Pleiades Invite Plenitude

Peeking through the trees, from the comfort of my red cotton hammock, I recognize different constellations shining bright in the dark blue sky. I have learned from the Kisêdjê, aka Suyá, Indigenous People in Central Brazil, that when we first spot the Pleiades (ngroro in the Suyá language), setting in the West at night, heavy rainfall is giving way to light scant showers. Being an urban Brazilian woman, I am better at understanding lunar calendars in the female life-cycle. But now the position of the Pleiades has much more to tell: the end of the muggy rainy season, and the beginning of the dry and cold one. Fish is still scarce, as rivers are full, making it a difficult catch.

But like sweet potatoes and new manioc tubers in the gardens, river creatures will be plentiful once the Pleiades rise in the East at dawn and high in the sky in the very early morning. We look forward to smoking fish, including the favorite tucunaré (Chichla occelaris), and digging up turtle eggs buried in the white sand of the Xingu River[1]. Plenitude, predicted by the Pleiades, releases dry season songs (tepkradi), through which the Kisêdjê people invite their neighbors to much awaited ambedi (dry season) ceremonies.

Our conversations about the Pleiades, and the Orion Constellation, also high in the sky in ambedi, help the Kisêdjê and other students at the Diauarum (black panther, in the Kaiabi language) School create a “Xingu Calendar,” depicting the huge variety of seasonal fruits, and game in the area.

Figure1
Cardinal Directions & the Compass Rose
(MARIOLA PAEN, 2019[2])

Figure 2
Xingu Calendar
(MARIOLA PEN, 2019)

Figure 3
The seven Pleiades stars setting in the West at night during the dry season in Central Brazil, invite plenitude
(MARIOLA PAEN, 2019)

Whispering through the treetops, warm wind enunciates ambedi, everyone’s favorite (dry) season. In the absence of rain, fish feed hundreds of villagers and their guests attending traditional intertribal ceremonies in the Território Indígena do Xingu, state of Mato Grosso (dense woods, in Portuguese). The vegetation is thick and the trees are tall, transitioning between the brushy savannah of Central Brazil into the Amazon rainforest of the north. Now in the dry season, from May to October, white sand beaches and small islands that pop up in the middle of rivers become favorite hunting and fishing spots. Inland ponds and creeks are more easily reached in dugout canoes, or even on foot, with flood waters quickly retrieving in the absence of rain. I can’t help but log in the steady reduction in cases of malaria due to less mosquitos and more steady use of mosquito nets.

In fact, Kisêdjê men, women, children and I are on a timbó fishing expedition near the Wawi River headwaters, located upstream from their village (Aldeia Ricô). It is early in the morning in July 1981, and I am 22 years old. We are carrying bundles of the timbó vine (Derris spp.) on our backs. (Timbó is temporarily toxic to fish and will allow us to catch them.) On our way, Kuiussi, the Kisêdjê headman, promptly spears a six-foot electric eel (Electrophorus electricus) in a small creek we cross over a log. His sons-in-law help him pull it ashore, avoiding its whipping tail which can deliver a 500-volt shock. Cut into harmless big chunks, the creature is soon roasted by the women on a makeshift grill by the lake, and stuffed into pieces of beiju (white tapioca flatbread).

Meanwhile, several young men get busy erecting a small dam to restrict the size of the fishing area to shallow waters. Others, on the shore, are working hard smashing the timbó vines with big sticks and pushing them into the pond, so the sticky sap starts intoxicating big and small catch. The poison works fast (but does not affect humans); children are already scooping up small fry in baskets. Young men are spearing bigger fish floating on their bellies from dugout canoes. It is a feast. At dusk we head back to the Xingu River and make our way to Aldeia Ricô, where elders smoke the catch.

