Transcript 0108_Aboriginal Numeration

Aboriginal Mathematics
Australian Aboriginal Mathematics
Tyson Yunkaporta writes, “In Australia, mathematical systems have been
developed over tens of thousands of years to create intricate kinship systems
ensuring genetic vigour. Similar systems were innovated millennia ago for
species breeding and classification. Weight systems were based not on
numbers, but on patterns on natural objects such as shells, conforming to what
western scientists have only recently "discovered" and labelled as the Fibonacci
sequence. Geometry was used in calculating time according to the angles and
postion of the sun, moon and stars at different times, governing predictions about
seasons and weather. This was also used for navigation.
“Although in many Australian Indigenous cultures numbers had no names beyond
three, large-scale quantifying was still used in records and calculations through
patterns and diagrams on rocks, trees, bark and message sticks. Many language
groups in New South Wales developed base five number systems. Calculators
for this were developed based on one-to-one correspondence, using materials
such as honky nuts (like a disposable abacus system), and served to perform
calculations of addition, subtraction, multiplication and division.”
Aboriginal Mathematics
2
Number
Robin Walker, an Aboriginal Education Worker in
Coober Pedy talked about asking an Anangu man in
the North-West of South Australia how many cattle he
had. He replied 'Tjuta' (lots). When Robin asked
"But how many?" he walked away and Robin thought
he wasn’t coming back but he later came back with a
handful of pebbles, one for each animal. The owner
of the cattle in this case clearly knew the number of
cattle he had because he had the correct number of
stones even if his language did not have a word to
express this number. He would be concerned if one
was missing and would be aware if an extra one
appeared.
Aboriginal Mathematics
3
Number Names
Aboriginal Mathematics
4
Birth Order Names
Aboriginal Mathematics
5
Aboriginal Concepts of Number
Message Stick
Aboriginal Mathematics
6
Algebra
Aboriginal Mathematics
7
Time
Aboriginal Mathematics
8
Seasons in Arnhem Land
Aboriginal Mathematics
9
Questions
for
you to try please:
Aboriginal Mathematics
10
Numeration
In the Murray River area of South
Australia, traditional local language
words for the English one, two, three
are:
ngungbai, bula, bula-ngungbai.
What would the number 4 be in the
local traditional language? _____
Aboriginal Mathematics
11
Numeration
In the traditional local language, the
English four (4) would be bula-bula
(literally 2 + 2).
/
//
///
////
ngungbai
bula
bula-ngungbai
bula-bula
Aboriginal Mathematics
12
The Martu Wangka (W.A.) counting system
one
two
three
four
five
ten
kuja
kujarra
kujarra kuja
kujarrakujarra
marakuja (hand-one)
marakujarra (hand-two)
What would the number seven (7) be in the Martu Wangka
counting system?
________________
Aboriginal Mathematics
13
The Martu Wangka (W.A.) counting system
1
2
3
4
5
6
kuja
kujarra
kujarra kuja
7
marakuja kujarra
8
marakuja kujarra
kuja
9
marakuja
kujarrakujarra
kujarrakujarra 10
marakuja
11
marakuja kuja 12
Aboriginal Mathematics
marakujarra
marakujarra kuja
marakujarra kujarra
14
The Anindilyakwa language of Groote Eylandt
is an example of a language with specific terms for one to five, ten, fifteen and
twenty which are not based on hands or feet (Stokes 1982:38)
one
awilyaba
two
ambilyuma
three
abiyakarbiya
four
abiyarbuwa
five
amangbala
ten
ememberrkwa
fifteen
amaburrkwakbala
twenty
wurrakiriyabulangwa
Despite this, Groote Eylandters would have been incapable of dealing
with larger numbers such as 150.
TRUE
FALSE
Aboriginal Mathematics
15
This is indeed FALSE
Tindale (1925: 129) bargained with
Groote Eylandters, demanding 150
spears which he indicated as 10 x
15 (10 fingers x 15 sticks). The
Groote Eylandters brought him the
correct number, 140 of them being
tied in bundles of twenty, because
that was obviously how they
preferred to group them.
Aboriginal Mathematics
16
Working with Aboriginal children and students
Aboriginal students, like all students have a range of preferred learning
styles. However, there is a cultural tradition of learning by observation
and imitation and not asking questions. When effective pedagogy is
used for Aboriginal students, all students will benefit because the
learning will be based around relevant, real activities.
Use methods which result in success. Different methods work with
different students. Some will benefit from using rulers for counting, times
table sheets, calculators and/or wooden blocks. Use of concrete
materials helps learning and understanding. Other students might
require an individual challenge.
TRUE
FALSE
Aboriginal Mathematics
17
This is indeed TRUE!
Aboriginal Mathematics
18
Number
Aboriginal languages generally had words for
numbers up to three. This sounds very simple in
comparison with the present Western numbering
system but was not as simple as it sounds. To
some extent, numbers were irrelevant with quality
being considered far more important than quantity.
Many Aboriginal people now use English words for
numbers within their own language, just as English
has adapted the number system from Arabic.
TRUE
FALSE
Aboriginal Mathematics
19
Once again, TRUE!
However much teachers use Aboriginal mother tongues to
start children off on the road to understanding maths, early
immersion into English is indispensable for its achievement.
There is no reason to fear that children so immersed in
school will "lose the culture", any more than Japanese,
Malaysian, Chinese and other children whose parents send
them to Australia and other English-speaking countries for
much of their schooling lose their culture or mother tongue.
If Aboriginal families do not want such immersion, it should
not be thrust upon them, but they should realise that the
price of rejection is exclusion from effective participation in
the mainstream activities of Australia and continued
dependence on others for their material welfare.
Aboriginal Mathematics
20
References:
http://www.aboriginaleducation.sa.edu.au/files/links/Aboriginal_culture_and_mat.pdf
http://www.youtube.com/watch?v=jMB3b4admzs
http://aboriginalrights.suite101.com/article.cfm/indigenous_mathematic_systems
http://www.fullbooks.com/Voyage-Of-H-M-S-Rattlesnake-Vol-2-of-24.html
http://www1.aiatsis.gov.au/exhibitions/e_access/serial/m0005975_v_a.pdf
http://quadrant.org.au/php/archive_details_list.php?article_id=419
Aboriginal Mathematics
21