts with the following editor’s note: “Will Adams was the first Englishman to make his home in Japan. His knowledge of shipbuilding made him so useful to the emperor that, although he was treated with honors and liberality, he was not allowed to leave the country. The Japanese of the street in Yedo which was named for him still hold an annual celebration in his memory. The letter from which the following extracts are taken—with modernized spelling—was written in 1611. It begins with his departure from the coast of Peru.” (Tappan, 1914, p. 325).
From his first works onwards, D’Ambrosio highlighted that what we call mathematics is a specific ethnomathematics—the one practiced by mathematicians at academic institutions.
Deleuze argues that “a theory is exactly like a box of tools. It has nothing to do with the signifier. It must be useful. It must function. And not for itself. (…). We don’t revise a theory, but construct new ones (…). A theory does not totalize; it is an instrument for multiplication and it also multiplies itself” (Bouchard, 1977, p. 208).
Here it is important to mention that to characterize academic discourses as Eurocentric means, in this context, to highlight the hegemonic mathematical discourse produced in Europe, and its cultural and social imposition in countries like Brazil since the colonization process started in the sixteenth century. To maintain the use of this adjective for school mathematics discourses reinforces the understanding of the “strong” family resemblances those discourses have with academic ones in Western society (Giongo & Knijnik, 2010).
In this paper, aphorisms from Wittgenstein’s book Philosophical Investigations will be expressed by PI# followed by the number addressed by the author to the aphorism.
As discussed in Giongo and Knijnik (2010), the language games that shape school mathematics discourse have strong family resemblances to those that constitute academic mathematics discourse.
Here I am referring to the three different land measurement language games practiced by landless peasants in the southernmost state of Brazil, which were discussed in Knijnik (2007) and in this paper.
The editor of the book (Foucault, 2010) explains in a footnote that the original French text was named “L’ordre du Discours.” The English translation was by Rupert Sawyer and was first published in Social Science Information, April 1971, pp 7–30.
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I would like to express my gratefulness to the colleagues Paola Valero, Tony Brown, and Margaret Walshaw for their important contributions to this paper.
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Knijnik, G. Differentially positioned language games: ethnomathematics from a philosophical perspective. Educ Stud Math 80, 87–100 (2012). https://doi.org/10.1007/s10649-012-9396-8