I am struck by the swift process of distribution of small and large fish alike, taking into account the number of people per household, elders, and previous debts — in the spirit of an economy of reciprocity (aka gift-exchange or gift-giving). Division holds sway above addition, subtraction, and multiplication in the Diauarum School. It becomes clear that the three principles of reciprocity that Indigenous Peoples share — the obligation to give, to receive, and to reciprocate — are in action (LÉVI-STRAUSS, 1949; FERREIRA, 2015). Gift-giving is beautifully expressed by mathematics teacher Jaime Llullu Machineri cited in Ferreira (1998):

Love is also used by mathematics: those who love or feel compassion for a relative, help the person and share goods with others.” Jaime Llullu Machineri. Mathematics teacher at the Aldeia Jatobá, on the Yaco River. Terra Indígena Mamoate, state of Acre in Northern Brazil (p. 3; my translation)[4].

This is the information we gather on our fishing, and gathering expedition (as we visit old plantation sites), which is used in our mathematics classroom:

Table 1
Fish and reptiles in local rivers and flooded forest areas in the Xingu River basin the Kisêdjê subsist on (a selection)

Elaborated by the Author

English	Portuguese	Scientific name
peacock bass	Tucunaré	Cichla ocellaris
golden trahira	jeju, traíra-pixuna	Oplerythrinus unitaeniatuas
barred catfish, barred sorubim	surubim, surubim-pintado	Pseudoplatystoma fasciatum
Piranha	Piranha	Pygocentrus and serrasalmus
electric eel	peixe elétrico/poraquê	Electrophorus electricus
string ray	Arraia	Elipsisurus stroglyopterus
Matrincha	Matrinchã	Characidae
redtail catfish	Pirarara	Phractocephalus
iau leporinus	Piau	Leporinus
yellow-spotted Amazon turtle	Tracajá	Lodocnemis unifilis

Table 2
Staple vegetables and fruit harvested from old Kisêdjê village gardens

Elaborated by the Author

English	Portuguese	Scientific name
manioc or cassava root	Mandioca	manihot esculenta
Yam	cará, inhame	dioscorean esculenta
sweet potato	batata doce	ipomea batatas
Banana	banana da terra	musa parasidiaca
Pineapple	Abacaxi	ananas comosus

Figure 4
Distance from the Diauarum Indigenous Post, Xingu Territory in Mato Grosso, to hospitals in Cuiabá, Ilha do Bananal, and Brasília
(Map crated by Nathan Embretson [5])

2 Malaria hits men, women, and children at the Ricô village

Trekking back from the timbó fishing expedition, 23-year-old Donbeti Kisêdjê, a father of three, stumbles along the pathway, barely able to keep up with 50 people ahead. His body temperature reads 40°C (or 104°F). Donbeti has shaking chills, profuse sweating, and nausea. He is carried in a hammock by family members to a canoe on the Xingu River. Upon reaching the Diauarum Indigenous Post, Donbeti, a health agent in training, seems to be in shock. His blood pressure is low. We immediately send out urgent radio messages to FUNAI neighboring headquarters in Cuiabá (capital of Mato Grosso), Goiânia (capital of Goiás), and Ilha do Bananal (state of Tocantins).

In a couple of hours, we hear from Ilha do Bananal: they have a doctor on call and malaria medication. But we still need an airplane. In despair, we consider distances from the Diauarum Post to our three desired destinations: Cuiabá, Goiânia, and Ilha do Bananal. Swift action is necessary and we wait for backup calls to save Donbeti. Given the fact that more than one million people die from malaria each year worldwide, every rescue is a victory[6]. Donbeti makes it to the Diauarum Post late in the evening. The next morning we are on the radiophone figuring out how long each flight would take to the three different destinations.

Hired to teach Portuguese and mathematics by the National Indian Foundation (FUNAI), I double as a practical nurse when outside health professionals are unavailable in the northern Xingu area — known as Baixo (Low) Xingu. Rivers flow North into the Amazon River. I work in the Diauarum Indigenous Post, an administrative unit of FUNAI, with a registered nurse, when she is in the area. Local Indigenous health agents help monitor infectious-contagious diseases, such as malaria and tuberculosis, malnutrition, dehydration and other ailments in children. I learn how to draw blood and scan for malaria and TB in our microscopes, donated by the Escola Paulista de Medicina in São Paulo (now Federal University of São Paulo).

