of receiving “more” goods because of principles of reciprocity (as seen in Chapter 1).
The apparently straightforward problem “Last night I caught ten fish, and gave three
to my brother. How many fish do I have now?” presents more than one solution.
The obligation to reciprocate means that the brother is going to give back the fish or
another valuable item, and this, too, enters into the calculation. The relationship among
“brothers” - in particular brothers-in-law in societies where marriage prescriptions
are very structured - often regulate exchange and inform calculations.
Exploring the various possible solutions to mathematical dilemmas is a stimulating
activity that brings into focus relationships that aren't necessarily numerical.
Discussions about the meanings of “more” and “less” during the workshop caused
mathematics teacher Alício Terena to reflect about social inequality in the west of
São Paulo state. Practically all the youth and adult Terena men and women work daily
as cheap laborers or peons on regional farms in exchange for a monthly minimum
wage. They work 12 hours a day cutting cane, ploughing the land or picking fruit
for the farmers, while their own garden plots are left unattended. The monthly
minimum wage (US $ 310 dollars in 2014) barely covers family basic expenses:
rice, beans, foodstuffs, clothes, medicine, tools, etc. The workers have no choice but
to accept buying goods on “credit” from the boss who sells them at inflated prices.
The debt continues to grow and can only be reduced with more work, which in turn
perpetuates a never-ending dependency by the Terena on the boss. This is known as
“debt-peonage,” a quite common form of slavery on and around Indigenous lands in
Brazil, and elsewhere around the planet (Ferreira 2005). For farm laboring Terena,
more work does not mean more money as one would expect. On the contrary, the
more you work as a bóia-fria or moon-lighting worker , the less you are able to
generate better life conditions. In the words of Alício Terena: “The more we earn,
the less we get because our debts continue to grow.” 3
The teachers concluded as well that certain situations, like the commercialization
of arts and crafts, hearts of palm, and agricultural products demanded specific types
of calculations. In these situations, to sell means to disconnect yourself from these
products in exchange for money. For example, if the Guarani shaman Francisco da
Silva makes 15 arrows, sells 5 and wants to know how many are left, the calculation
is 15 minus 5. In the same way, if the price of each piece is $10 then the total sale is
$50 because the sum is the value of each arrow times 5.
Guarani teacher Poty Poram, introduced above, assessed that “Learning
mathematics in this way is important, because it is not only knowing how to count,
but learning to think about life. Knowing that Indigenous knowledge is important
gives us the will to research Guarani mathematics among the elders.”
Elementary school teacher Lidiane Krenak, who is also responsible for the
Financial Council of the Vanuíre Indigenous Area in the west of São Paulo state, raised
the question of gender in relation to mathematical activities on the reservation by
discussing the difference between “women's mathematics” and “men's mathematics”
for the Krenak people: “The Krenak woman is the one who needs to be more involved
with mathematics. It is she who calculates the food and firewood needed to cook and