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It’s time we draft Aussie Rules to tackle Indigenous mathematics

When discussing how to embed Indigenous Australian knowledge and practices into the Australian national curriculum effectively - particularly the maths curriculum - there’s no better place to start than…

Mathematics and Aussie Rules have quite a lot in common, which should be used when considering curricula for Indigenous – and non-Indigenous – students. AAP

When discussing how to embed Indigenous Australian knowledge and practices into the Australian national curriculum effectively - particularly the maths curriculum - there’s no better place to start than analysing our own distinctively Australian national sport: AFL, the winter game.

Why, you might ask. Well, have you ever wondered why Indigenous players frequently excel at Aussie Rules, where they are vastly over-represented in the national AFL competition?

In populist discourse, the exceptional ability of some Indigenous players is frequently ascribed to “natural talent”. This is actually a soft racism, uncomfortably akin to the Social Darwinism expressed via the now-infamous “ape” comment directed at a gifted Indigenous player during a recent AFL match.

The interrelated concepts of “natural ability” and “genetic endowment” are ultimately furphies, because they fail to take into account learned cognitive factors routinely brought into play by some Indigenous AFL players - and the hard work that goes into their success.

Elite footballers aside …

This apparently remarkable aptitude on the AFL field is readily observable in matches between groups of young Aboriginal men who live in Australia’s remote rural communities.

Throughout most of the 1980s and into the early 1990s I lived and worked, mostly as school principal, in such a desert community, the Warlpiri settlement of Lajamanu in the Tanami Desert about half way between Alice Springs and Darwin. Along with other community members, I revelled in watching the home games, in which young Warlpiri men played dashing, thrilling football.

The seemingly superhuman exploits of the youthful, although mighty - according to local graffiti - Lajamanu Swans, who played electrifying footy in their bare feet on a dusty and grassless “oval”, a circular tract of rock hard red earth, is something I’ll never forget.

Football at Balgo Hills, Western Australia. yaruman5

Even smaller kids frequently showed outstanding skill in their capacity to grab hold of an airborne Sherrin flying from any direction whatsoever, while running at full pelt, and in their ability to find a passage through a narrow corridor, and in the finely tuned accuracy of their near-vertical jumps.

In what ways might Indigenous youths’ early childhood learning experiences and socialisation patterns lead to greater-than-average success in the game of AFL? Before attempting to answer this question, it is necessary to identify what makes the Australian game unique as a game of football.

How AFL stands apart

Unlike other football codes AFL does not have an offside rule, making it a multi-directional sport.

Moreover, it takes place on a very large oval-shaped field, requiring of players 360° of spatial consciousness, with the need to update and re-align oneself in space continuously, with split-second judgement and timing. The requirement of 360° spatial cognisance and responsiveness, a byproduct of the no-offside rule, is arguably AFL’s most salient feature, differentiating it from other football codes.

Indeed, one of AFL’s two major antecedents is an Indigenous Australian game with demonstrable kinship connections to today’s AFL (the other one is Irish Gaelic football). As the late Paddy Patrick Jangala, the first professional Warlpiri linguist, attested in the Warlpiri Dictionary Project in 1987:

Purlja, ngulaji yangka kalalu ngurrju-manu nyurruwiyi wita japujapupiya wampanajangka, wirrijijangka, manu janganpajangka wirrijijangka yumurrujangka. Ngulaji kalalu panturnu kankarlarrakari ngulakalalu puuly-mardarnu manu kalalunyanu warru kujurnu yapangku. Yarlpurrukurlangumiparlu. Yangka purljangkaji manyungka.

[Purlja is a small ball, which they used to make in the old days from string spun from wallaby fur and from possum fur. They used to kick it up in the air and then grab hold of it and throw it around to each other. Only age-mates (yarlpurrukurlangu) played on the same team. That is when they played with the “purlja”.]

So, for what precise reasons do so many Indigenous players find the 360° attribute of the game to be such a good fit, in cognitive terms? Traditional Aboriginal mathematical systems are largely founded upon spatial relationships rather than on numbers, which is the case in Australia’s dominant culture.

A different spatial outlook

Australia’s Indigenous languages are rich in spatial terminology. As linguist Mary Laughren once noted:

Desert children’s ability to handle directional and spatial terminology in particular is taken as a sort of intelligence test similar to the counting prowess test among Europeans.

This ability, to handle sophisticated terminology about space and directionality with confidence and accuracy, and the concomitant skill in land navigation even when one is completely surrounded by desert, is inculcated into children from the earliest infancy, even today. My own observations based on more than a decade of living at Lajamanu confirm this, and the former principal of Yuendumu School, Pam Harris, has written about it extensively.

Wide open space, with few landmarks, near Lajamanu. Christine Nicholls

Preschoolers, only two or three years of age, could confidently name all the cardinal directions by the time they entered school and instantly apply them with almost 100% accuracy no matter what environment they found themselves in – a learned skill essentially deictic in nature, that most children in our dominant culture Australia are still struggling with at 15 or 16 years of age.

Wendy Baarda, a teacher and linguist who has been living for many years at the Warlpiri settlement of Yuendumu (where little Liam Jurrah, and many others like him, first kicked a footy) drew attention to this commonplace linguistic and deictic ability in the following anecdote:

One of the school’s Warlpiri Literacy workers was walking along carrying her baby who was about 18 months old. A bystander (another Warlpiri adult) called out to the child to get its attention. The child heard the voice but could not locate the person, so the speaker called out again, this time supplying the direction in which the child should look: ‘Kakarrarni’ - towards the east. Immediately the baby turned its head and looked in the right direction, towards the speaker.

One important difference, in relation to the dominant culture of this country, is that a person’s limbs (“left” or “right”) are not to be regarded as fixed entities in relation to self, as is implicit in the formulations “left” and “right”. Rather, they are conceived within a much broader context of spatial relationships with respect to the exterior world. So, in accordance with the specific spatial circumstance, a person might talk about one’s north, south, east or west hand (or leg).

dev null

When one is continually on the move (or run) within 360° of open space, albeit with the intention of reaching specific goalposts within that space, the formulations of “left” and “right” in relation to one’s own body have little or no meaning. This form of spatial apprehension is not restricted to people in the Central or Western Deserts of Australia, but ubiquitous throughout Aboriginal Australia, and as a method of orienteering one’s way through space, survives even where the local languages are faltering.

The American linguistic anthropologist John Haviland has written about the importance of cardinal directions for the Guugu Yimithirr (alt. Guugu Yimiddhir) people of Northern Queensland, in terms of position finding while in motion:

… Speakers of the Australian language Guugu Yimithirr (hereafter GY) at the Hopevale community near Cooktown, in far North Queensland, make heavy use in discourse about position and motion of inflected forms of four cardinal direction roots - similar in meaning to north, south, east, and west. The system of cardinal directions appears to involve principles for calculating horizontal position and motion strikingly different from familiar systems based on the anatomies of reference objects, including speakers and hearers themselves.