But I am a school teacher, not a registered nurse. So I study everyday what do to in the absence of a health professional, using the Spanish (and first) edition of Cuando No Hay Doctor(WERNER, 1973), sent by my father Jorge. I am often at a loss, and overworked day and night making house visits and dispensing medication for malaria and tuberculosis. Despite the abundance of food and water in Xingu area, in the 1980s several Indigenous Peoples, mainly children in the Xingu Territory, but also throughout Brazil, are suffering from malnutrition and dehydration — in many cases because of malaria, pulmonary, and TB infections. The idea that comida de caraíba (white people food) is better than comida de índio (indian food) has become pervasive since at least 1961[7].

That was when the Parque Nacional do Xingu (as it was originally called) was created by the Brazilian government, to conveniently confine 17 different Indigenous nations into a “Park.” Indigenous Peoples, such as the Panará and the Kaiabi, were brought from further north to the Xingu River basin, where other native societies already lived. The well-documented initiative of “relocation” and “assimilation,” practiced worldwide, set free Indigenous lands around the Território Indígena do Xingu (TIX) for corporate multinational interests (cattle and agricultural developments, mostly). Such is the case of the Kisêdje people, whose Wawi ancestral land was cut off from the borders of TIX in 1961. In 1998 the Kisêdje won a landmark court case against big landowners, discussed ahead.

Meanwhile, it is essential to point out that, yes, hunting, gathering, fishing and the ability to plant gardens has afforded the Kisêdjê access to, and development of, food sources. However, climate change, and the encroachment of big farmers and multinational corporations that practice mining and deforestation (using toxic chemicals), and now build hydroelectric dams (Belo Monte, essentially), have limited the people’s ability to rely exclusively on an abundant ecosystem, as they once did. “Diseases of civilization,” such as diabetes and cancer, in addition to malaria and tuberculosis, are now commonplace (FERREIRA & LANG, 2006). This is why the Oral Rehydration Solution is included below in our real-life mathematics classroom activities.

How to calculate a life-saving Oral Rehydration Solution (amount per person)

Table 3
Oral Rehydration Solution (ORS) Calculation Chart

Ferreira (1998, p. 145)

Weight in kg or lbs	3 to 4 kg 6.5 to 9 lbs	5 to 8 kg 9 to 18 lbs	9 to 11 kg 19 to 25 lbs	12 to 14 kg 26 to 31 lbs	15 to 50 kg 33 to 110 lbs
During first 4 to 6 hours of dehydration (in ml or tsp)	200 to 400 ml or 0.7 to 1.5 cups	400 to 600 ml or 1.5 to 2.5 cups	600 to 800 ml or 2.5 to 3.5 cups	800 to 1000 ml or 3.5 to 4.0 cups	1200 to 4500 ml or 4.0 to 19 cups
Note: If diarrhea continues, use method 1 or 2 below to prevent recurring dehydration
Method 1. After every diarrhea give	50 ml or 0.2 cup	100 ml or 0.4 cup	120 ml or 0.5 cup	150 ml or 0.7 cup	200 to 400 ml or 0.7 to 1.5 cups
Method 2. Throughout 24 hours give	400 ml or 0.7 to 1.5 cups	600 ml or 2.5 cups	800 ml or 3.5 cups	1000 ml or 4 cups	2000 ml or 8 cups

Figure 5
Wawi Indigenous Territory, ancestral Territory of the Kisêdjê people, adjacent to the Xingu Indigenous Territory
(MARIOLA PAEN, 2019, adapted from RICARDO, 2000, p. 628)

3 Twelve underwater animals help the Kisêdjê win the court case Hélio Salvador Russo FUNAI and Kuiussi Suyá in 1998[9]

Never in my wildest dreams, did I see it coming: The successful repossession (and rebuttal to farmers) of the Terra Indigena (TI) Wawi, being attributed by the Kisêdjê to 12 underwater animals, including the anaconda (Eunectes murinus), the sting ray (Elipisurus strogylopterus), and the river turtle (Podecnemis expansa); (Figure 6). Their transformative energy “opened the white men’s heads” to the existence of different worldviews — and, consequently, to very diverse map-making and land distribution systems (FERREIRA, 2015, p. 59).

