Geography Reference
In-Depth Information
These two examples clearly show that there is no direct relationship between the
amount of corn and cakes, and between the number of bullets and deer. The solutions
for these problems involve other principles and values that transcend their purely
numerical context.
Leandro explained the answer for his own problem: “My father will kill 3 or 7
deer, as many as possible.” Since it has become very difficult to hunt down any kind
of game on the reservation due to deforestation, taking a “whole box of ammunition”
is a way of guaranteeing the hunter's success. More important than the exact number
of deer to be killed is the possibility of securing a large quantity of food at any one
time.
Nancy, in turn, offered the following solution for her own situation: “My mother
will make 3 laaaaaarge cakes, for everybody to eat.” Generosity, an important virtue
for the Xavante people, is informed by the principle of reciprocity, which involves
the obligation to give, to receive, and to reciprocate (Lévi-Strauss 1969, Mauss
1990). Nancy's 3 cakes thus had to be very large in order to provide food for the
entire village. Again, the exact number of cakes was less important than their sizes,
an aspect of the situation that also transcends the purely numerical aspect of the
problem-solving activity.
In sum, the quantities expressed in the examples offered by Leandro and Nancy
were not mere abstractions divorced from their contexts, but values that were
intimately connected to basic principles of Xavante culture played out in daily
activities. The situations created by the children do not obey idealized models
of arithmetic problems to be solved in a classroom setting, in which a simulated
situation expressed in words is only a support for strictly numerical relations that
should be worked out (Lave 1988). Furthermore, dividing the meat according to the
size of the household is yet another example of proportional thinking in mathematics,
as indicated in Chapter 4.
The notion of totality or wholeness is more important to the Xavante worldview
than unitary values. In other words, relations between groupings, collections, or
totalities (bullets
versus
deer; corn cobs
versus
cakes) are more significant than the
discrimination of small quantities or individualized units. The symbolic features of
these dynamic exchanges transcend the purely economic aspects of the transactions,
and indicate that different categories of value are at stake. People's social relationships
also give structure to their mathematical activities, as does their political interaction.
Final remarks
The issues that have been raised so far in this chapter indicate, among other things,
that the Xavante concept of number stems from a two-to-one correspondence. Unlike
the Euclidian definition of a unit as “that by virtue of which each of the things that
exist is called one,” among dialectical societies I would suggest that each of the
things that exist is called two -
maparané
- or a couple because it is necessarily
formed by a pair of ones -
mitsi
- a lonely self. In this light, the Western concept of
number, based on a one-to-one correspondence, does
not
appear as a universal value,