Rather than calculating location relative to inherent asymmetries in local reference objects, or from the viewpoint of observers themselves characterised by such asymmetries, the GY system apparently takes as its primitives global geocentric coordinates, seemingly independent of specific local terrain and based instead on horizontal angles which are fixed, as it were, by the earth (and perhaps the sun) and not subject to the rotation of observers or reference objects.

‘Salt on Mina Mina’ by the late Warlpiri artist Dorothy Napangardi. AAP

While I have barely touched upon the complexity of these systems here, they have largely survived, not always in intact form, the vagaries of colonisation. Their survival is most evident in rural, tradition-oriented Aboriginal communities, but it persists across generations, following Indigenous diasporic movement into Australian country towns and big cities.

This culturally specific form of mathematical knowledge, intergenerationally transmitted, imparted in its most intact form via Aboriginal languages, plays itself out not only on the AFL field but in tradition-oriented Aboriginal art, and has an important role in other Indigenous knowledge.

The ability to apply such knowledge is a product of nurture, not nature – it cannot be genetically transmitted any more than it is possible to transmit concepts about number and computation to other little Australians, except via processes of acculturation.

What are the educational implications?

In February 2011 the Australian Institute for Teaching and Learning (AITSL), a contributor to the Australian Curriculum, Assessment and Reporting Authority (ACARA), released a document titled National Professional Standards for Teachers. One of AITSL’s key categories was titled “Professional Knowledge”. Its Standard 2, which reads:

Know the content and how to teach it

has several subsections, of which Focus Areas 2.4 and 2.5 are relevant in this context.

Focus Area 2.4 reads as follows:

Understand and respect Aboriginal and Torres Strait Islander people to promote reconciliation between Indigenous and non-Indigenous Australians

while AITSL’s Focus Area 2.5 has as its major thrust Literacy and Numeracy strategies. The idea of an integrated curriculum is thus intrinsic to the conceptual approach mandated by those charged with overseeing the writing of the as-yet not-fully-rolled-out (or even completed) Australian National Curriculum.

Rusty Stewart

Nonetheless, educators contributing to, writing and implementing these national curricula will be expected to “embed” literacy and numeracy strategies as well as Indigenous knowledge/s into diverse subject areas, including English and the arts.

Such a cross-curricula approach means that into the foreseeable future Australian maths and science education will need to be conceptualised outside of what are often perceived as those disciplines’ own self-referential silos.

There is an opportunity here to include such Indigenous knowledge in the new mathematics and science curricula, especially. There are many potential applications for spatial analysis in fields beyond the playing field: in computer science, mining, astronomy and many fields of research. It will enrich all Australian children to learn a little about Indigenous mathematics in the new curriculum, and will provide Aboriginal kids living in “outback” Australia and others too, a real chance to shine.

We have a clear choice here. The easiest, most likely option is for teachers implementing the new national curriculum to pay mere lip service to such integrated curriculum approaches.

The more difficult pathway will involve taking these ideas and shaping them into a curriculum that goes beyond inclusion of “Indigenous perspectives” but foregrounds “Indigenous knowledge” at the level of the episteme.

Join the conversation

523 Comments sorted by

  1. Kerri Worthington

    housekeeper

    Referring to one's own 'left' and 'right' in spatial terms makes so much sense, far less confusing. But let's not hold our breath for this type of maths to be taught in all schools. The national curriculum may talk about understanding aboriginal cultures but it's not the same thing as actively incorporating their mathematical systems etc into mainstream programs.

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Kerri Worthington

      Thank you for this comment, Kerri. I guess it's difficult to understand the extent to which our own cultural understandings are highly specific to our own culture, when we're so deeply immersed in it.

      As I've written: One important difference in relation to the dominant culture of this country is that a person’s limbs, ‘left’ or ‘right’, are not to be regarded as fixed entities in relation to self. Rather they are conceived within a much broader context of spatial relationships - a person might…

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    2. Stephen Ralph

      carer at n/a

      In reply to Christine Nicholls

      The cardinal points as such would not have existed pre-contact days either.

      I would think that all no-urban communites etc in the dim past would have developed their own systems for distance, direction and travel.

      Studies into the use of the sun, moon and stars shows how important these were.

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    3. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Stephen Ralph

      Dear Stephen,

      Thank you for your comments. On one point I can absolutely assure you: and that is that the cardinal points definitely existed in pre-contact days.
      For example, a medical doctor called David Lewis travelled with some first-contact Aboriginal men around the desert as far as Lake Mackay (Wilkinkarra) and recorded them as saying: "We knew north, south, east and west before the white man and his compass."

      I'd be happy to send you the references if you wish to follow this up!

      Best wishes

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    4. Stephen Ralph

      carer at n/a

      In reply to Christine Nicholls

      I'm not arguing that were not in existence - in fact Wikkipedia says that indigenous Australians had as many as 6 "cardinal" points.

      My point is that although I.A. (and others societies of the time) used these reference points, they would have not been N.E.W.S and left and right....but words or symbols representing their indication of direction.

      We use the word "north" to indicate direction and other references, but north would be mean nothing in pre-contact days.

      Perhaps we are arguing semantics.

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    5. Frank Baarda

      Geologist

      In reply to Stephen Ralph

      So the sun didn't rise and set in pre-contact days?
      I've lived on Yuendumu for ages and have marvelled at the rapid fire "kakarara", "yatijarra" etc (East North) so much more tactically useful than the two dimentional "give it here".
      Our preocupation with the North arrow I think derives from the ancient dicovery of the lodestones.
      Warlpiri people tend to align maps according to the real attitude of the land the maps represent.
      Yes indeed they had no north south east and west, they had no English at all.

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    6. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Frank Baarda

      Excellent & relevant post!

      Regarding the way 'the west' understands the cardinal directions, it is VERY different from what you describe - for example, let's be specific, in The Australian, (Tuesday February 21, 2012, SPORT Section, p 44), there was a photograph of an aggrieved-looking (the late lamented Australian cricket captain) Ricky Ponting. On the previous day Ponting had been ‘dumped’ (to use the word used by the journalist Peter Lalor in his accompanying article on the same page) from…

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    7. Frank Baarda

      Geologist

      In reply to Christine Nicholls

      Far from fluent. Warlpiri is far more complex for an adult to master not least because it encompasses such a different worldview which your article touches on. European languages and thinking have a great emphasis on time, Australian Aboriginal languages and thinking on the other hand (left or right?!) are thoroughly spacial. It is this space/time difference which is a root cause of much misunderstanding, lack of communication and ultimately unjust ethnocentric assimilationist policies Aboriginal Australia has been and continues to be subjected to by the dominant culture.
      As for postulating that spatial thinking is behind AFL footy prowess is a stroke of genius. Thank you for one of those "why didn't I think of that? " enlightening moments Christine!