What startles me the most, as the official anthropology expert witness, is the fact that a Chief Justice in the state of Mato Grosso has accepted our argument that three political and ceremonial Kisêdjê leaders — Kuiussi, Romdó, and Intoni Suyá (as named in the court case), have claimed that their knowledge and power stems from 12 animals and supernatural creatures shown below (Fig. 6 and Table 4).

Figure 6
The 12 underwater creatures (
(INTONI SUYA in FERREIRA, 2015, p. 68)

Strikingly, these fish-like beings appear as both animal and human in Kisêdjê cosmology. Although in 1998 the Kisedjê (Suyá) won in the court system the official possession of their Wawi territory, adjacent to the (then called) Xingu Indigenous Park, farmers who “owned” or held property titles to the Kisedjê/Suyá (Wawi) land still claimed they deserved compensation for “lost profits” of lands they illegally owned, but “invested” in.

Figure 7
Intoni Suyá, drawing the 12 underwater creatures: “We learn from water creatures how to protect our land”
(Photo by Mariana K. L. Ferreira, 1998)

Table 4
The 12 underwater creatures and their powers, who taught the Kisêdjê how to act accordingly in order to save the Wawi Indigenous Territory in court from big land owners

Ferreira (2015, p. 68-69)

Portuguese	English	Power
1. Peixe flauta	Flute fish	Only moves when other fish do
2. Chefe do peixe flauta	Boss of the flute fish	Kisêdjê leaders can overrule the flute fish and act in isolation if needed
3. Peixe preto	Black fish	Surfaces as a canoe, the Kisêdjê’s main means of transportation
4. Peixe agulha	Needle fish	Floats on the water’s surface, without raising suspicion, to survey what’s taking place on land
5. Peixe peneira	Sieve fish	Swims swiftly against the current without being deterred
6. Sucuri	Anaconda	Strong and fearless. Created rivers by breaking underground waters loose
7. Peixe cavalo	Horse fish	Strong smelling horse that is able to survive underwater and in other hostile environments
8. Socó	Stork fish	Can also fly, surveying the land from the sky
9. Peixe cabaça	Gourd fish	Disguises itself in the mud and pretends to know nothing, but is very knowledgeable
10. Ser humano	Human being	Very powerful. Lives underwater, and can tell all fish to move together at any given time
11. Arraia	Sting ray	Lives underground and also underwater. Can become invisible and sting when threatened
12. Ser humano	Human being	Another human being who also lives underwater and watches out for the headwaters, lagoons and rivers of the Kisêdjê people. All humans come from the waters

The Kisêdjê are notorious for their victory regaining control of their ancestral Wawi territory in the Hélio Salvador Russo FUNAI and Kuiussi Suyá 1998 court case. Wawi, their ancestral territory, was left outside the official demarcation of the (then called) Xingu National Park in 1961 (Fig. 5). Today, about 450 Kisêdjê live in the TI Wawi (contiguous to the TI Xingu), after its official demarcation in 1998.

The Kisêdjê have been very active with respect to environmental issues affecting their rivers and forests. They have been strongly opposed to the aggressive invasion and deforestation of their lands by soybean farmers, like other Indigenous and riverine communities in Brazil. And they are adamantly against the Belo Monte dam because of its tremendous environmental impact. Mathematics education, in particular map-making skills, and the ability to organize in tandem with other Indigenous Peoples nationwide, have been vital to their success in guaranteeing ancestral land rights.

The Associação Indígena Kisêdjê (AIK) has invested in sustainable agricultural projects in partnership with other local and national organizations. In 2006, a successful initiative took off involving the plantation of pequi (Caryocar Brasiliense) trees, which is native to the area. The Pequi fruit is a staple of the Kisêdjê diet, and also used as a body moisturizer, medicine for respiratory problems, and insect repellent. Today, this successful project, part of the “Projeto Sociobiodiversidade Produtiva no Xingu,” has expanded to more than 60 hectares of pequi trees, with the extraction of pequi oil as a sustainable source of income for the Kisêdjê people. Hopefully, the project will become self-sufficient and independent from federal funding, given the drastic cuts to the “Fundo Amazônia” by the current (2019) President of Brazil.

