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

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# 0108_Aboriginal Numeration