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  2. terry lockwood

    maths/media/music/drama teacher

    Fascinating stuff, Christine.
    With the increasing use of GPS for navigation, I suspect cultures around the world will become even less familiar with the natural cues for direction. I navigate by the sun when i am in unfamiliar territory.

    It might also be a bit of a stretch to suggest that 'Joe Public' really thinks that the Indigenous players' spatial ability is genetic as opposed to cultural. I don't think Joe thinks that deeply.

    It would be interesting to see Indigenous players try to teach other players how they see the world spatially. Would the recipients be receptive? Can it be articulated? In my experience of working with footballers and the geometry of goal-kicking, they are a conservative lot.

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to terry lockwood

      Hello Terry,

      It is difficult to take issue with anything you've said here - I agree with every word.

      Especially, I agree with your thoughts about the putative loss of touch with cardinal directionality on the part of the dominant culture - this continuing lack of familiarity with cardinal directions as a navigation aid, and knowledge resource, will result in a wider cultural loss...

      It is time to accept Indigenous people as teachers about a differently-conceptualised approach to mathematics, not placing them as perpetual learners - before this globally endangered knowledge actually disappears, for want of acknowledgement..

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    2. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to terry lockwood

      You are right Terry about the navigation aids that we use today perhaps interrupting the normal cognitive processes we use for getting around...

      this is on reason why knowledge of spatial terminology, and how to apply it, will never become truly redundant, and there's still a lot to learn from
      'traditional' Aboriginal mathematical systems...

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    3. Mal Jones

      logged in via email @gmail.com

      In reply to terry lockwood

      And I was good at singing and picking up on syllables much more quickly than my peers at a young age.. My older sister is a terrible singer.. so is this also nurture?

      Why has my sister -given more years of exposure to possible sources to learn music from - blurted out such poorly controlled and aimed notes and stuff..?

      When I, before school age amazed people with my abilities..

      People who have a head injury sometimes lose the ability to control their voice well.

      I'm not foolish for thinking there may be a genetic component to the skills people have.. Nurture can help an awful lot.

      Could a simple test for auditory/ visual / kinesthetic preferences help here.

      I think the author of this article mentioned that some indigenous Australian children demonstrated a better use of their visual memory.. most people are visual.. so in that case the kids had simply been taught to nurture a skill more people could learn too.

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  3. Stephen Ralph

    carer at n/a

    Fascinating, but don't know if this is just a long bow drawn to hit a pre-determined target, or not.

    After all young "white" kids have been kicking footballs around for a century or so and many are duds at mathematics.

    If many "black" kids (male of course) had to choose b/w footy and mathematics, I would bet on the choice.

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    1. terry lockwood

      maths/media/music/drama teacher

      In reply to Stephen Ralph

      I assure you that most white kids will choose maths over footy too Stephen.

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    2. terry lockwood

      maths/media/music/drama teacher

      In reply to Stephen Ralph

      silly me I did mean footy over maths - i should check more carefully before hitting 'post comment'

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    3. Stephen Ralph

      carer at n/a

      In reply to terry lockwood

      I thought you may have, but as a maths teacher, I thought you also may be defending your territory.

      cheers.

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    4. Sean Manning

      Physicist

      In reply to Stephen Ralph

      Football only pays more if you apply a flawed statistical analysis. If you take the average income for all people who pursued only football as a career (not only the successful people) and compared it to the average income for all people who pursued mathematical careers (not just mathematicians but anything inherently quantitative and therefore requiring a solid mathematics education) I am quite sure you will be proven wrong. Simply put, mathematics provides you with more options for your career and a longer career.

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    5. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Sean Manning

      Agreed Sean...and in addition mathematicians working in all of the applied fields to which you allude do not routinely end up with arthritic bodies in middle age and beyond, as a result of too much contact sport...

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  4. Ben Cooling

    Web Developer & Programmer

    Attempting to subscribe some intrinsic significance between the author's elected code of choice and the indigenous population comes across as unconvincing proselytizing. The article does have some interesting points that would have been better served decoupled from AFL centric rhetoric.

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    1. Stephen Ralph

      carer at n/a

      In reply to Ben Cooling

      To me it sort of outlines the obvious.......I mean coastal communities eons ago new about marine travel, ocean currents and direction etc

      Agrarian communities new about farming techniques, seasons and crops.....etc

      The skills were not representative only of black, white, yellow or brown etc.

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    2. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Ben Cooling

      Hello Ben,

      Thank you very much for your comment, and I agree with your point about the perils of oversimplification. I'd like to assure you first that in putting forward this view, I don't hold any particular candle for AFL - but the point made here us that AFL IS unique in its 360 degrees field coverage enabled by the *absence* of an offside rule. (I was largely brought up in Sydney at a time when Rugby really ruled and went to see my brother playing Rugby Union for his school and had never even…

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    3. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Stephen Ralph

      Hello again Stephen,

      To follow up again you may be interested to read the 1994 book 'Macquarie Aboriginal Words

      (http://trove.nla.gov.au/work/23178838),

      which lists (obviously pre-contact in origin) vocabularies from many Australian (the linguistically correct name for the 250 or so distinct Aboriginal languages that were in situ in Australia BC - Before Cook) all around Australia, and many of these have words for the cardinal directions 'north', 'south' 'east' and 'west', indicative of the rich spatial terminology in this area - I think that you would find it fascinating.

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    4. Ben Cooling

      Web Developer & Programmer

      In reply to Christine Nicholls

      Thanks Christine, I did enjoy your article and view point. I think there is a lot of value to be found in finding the intersection between sport & academia, braun & brain etc instead of conceiving it as an unassailable dichotomy. On the flip side, I think this could also only foster a more sophisticated & genuine dialogue around sport as well; perhaps one day the lazy 'natural skill' cliche you mentioned could even be retired?

      Having said that I'm not convinced of how or even why the AFL needs…

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    5. Martin Quirke

      Architect (UK Registered), PhD Candidate at University of Newcastle

      In reply to Christine Nicholls

      Interesting article Christine,
      I did find the link between maths and AFL a little tenuous. As you have hinted, perhaps this is partly due to 'conditioning' and resultant pre-conceptions. Maybe we need a diagrammed example?

      I agree that a link does exist between mathematics and spatial cognition. Mathematical ability has been correlated with navigation ability in the sport of orienteering (e.g. Notarnicola et al. (2012)) Perhaps this could strengthen your proposition re spatial comprehension from a global (cardinal), rather than relative (object / person) centered point of view, as simply another form of mathematical cognition?

      Again, as you point out: the key will be in finding a meaningful way to immerse this into curriculum so footy obsessed kids feel more engaged with the content : diagramming football strategies in maths class perhaps?

