Geography Reference

In-Depth Information

understanding of the field of mathematics. It reduces mathematics to simple

relations between numbers and sign operations. That is to say, mathematics becomes

simple arithmetics which underestimates the true sense of mathematical knowledge.

Brazilian mathematician Ubiratan D'Ambrosio defines etnomathematics in several

of his publications as “The art or technique of explaining and knowing” (1990, 1999,

2001). From this perspective, social groups, such as the Xavante, count, measure

relate, classify and infer mathematical relations in significantly different ways since

their worldviews vary considerably.

Mathematicians have long argued that numbers are not necessarily numerals, but

social categories that represent a way of bringing together a group or collection of

elements (Russell 1963). This is precisely the case of the Xavante socionumerical

system in which numbers are represented by social relationships, as I have argued

before (Ferreira 2001a). Known for the complexity of their social organization,

dialectical societies, such as the Xavante and other Gê-speaking peoples of Brazil,

including the Suyá and the Kayapó of the Xingu Indigenous Park (see Part I in this

volume), count, measure, order and classify time, space, and other dimensions and

aspects of the universe using categories and norms that are governed to a large extent

by their kinship system.

As mentioned throughout this topic, in order to understand the conflicts and

tensions that arise inside mathematics classrooms, and in daily activities that

require mathematical reasoning, we must take social and cultural dimensions into

consideration, and local historical perspectives into account. Cognitive abilities

are of minor importance: various studies have shown that such skills are universal,

and that cultural differences in cognition reside more in the situations to which

particular cognitive processes are applied than in the existence of a process in

one cultural group and its absence in another (Piaget 1952, Cole et al. 1971,

Lave 1988).

Different worldviews - the socially constituted world and its cosmological

foundations - and the everyday experience of active individuals account for the

diversity of strategies of mathematical reasoning. In other words, different cultures,

and individuals within any given culture, proceed differently in their logical schemes

in the way they manage quantities and, consequently, numbers, geometrical shapes

and relations, measurements, classifications and so forth (D'Ambrosio 1990:17). It is

essential to comprehend the historical situation and the cosmological underpinnings

of a dialectical society, such as the Xavante, in order to understand how mathematics

is construed in the everyday lives of Indigenous Peoples.

Mathematical knowledge is an intrinsic part of Xavante cosmology, that is,

mathematics is an important element in how this Gê-speaking people constructs

its universe and thinks of itself and other beings within it. A cosmology can be

understood as a theory of the cosmos in which societies map space, time and the body

in order to create order and make sense of the world. This ever-changing world order

both orients and is informed by the daily lives of the Xavante people, in the ways in