Figure 8
Romdó Kisêdjê, the shaman-jaguar, surveys Wawi ancestral territory
(Photo by Mariana Ferreira (1998)

4 Afterthought: Successes of Indigenous Mathematics Education

Rowing against the current

That is what I never thought I needed to do when crossing the Xingu river from the Diauarum Indigenous Post to the white-sanded beach across, looking for turtle eggs or crabs, in my tiny dug-out canoe with my dog Maçã in the early 1980s. She wasn’t much help, so I thought, other than barking at animals (deer, tapir, turtles, snakes) swimming around us, and keeping us company. I just thought I could keep the creatures astray by hitting them on the head with my paddle (that’s when I’d lose balance and fall in the water). But I did learn a precious canoeing lesson from Maçã, when we first capsized: Swim upstream in order to land where you want to be (downstream). Unlike me, the dog had a great sense of direction, because she understood the power of the current you have to fight against. I often thought about this lesson when I was stranded downstream, walking for hours on the margins of the Xingu river, hoping to fetch a ride from canoes or motorboats headed upriver back to the Diauarum Post in the Xingu Territory, where I worked. Maçã was already waiting for me there. I was told that she knew how to navigate the river: swim upstream for survival. What a great lesson.

Swim upstream for survival

I thought of this lesson everyday in the mathematics classroom at the Diauarum School in northernmost Xingu Territory. Fight against the monsters (lutar contra os monstros), as one of my students put it, referring to the Brazilian military dictatorship (1964-1985), which kept a close watch on our “subversive” activities of learning how to read and write. All of my Paulo Freire books had fake covers (following my father’s advice). First readers we wrote and map books we drew were scrutinized by FUNAI. In retaliation, we received no supplies and could only rely on family donations from São Paulo.

Swim upstream

Create our own pedagogical materials, which we did, using an alcohol-run mimeograph to print reading matter — primarily the Memória do Xingu (Xingu Memory) monthly newsletter, and annual Xingu Calendars, mentioned above. We disguised history as myth. Copies of maps were taken by informal sympathizers, flown in and out of Xingu for other reasons, just in case originals were lost or destroyed. Radio messages were sent in different languages, promoting our school curricula and asking for help from nearby schools. We attracted students from faraway villages in the Xingu Territory: North and South students flocked from the Mēbêngôkre (aka Kayapó), further North (who now live in their own Kapoto Territory and elsewhere); and South, such as the Trumai, Kukúro, Kalapalo, and other peoples from the Baixo Xingu. One by one, Indigenous schools started mushrooming in the Xingu Indigenous Territory, with support coming mostly from the Instituto Socioambiental headquarters in São Paulo, and private donations.

This is the result of the strong Indigenous Peoples’ Movement in Brazil, starting in the 1970s, during the dictatorship, which led to the birth of multiple indigenous organizations and NGOs that still prevail today. I began volunteering at the Comissão Pró-Índio de São Paulo, in 1977. COPIAR — “Comissão dos Professores Indígenas do Amazonas,” represents more than 80 Indigenous organizations today, fighting for education equity and social justice in the Brazilian Amazon. And there are many, many others.

Now, what are academics doing about this struggle? Are we, mathematics educators fighting for Indigenous Peoples’ rights to quality mathematics education? In general, yes. Ethnomathematicians are increasingly proposing new mathematics curricula for schools (indigenous or not), based on real-life situations, as mentioned above. However, some high-profile articles still ask: “Is There Mathematics in the Forest?” (ALMEIDA, 2019). The author, an anthropologist, offers several mathematical equations based on kinship as evidence that, yes, there is “mathematics in the forest.”

Kinship relationships can be coded and reckoned, as the argument goes, and thus used as predictable outcomes of mathematical reasoning. True, any everyday activity that involves people in action can be translated into an algorithm, by using social relationships as numerals, as I have argued before. The beauty of ethnomathematics, however, as my father Jorge Leal Ferreira — a physicist and mathematician at heart — called the “pearls of mathematics,” is the fact that mathematics is what we do in everyday life.

In this respect, we invite your eye to gaze at stars, look down to the earth, above at elders, over to the children, and realize that we are all ethnomathematicians, deep inside.