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    6. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Ben Cooling

      Thanks Ben.

      There are other ways of applying similar Indigenous knowledge to other sports, especially when it comes to factoring in wind direction, which also has a pronounced effect on certain (outdoor sports). This can be applied to Rugby, athletics etc as well.

      For more info. on this please see the acclaimed Australian linguist David Nash's recent article on Indigenous terminology relating to wind direction :

      http://www.tandfonline.com/eprint/7weYMqJeF5fye7IghFVR/full

      and let us know what you think!

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    7. terry lockwood

      maths/media/music/drama teacher

      In reply to Ben Cooling

      'cept that any mention of AFL makes me wanna read it. Sorry!

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    8. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Martin Quirke

      Hello Martin,

      Thank you so much for this post, which I've been thinking about over the past 24 hours.

      As an architect, are you interested in producing such a diagrammatic model of (AFL) football strategies?

      I think that you are into something there, and that could be very useful...

      More later...

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    9. Mal Jones

      logged in via email @gmail.com

      In reply to Ben Cooling

      Some people do have natural skills and some people do not.

      Unfortunately the awesome bowler Alan Donald from South Africa put his energy into helping an ugly (styled) bowler from New Zealand who should not receive that privilege. The bowler should have been directed into a different field than sport because he is not good to watch..

      He received lots of coaching and camps in his youth like a spoilt brat.

      There are people who can't help but move well to the music when they hear it. This…

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    10. Mal Jones

      logged in via email @gmail.com

      In reply to Martin Quirke

      Rather than boring the whole class with football perhaps the coaches could impart some maths knowledge to the kids.

      When I took up cricket the other kids knew about calculating their averages and so on many years before we learnt it in highschool.

      Up skill the coaches and the teachers and start paying them better and stuff. Coaches do it for free with young ones but go for qualifications.

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    11. Gail Carnes

      Consultant

      In reply to Mal Jones

      There's no doubt that individuals have their own particular abilities. Those abilities could be inherited as a genetic predisposition or taught because they are valued within a particular community. Regardless of the source of one's ability, if one is particularly adept at something, such as music, maths or spatial ability, then others could potentially learn from them. However, a problem arises when one society does not understand or appreciate the natural abilities possessed by people of a different…

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    12. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Gail Carnes

      Yes, thank you, I checked this link out early this morning - it throws an interesting light on some of the differences between soccer as a football game and Australian Rules.

      I'm not sure whether anything has been attempted in relation to the vectors involved in Australian Rules (AFL) footy, because studying the vectorial qualities of the game both in terms of ball movement and human movement around and across the field, as well as back and forwards, and representing these diagrammatically would potentially add to the knowledge base in this instance. Frank Baarda commented earlier about Warlpiri facility in vector addition, that he observed whilst working with the men in his capacity as a geologist based at Yuendumu, and Martin Quirke, an architect who commented earlier in this discussion, also made a comment related to this matter of mapping the movement.

      I wonder if Martin Q. would be interested in taking it further and working on a diagrammatic representation thereof?

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  5. Donald Richardson

    artist/writer

    I don't know enough about either football (I had to look up 'offisde rule'!) or mathematics to comment on the thesis, but experience has shown me that we are unwise to discount either nature or nurture. Both footballers and mathematicians are both 'born' as well as 'made.'
    But I think that 3D acuity (the ability to note subtle land-marks) is the stuff of both successful hunting and the ability to make visual representations - which I have observed seems to be innate in some Aboriginal children (or learned early). Does diexis stretch to the making of art?

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Donald Richardson

      Yes, that's quite true about nature/nurture both having significant roles in this; it is also very obvious that a person’s body type, physiology and physical fitness all play significant roles in any sporting achievement, as does their personal psychology (ie drive to succeed) and also to put in the sheer hard work required for success.

      And yes - I do believe that art making is to some extent at least (the unanswerable question is, to what extent?...this is impossible to quantify...) a demonstrably culturally anchored and deictic pursuit/endeavour...if you're interested I will post up some more info...thank you for your comment.

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    2. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      Christine, it would be interesting to check your theories against NAPLAN Mathematics results of these Aboriginal communities.

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    3. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to David Thompson

      You're right about that David - it would allow tradition-oriented Indigenous kids (especially those who still speak their ancestral languages) to shine in the area of knowing and being able to apply cardinal directional terminology - and possibly lead to a less than impressive performance from those on the other side of the colonial divide...and the Naplan tests may also need to be translated into Indigenous languages to constitute a level playing field approach..perhaps a step too far for those behind the tests???

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    4. terry lockwood

      maths/media/music/drama teacher

      In reply to Donald Richardson

      FYI Donald, Australian Rules is may be more akin to basketball than soccer or rugby.

      And I don't have any desire to understand the offside rule.

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    5. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      Actually, Christine, my point was that we already know how these communities perform in NAPLAN Mathematics tests. Abominably.

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    6. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to terry lockwood

      Nonetheless, Terry, regardless of the team sport, almost all of them require an excellent sense of spatial apprehension, including soccer, Rugby, basketball, netball - it is just that AFL is par excellence, the sport that requires this 360 degrees awareness...and constant vigilance (whilst on the run, often) in relation to that 360 degrees of potential activity...

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  6. Steven Newton

    Teacher, Student

    Interesting article, however I am unconvinced that the path to "understand and respect Aboriginal and Torres Strait Islander people to promote reconciliation between Indigenous and non-Indigenous Australians" can be found in such simplistic yet tenuous linkage of dominant and non-dominant thinking within the Maths curriculum. Your last few paragraphs sum it up and I fear 'lip-service' is all many teachers will be able to offer as the national curriculum facilitates the inclusion but not the the 'embedding' of indigenous knowledge (or any other knowledge) and as far as education being 'conceptualized outside of what are often perceived as those disciplines’ own self-referential silos', this is a pipe dream whilst neo-liberal policies drive the education reform agenda.

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Steven Newton

      Hello Steven,

      Yes, I do take your point on this Steven, and think that (sadly)what you've written here represents the realpolitik of the situation. And of course no single initiative or idea can or will lead to Reconciliation. A range of different strategies and tactics will obviously need to come into play simultaneously. And most of all, ***recognition*** of these unique Indigenous ways of engaging with the world, whether that be mathematically, or in other fields, needs to be part of the…

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    2. Steven Newton

      Teacher, Student

      In reply to Christine Nicholls

      I agree with the 'conciliation' argument yet am troubled by your last paragraph. I am also a little troubled by the fact that it seems par for the course in this type of discussion to roll out the time spent working and living in indigenous communities as some sort of 'credential' on the topic, I have too, and people, its not!

      However, I agree, a hard to achieve goal shouldn't be the reason for inaction but the act of doing something isn't synonymous with achieving something.