References

ALMEIDA, Mauro William Barbosa. Is there Mathematics in the forest? HAU: Journal of Ethnographic Theory, v. 9, n. 1, p. 86-98, 2019.

BRASIL. Ministério da Educação. Secretaria de Educação Fundamental. Atlas geográfico indígena do Acre. Rio Branco: Comissão Pró-Índio do Acre, 1998.

Comissão Pró-Índio do Acre (CPI ACRE) Geografia Indígena. Professores Indígenas do Acre. Rio Branco: CPI-Acre, 1992.

D’AMBROSIO, Ubiratan. Etnomatemática: arte ou técnica de conhecer e aprender. São Paulo: Ática, 1990.

FERREIRA, Mariana K. Leal. Mapping Time, Space and the Body: Indigenous Knowledge and Mathematical Thinking in Brazil. Rotterdam: Sense Publishers, 2015.

FERREIRA, Mariana Kawall Leal. Madikauku: os dez dedos das mãos — Matemática e povos indígenas no Brasil. Brasília: Ministério da Educação / Secretaria de Educação Fundamental, 1998.

FERREIRA, Mariana Kawall Leal. (Org.) Livros de Mapas de São Paulo. Brasília: Ministério da Educação / Secretaria de Educação Fundamental, 1999.

FERREIRA, Mariana Kawall Leal. Acting for Indigenous Rights: Theatre to Change the World. Minnesota: University of Minnesota Human Rights Center, School of Law, 2013.

FERREIRA, Mariana Kawall Leal; LANG, Gretchen C. (Ed.). Indigenous Peoples and Diabetes: Community Empowerment and Wellness. Durham: Carolina Academic Press, 2006.

FERREIRA, Mariana Kawall Leal; SCHIESARI, Luís. Livro de Mapas da Associação Xavante Warã. Mato Grosso: Terra Indígena Sangradouro, Aldeia Idzô’uhu, 2002.

FRANCHETTO, Bruna. Céu, Terra, Homens. O calendário Kuikúro. In: FERREIRA, Mariana Kawall Leal (Ed.). Idéias matemáticas de povos culturalmente distintos. São Paulo: FAPESP/MARI/Global, 2002, p. 101-118.

GAVAZZI, Renato Antônio. (Org.). Geografia indígena: Parque Indígena do Xingu. São Paulo: Instituto Socioambiental, 1996.

LEA, Vanessa Rosemary. Área indígena Kapoto: laudo antropológico. Campinas: Instituto de Filosofia e Ciências Humanas da Universidade Estadual de Campinas (IFCH/Unicamp), 1997.

LEA, Vanessa Rosemary. Parque indígena do Xingú: laudo antropológico. Campinas: Instituto de Filosofia e Ciências Humanas da Universidade Estadual de Campinas (IFCH/Unicamp), 1997.

LÉVI-STRAUSS, Claude. The Elementary Structures of Kinship. Boston: Beacon Press, 1949.

PEZZUTI, Juarez; CARNEIRO, Cristiane; MANTOVANELLI, Thais; GARZÓN, Biviany Rojas. Xingu, o rio que pulsa em nós. São Paulo: Instituto Socioambiental (ISA), 2018.

RICARDO, Carlos Alberto. (Org.). Povos Indígenas no Brasil, 1996/2000. São Paulo: Instituto Socioambiental, 2000.

RICARDO, Fany Pantaleoni. (Org.). Interesses minerários em Terras Indígenas na Amazônia Legal brasileira. São Paulo: Instituto Socioambiental, 1999.

RURI’õ, Lucas; BIASE, Helena de Stilene. Daró Idzô’uhu Watsu’u. A História da Aldeia Abelhinha. São Paulo: Master Book, 2000.

SILVA, Maria Aracy Lopes da; RODRIGUES, Maria Carolina Young. Histórias de verdade. São Paulo: Secretaria Municipal de Cultura, 1992.

WERNER, David. Donde no hay doctor: guia para los campesinos que viven lejos de los centros medicos. Ciudad de Mexico: Editorial Pax-Mexico, 1973.

Notes

Alternative link

https://periodicos.ufop.br:8082/pp/index.php/revemop/article/view/3528/3156 (pdf)