      I personally…

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    3. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Steven Newton

      This is an academic network aimed at putting forward ideas to others about ideas, and ideas lead to possible courses of action.

      What are the possible courses of action that you view as more potentially more effective?

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    4. Steven Newton

      Teacher, Student

      In reply to Christine Nicholls

      My greatest concern is that while academia puts forward ideas, it is generally others who implement the courses of action. Politicians who change the course of action to suit budgets, teachers who change the action to fit with the resources already purchased. A very cynical view I will admit, but am I wrong?

      As you mentioned, reconciliation is perhaps an inaccurate term and I would argue the current view by many policy makers, principals, teachers is in itself inaccurate. You mention 'recognition…

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  7. Eva Cox

    Professorial Fellow Jumbunna IHL at University of Technology, Sydney

    Fascinating Chris, even without a clue about AFL. I did some work last year looking at various literacies to add to the mix for Indigenous early childhood learning and this stuff fits very neatly with my attempts to convince early childhood teachers that the gap between Indigenous children and others was often two sided rather than a deficit by one group. This article contributes nicely to the debates about how to recognise other epistemologies and understand other ways of describing what is. Then more Indigneous parents would not need to feel they are seen as having nothing to offer. Recognising alternate views allows exchanges between equals not filling up the gap with our views and assumptions

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Eva Cox

      Thank you Eva for your post. You are quite right about the prevailing view being that the deficit is one-sided, rather than there being knowledge gaps on both sides. And there is the additional problem of not many people being able to disentangle what is culturally-received and inculcated knowledge, and innate knowledge. This was driven home to me many years ago at Lajamanu, when as school principal I had to administer an IQ test to all the kids in the school (at the time about 250). One of the items…

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    2. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Eva Cox

      PS it struck me in retrospect that many young Australian kids of Asian background would have failed that assessment item too, if they had grown up using chopsticks...

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    3. Stephen Ralph

      carer at n/a

      In reply to Christine Nicholls

      The list of examples could be endless re this issue.

      Many urban kids think milk comes from cartons (so they say).

      Surely the most important issue with indigenous education is to allow I.A. to compete in the workforce. To be able to choose to become a footy player or a mathematician, or a ballet dancer.

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    4. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Stephen Ralph

      Thank you Stephen!
      To compete in the work force, we need to be broadly educated people. I really don't understand what the problem is in including some knowledge from differing cultural groups (especially the cultures - plural - of Australia's original inhabitants) into the curriculum.

      To continue discussing this in relation to maths:

      The number strand, usually starting with counting, is routinely taught before other mathematical knowledge in mainstream Australian infants and primary school…

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    5. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      Except Christine Asian kids perform extremely well academically, even after migrating from as far away as China and Korea. They perform especially well in Mathematics. And yet, your Warlpiri kids perform atrociously.

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    6. Jon Hunt

      Medical Practitioner

      In reply to David Thompson

      I think you miss the point David. Asian kids do well because they are brought up in a different environment. The classical stereotype is that they study 25 hours per day. They have an arithmetical mindset. Aboriginal people are different which is an important point this article is trying to make.

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    7. Stephen Ralph

      carer at n/a

      In reply to Jon Hunt

      We're all different, and yet we are all the same in a zen sort of way.

      Way back we all came from the same stock.

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    8. Jon Hunt

      Medical Practitioner

      In reply to Christine Nicholls

      IQ tests don't necessarily take into consideration culture, education or environment. Why do the test in the first place? Were they trying to prove something?

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    9. Frank Baarda

      Geologist

      In reply to David Thompson

      As with all NAPLAN testing the result is dependent on the questions asked. When it comes to year three English for instance, I've often posed the question of how well would Melbourne kids go if their questions were posed in Warlpiri. This isn't even going into context.
      In this discussion I think the question of how can Indigenous knowledge and thought processes be included into a national curriculum so that all Australian children can benefit from this wonderful (but sadly almost not recognised…

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    10. David Thompson

      Marketing Research

      In reply to Frank Baarda

      "I've often posed the question of how well would Melbourne kids go if their questions were posed in Warlpiri."
      Well how do Melbourne kids from China, India, Argentina, and Iran do in NAPLAN?

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    11. David Thompson

      Marketing Research

      In reply to Frank Baarda

      And that still doesn't explain why Warlpiri kids perform so badly in Mathematics, despite this alleged spatial superiority.

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    12. Jon Hunt

      Medical Practitioner

      In reply to David Thompson

      David, you are trying to allude to something. What is it?

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    13. Frank Baarda

      Geologist

      In reply to David Thompson

      I've been asked that question before.
      I believe at least a partial answer lies in the ability of children to learn language by immersion.
      I'm glad you picked Argentina.It so happens I did my primary education there. I learned Spanish by immersion (Dutch is my mother tongue), I can't remember the process, it just happened, I am not consciuos of ever not being able to speak listen write and read Spanish. Exposure to English was minimal (it took me years to realize that "Jesus Jolly goo felo" wasn't…

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    14. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to David Thompson

      Hello again David! I think that both Jon and Frank have already answered this as well as I can, so all I'll add is that it is possible to construct a test on culturally-specific knowledge that anyone could fail.

      So if we tested non-Indigenous kids of 5 or 10 on their ability to apply their knowledge of the cardinal directions in a rapid fire manner, then their results on such tests would be far inferior to Warlpiri kids in Lajamanu, Yuendumu, etc, and other Aboriginal kids elsewhere in northern Australia - in which case you'd have to admit that the non-Indigenous kids have done 'atrociously' in relation to Warlpiri kids!!!

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    15. David Thompson

      Marketing Research

      In reply to Frank Baarda

      Frank, in other words, performance on Year 3 NAPLAN Maths assessments is not dependent on English fluency. So if this Warlpiri (and other Indigenous) culture and language is so mathematical, why do they perform so spectacularly badly compared to immigrants from newly arrived NESB kids in Victorian schools?

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    16. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Frank Baarda

      That's right Frank - and to explain further, David, the NAPLAN maths tests are number-centric, and that is supported by the broader cultural practices of the dominant culture, whereas in the latter case, spatial concepts receive relatively (and considerably) less airing in the curriculum...& also in the testing program!

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    17. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      Christine, I’m not aware of anybody who thinks any knowledge is “innate”. I certainly don't.
      “So if we tested non-Indigenous kids of 5 or 10 on their ability to apply their knowledge of the cardinal directions in a rapid fire manner...you'd have to admit that the non-Indigenous kids have done 'atrociously' in relation to Warlpiri kids!!!”
      Without a question. But not atrociously in ‘Mathematics’ or even ‘spatial thinking’.

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    18. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      The example you gave of the Lajamanu “IQ test” that asked questions about correct cutlery arrangement is certainly an example of very poor/backward understanding of assessment by whichever bureaucracy made you test the kids that way. How long ago was it? It sounds like something before WWII. I’m not an expert in that area, but I was under the impression that mandatory IQ testing of Australian school kids ended many decades ago? I am aware of a few IQ tests used in kids today, and they have been developed over the past few decades with a very high cultural sensitivity. The two that immediately spring to mind, which according to your points, would suit Aborigines very well are the Cattell Culture Fair Test and the Ravens Progressive Matrices. Both are completely non-verbal AND non-numerical, focusing only on patterns and spatial relationships.
      http://en.wikipedia.org/wiki/Cattell_Culture_Fair_III
      http://en.wikipedia.org/wiki/Raven%27s_Progressive_Matrices

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    19. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to David Thompson

      Well first, I can assure you that I wasn't even around prior to WW11, David!

      At this point I think I need to know your definition of 'mathematics' - does it include space + time, or just number?

      Dr Google isn't necessarily the sine qua non in terms of setting the parameters here...

      So, over to you -

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    20. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      Christine that is a very good question, which I have no doubt minds far finer than mine have debated for yonks. But I can say is that (i) While Mathematics is based on Arithmetic, Maths most definitely is not "just number". (ii) And not only do I agree that space is part of Mathematics, I also argue, space might be the most significant. (ii) Time is also part of Mathematics.

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    21. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to David Thompson

      So, now I really do not understand your position - why are you excluding Indigenous space/time concepts from 'maths' - to which category they certainly belong - if, as you say, maths is more than 'merely' number?

      These concepts are no more innate - or - folkloric than those of the dominant culture.

      Let's just consider TIME for instance - Indigenous concepts of time are in part (but by no means entirely) linked to events, whereas there's a misconception that 'time' is not linked to events but…

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    22. Jon Hunt

      Medical Practitioner

      In reply to Christine Nicholls

      A bit of an aside, but I asked an Aborginal person today when they were planning on travelling back home. Their response was "when the road dries". I suggested that they could perhaps be more precise, but that was as accurate as I could get. It was important to me for logistical reasons that I have a more accurate answer, but they seemed disinterested in even estimating when this would be.

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    23. David Thompson

      Marketing Research

      In reply to Frank Baarda

      Frank, given the current clearly unsatisfactory approach to teaching language to Warlpiri children, I personally would strongly support any movement to have the kids taught their Mathematics in their own language. The kids could still sit the exact same NAPLAN test as everybody else, except the written instructions would Warlpiri, not English. This sort of arrangement works perfectly fine in international testing. For example, Australian, Chinese, Finnish, and Japanese children all take exactly the same Maths PISA test, except in their own language.

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  8. John Clark

    Manager

    A remarkable example of an author arguing against her own proposition. At the outset Christine assures us that there is no inherent difference, since to do so invites the charge of racism. She then goes on to produce evidence of an aptitude that endows the young athletes with special skills and an ability to excel at the game by greater application and effort.to gain their disproportionate impact on the game. Why is it so vital to deny that they have a natural talent, which, when nurtured, can enable them to participate at the highest level?

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to John Clark

      Dear John,

      Thank you for your response (from sophistry.com?)

      The flaw in this argument is that I'm not talking about purely 'natural' aptitude, either with respect to the cultural learning of non-Indigenous kids or tradition-oriented Indigenous kids, but what is INCULCATED, ENCOURAGED, & VALUED culturally in each case.

      We need to separate culturally-socialised knowledge (ie passed down by cognitive processes) from genetically-endowed gifts - and while all seeming 'gifts' are a product of both, the former is always needed to bring the latter into a form of public success.

      ...many a rose is born to bloom unseen...

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  9. Marcus James Dilena

    Retired

    Fascinating stuff. I am not an expert on education, spatial orientation, or especially AFL football (I barrack for the Crows). But I have lived and worked with Warlpiri people in Lajamanu and Yuendumu. As I have worked with other Indigenous people in the Northern territory and in PNG. Once again it is unfortunately observable that some comments, sincere that they may be, come from Western assumptions that all technology and learning emminates from the so called developed countries. It is an unfortunate…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Marcus James Dilena

      Hello Marc,

      Totally agree with your post - very focused.

      I have just been watching the excellent Australian Story tribute to Mr Yunupingu, and although it is terrific, I couldn't get my head around the fact that not one of the non-Indigenous persons interviewed (all very decent people) could not pronounce the name of his band or even his family name correctly...we need to get past this deep monolingualism and deep monoculturalism... and soon.

      And as you say, the fact that dominant cultural coordinates prevail is part of this problem...looking forward to more posts from you, Marc...

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  10. John Clark

    Manager

    Christine, my initial comment was based on the AFL reference. I have reread your post in greater detail. It is not at all remarkable that desert dwelling people have an innate sense of direction nurtured from birth, since it has been central to their survival. Other ethnic groups in similar circumstances exhibit the same skill, eg, Innuit, Taureg peoples. A more striking example comes from seafaring cultures, think Kontiki. Peoples without this need have lost the skill by evolution. It still…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to John Clark

      Good afternoon John.

      I agree that there are other groups in the world whose finely-honed mathematical abilities aren't based wholly on number, but on spatial relationships. The evidence is there.

      But there is nothing separatist about engaging with different ways of thinking - this is about coming closer together, not growing further apart.

      Regarding the teaching of Aboriginal languages, this is highly practical when it comes to the teaching of Aboriginal children who do not speak English…

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  11. Jon Hunt

    Medical Practitioner

    I have for some time known that Aboriginal people apparently do not have words to describe numbers more than a few, making me think they have a different way of viewing the world. This may be a little off the point, but I have a friend who is Singaporean and when he is home in Singapore he can emerge from a underground walkway and know exactly where he is, whereas I am completely lost. However, when we go bushwalking I seem to know easily where North is yet he is mostly completely lost.

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    1. David Thompson

      Marketing Research

      In reply to Jon Hunt

      Jon, all Mathematics is based on Arithmetic. Somehow, I'd be suspicious of any claim about the mathematical ability of a people whose command Arithmetic stops at the number two. ;)

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    2. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Jon Hunt

      Dear Jon (and David),

      Thanks very much for your posts.

      The general Australian public’s lack of knowledge about Indigenous Australian mathematical systems and practices, and the absence of recognition of those systems and practices even when they are known, has sometimes given rise to ignorant and (or even in some cases, frankly racist remarks) about Indigenous mathematics. The dominant discourse suggests that there is NO Indigenous maths based on number or on any form of maths for that matter…

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    3. Jon Hunt

      Medical Practitioner

      In reply to Christine Nicholls

      Hi Christine, well I am pretty naive and it would not surprise me if I was incorrect. I have had a bit to do with Aboriginal people but not really felt comfortable enough to interrogate them about their mathematics. Forgive my ignorance, but how are spacial relationships considered mathematics? If so, it seems to be a specific form of mathematics (I am thinking of trigonometry as our equivalent). I have spent too much time a long time ago studying mathematics at an abstract tertiary level to think of things in a different way.

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    4. Frank Baarda

      Geologist

      In reply to Jon Hunt

      Vector addition is yet another mathematical thought process. I've found that Warlpiri people are very good at it albeit on a subconcious level (dare I say "natural"!)
      I was involved in a geophysical survey once that involved straight parallel motor vehicle driven lines. I took readings at speedometer intervals. I made a pact with the Warlpiri driver- "I want you to go west, I don't care how much you weave to avoid mulga stumps, but you have to fix any punctures". This was many years before GPS…

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    5. Jon Hunt

      Medical Practitioner

      In reply to Christine Nicholls

      Christine, If I can be perhaps be critical I think this article presumes some knowledge of mathematics, navigation and Indigenous languages; I may be incorrect but isn't this meant to be a forum for laypeople? I have had to read the article a few times to get the gist of what you mean, but perhaps I am a little slow. I had to look up 'cardinal directions' although I was pretty sure I knew what these were I had to check...!

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    6. Jon Hunt

      Medical Practitioner

      In reply to Jon Hunt

      I also had to look up what 'inclulcated' means!

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    7. Jon Hunt

      Medical Practitioner

      In reply to Jon Hunt

      Which I seem to have spelled incorrectly..

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    8. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      Christine, Arithmetic is NOT merely "one strand of mathematics..." it is the foundation on which all mathematics is built. Where you are going wrong on this whole subject is that "indigenous mathematics is "a learned skill essentially deictic in nature, that most children in our dominant culture Australia are still struggling with at 15 or 16 years of age."
      The way you have reported Warlpiri (and alleged Indigenous groups in general) language and mathematics shows the exact opposite of deixis. In fact, their language and spatial understandings are very limited, trapped in a prism of cardinal directionality. What you call the "dominate culture" is linguistically and mathematically rich in BOTH cardinal and relative directionality. Unless the Warlpiri are educated like the rest of us they will never be able to grasp mathematics.

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    9. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      "To begin, Indigenous numerical systems are not Base 10, which means that it has perhaps been easy to take on board a view that Indigenous innumeracy was the norm. And as I've explained in the article, in terms of Indigenous maths, spatial relationships are considerably more important than vice versa."
      Except in "dominant Australian mathematical cultures", spatial thinking is overwhelmingly not "decimal", but sexagesimal. That spatial thinking is known as "geometry", "trigonometry", and "astronomy".

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    10. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to David Thompson

      Yes, we do have a relatively rich cardinal directional vocab. and terminology in the dominant culture - no one can deny that. But how many kids (or even adults) in our dominant culture can actually APPLY that knowledge in an almost effortless manner, with apparently little or no thought, ie to the point of its being an almost-automatic response?

      I do not know many.

      But in terms of number, as a result of having had addition, subtraction and multiplication and division tables drummed into us…

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    11. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Jon Hunt

      Jon - you are right in that the article traverses a number of areas of knowledge that are perhaps not mainstream, but I do think that you and others have grasped its major thrust...and of course, it is in a sense your experience in coming to terms with it is more or less the reverse process that many Indigenous language speakers have to go through on a daily basis, i.e. grappling with what is for them an essentially foreign language, English, and the equally foreign concepts that accompany that language, including that pertaining to maths/numeracy in the dominant culture...the only really difference is that they have no choice but to do so...

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    12. Mal Jones

      logged in via email @gmail.com

      In reply to Christine Nicholls

      There's got to be something more than this.. My sister picked up Maths and I have not in all my years.. My Mother many years before me did not pick up maths. My father did.

      We were all exposed to the same sorts of drills as you I'd imagine..

      So there is likely some "nature" component to some skills and not only nurture..

      If you want to teach my sister to sing it's gonna take a lot of effort, encouragement and correcting.. if you wanna teach me to sing it's gonna be a bit of a breeze really…

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    13. Mal Jones

      logged in via email @gmail.com

      In reply to Mal Jones

      Very good article though.

      I would like to learn some indigenous maths.. May be I can do well at it. The passing things backwards rules in other sports makes no sense to me..

      Maybe I would have done well at AFL

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  12. John Clark

    Manager

    Christine - I find it difficult to debate someone so passionate, and so capable of presenting a point of view cogently and politely. I should therefore save my input for another time and place. The problem is that your opinion is supported by your qualifications, and therefore likely to influence others who may be less critical in their reasoning. Many of your supporting arguments are well intended, but false (that is of course opinion). Eg, Australia is monolingual and monocultural. Nothing…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to John Clark

      Dear John,

      Thank you for your interesting post, which is good for thinking with...I must go to work exceedingly early tomorrow, so let it suffice that I make one comment now, with more comments to follow soon.

      It is a not unnecessarily emotional comment, because it is inflected by historical truth.

      As Australian English first language speakers, as is the case with other first language-speakers of English (e.g. many, but definitely not all, English people and many but definitely not all people…

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    2. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      "Monolingualism can make people lazy."
      Indeed. That is why it is completely inappropriate for "dominant culture" academics to campaign to deny Indigenous peoples the mind-expanding and social participation advantages of the education the rest of us have access to.

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    3. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to David Thompson

      Hi David,

      I honestly don't know of ANY 'dominant culture' academics or anyne else for that matter, either Aboriginal or non-Aboriginal 'campaigning' against Indigenous people's access to a decent education, in the way that you describe.

      Where is the evidence base to support this?

      Who are these people campaigning to deny Aboriginal pepole such rights - who are they, exactly?

      A stronger evidence base is needed here, please!

      An evidence base woiuuld expands

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  13. Will Owen

    Librarian

    Very early on in my encounters with Aboriginal people, I was in the small community of Amoonguna near Alice Springs. I was talking to an artist from whom we were purchasing some small canvas-board paintings and exchanging information about where we came from. Since it was near holiday times, I asked if he had plans to travel "back" to his country. As I said that, I unconsciously tilted my head "back." He immediately picked up on the gesture and corrected me by pointing in the direction in which his country lay. I was dumbfounded: I probably couldn't do that right here in the town I live in in North Carolina (USA).

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Will Owen

      The artist's seemingly effortless gesture towards his country masks the depth of the early and life-long learning experience underpinning that gesture.

      Such spatial acuity is evident Central and Western Desert artists who did not grow up in houses during their formative years, thereby enabling a different kind of ‘eye’ or visual consciousness to emerge and develop. This is reflected in their remarkable artwork.

      Thank you, Will, for this lovely story, elegant in its apparent simplicity - but which also reveals a good deal about the topic under discussion. More posts please!

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  14. Gail Carnes

    Consultant

    Astuteness in traditional cultures regarding spatial relationships also extends to astronomy.

    Australian Aboriginal Astronomy: Overview

    Ray P. Norris, Duane W. Hamacher

    ABSTRACT: The traditional cultures of Aboriginal Australians include a significant astronomical component, perpetuated through oral tradition, ceremony, and art. This astronomical component includes a deep understanding of the motion of objects in the sky, and this knowledge was used for practical purposes such as constructing calendars. There is also evidence that traditional Aboriginal Australians made careful records and measurements of cyclical phenomena, paid careful attention to unexpected phenomena such as eclipses and meteorite impacts, and could determine the cardinal points to an accuracy of a few degrees.

    http://arxiv.org/pdf/1306.0971v1

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Gail Carnes

      Thank you very much for this informative and relevant post, Gail, especially for the link to the article, which I hope that others will read, too. I'd also like to draw your attention and that of others reading this post, to the article about Torres Strait Islander astronomy that's also streaming live right now on The Conversation, and has been written by Duane Hamacher, one of the co-authors of the article you've drawn our attention to here...
      It's a terrific article in a number of ways. One particular aspect of this that interests me is the level of 'embeddedness' of Indigenous science in narrative, and the Torres Strait Islander narrative related to astronomical knowledge presented in the latter article is particularly telling...

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  15. Ian Davidson

    Retired

    Christine, your article demonstrates vividly that Indigenous people have a spatial awareness far superior to that of the non-Indigenous population, but you seem to regard it as self-evident that this awareness can be classed as mathematics.

    The spatial awareness you describe must involve a sort of internal calculus but that does not amount to mathematics as it is commonly understood; moreover, I suspect it cannot be imparted to others. Can you envisage an Indigenous footballer enhancing the playing…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Ian Davidson

      Ian - to respond to each of the entirely valid points you make in this response, one by one: In terms of whether what I'm describing/evoking/discussing in this article is, or is not, 'mathematics', perhaps this is to some extent a matter of nomenclature. It is however generally accepted by teachers today that spatial reasoning, spatial ability, and the ability to visualise these and internalise them within one's broader cognitive/conceptual framework, do, broadly speaking, constitute mathematical…

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  16. Zac Hughes-Miller

    Student

    I can definitely attest to the 360 degree effect of AFL, I grew up playing Rugby, where your opposition is required to be on the other side of the ball, and hence your spatial awareness is concentrated on 180 degrees (maybe a little bit more so you know where the guy you will pass the ball is). Anyway, i started playing AFL when i was around 14, and you quickly realise how differently your awareness needs to be after you've been chased down a few times.

    The rules of AFL also heighten the need…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Zac Hughes-Miller

      A great piece of commentary Zac, and it's also good to hear from someone who has actually played the game - which is something that no one else has 'admitted to' (although that doesn't rule it out of course).

      I've 'recommended' this comment to others, to draw their attention to it...

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  17. Donovan Baarda

    Software Engineer

    I grew up at Yuendumu and learned Warlpiri as my second language. I also consider myself to be pretty good at maths. I'm always frustrated by comment threads like this and weary of trying to post anything. It's like trying to explain Laplace transforms to to someone who didn't go past basic maths. There is so much foundation knowledge missing I don't know where to begin. So I'll just throw in a few random comments;

    Warlpiri as a language is very rich on directional/spatial stuff, and weaker in…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Donovan Baarda

      Brilliant posting, Donovan...and I hope that political parties & independents of all persuasions will read this, and register your comments.

      It would be useful for you expand/expound on the Warlpiri Base 3 numerical system; this would be instructive to many...

      Ngulajuku...

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    2. Christina Davidson

      CEO at ANKAAA - The Association of Northern Kimberley and Arnhem Aboriginal Artists

      In reply to Donovan Baarda

      Thank you, I really enjoyed reading your comments. And can't agree more about your final remarks about poverty - and the levelling it imposes.

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  18. Zac Hughes-Miller

    Student

    I recall hearing about how growing up in an urban environment exposes people to so many right angles that they find the trigonometry side of mathematics significantly easier to learn than their non-urban counterparts, in this area of mathematics understanding of right angles, parallel lines, and other relationships between straight lines is integral.

    A quick google scholar search failed to find it, though there is wealth of research on the cultural differences in spatial frames of reference and…

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    1. David Thompson

      Marketing Research

      In reply to Zac Hughes-Miller

      Zac, the science is in, and the Warlpiri are absolutely abysmal at Mathematics. But then again, so are just about all public school teachers.

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    2. Duane Hamacher

      Lecturer and ARC Discovery Early Career Researcher at UNSW Australia

      In reply to David Thompson

      David, if you are really interested in learning more about the subject, I recommend you read the vast literature on the history and philosophy of science and mathematics. In particular, you should focus on the mathematical frameworks, systems, and number systems of Aboriginal people.

      Read about the mathematics of Warlpiri kinship systems:

      Gilsdorf, T.E. (2012). "Introduction to Cultural Mathematics: With Case Studies in the Otomies and Incas." John Wiley & Sons, pp. 65-69.

      Learn about how…

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    3. David Thompson

      Marketing Research

      In reply to Duane Hamacher

      Duane, I have long been all over the history of Mathematics and Astronomy. In fact, one of my top handful of loved historical personages was the Persian mathematician and Astonomer Sharaf al-Dīn al-Ṭūsī, and his genius Tusi-couple. But I am also completely up to date on all recent results of Warlpirri at Mathematics. NOW, time for YOU to get up to date, coz as I said, 'the science is in'.

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    4. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to David Thompson

      Hi David,

      With the greatest respect, I do not think that you have really engaged with the entirely valid points made by Zac in his two postings.

      Words like 'abysmal', 'atrocious' etc etc as a form of blanket dismissal of almost all public school teachers and the entire Warlpiri nation's mathematical ability simply doesn't wash in forums of this nature, where people (see for example, Duane in his posting) need to offer some research evidence to support their views...

      So, on what specific research are you relying to support these views? Or purveying?

      I'm hoping that you do have some research base to support the above views...because otherwise it's very difficult to engage with them seriously...

      You seem like a decent person so the ball is now in your court right now!

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    5. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to David Thompson

      What 'science' are you citing, specifically? Duane has provided a list of peer-reviewed research publications, so it't time for you to show the rest of us your research basis!

      Best regards...

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    6. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Duane Hamacher

      Hi Duane,

      Thank you for your post and I totally agree, that not just one but many PhD students should take up this challenge. The astronomical knowledge that you have discussed in your excellent article (currently on The Conversation now) as well as Indigenous mathematical knowledge is not just locally endangered but globally endangered, and its incumbent on all Australians to do something about this before further attrition takes place...& the same applies to the globally threatened remaining Australian Aboriginal languages.

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    7. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      Christine, you are an Education academic, who has 20 years of actual experience teaching and running Warlpiri schools. Are you telling me you are not aware of the performance of these kids in mathematics and cognitive assessments, including visuospatial skills? If you genuinely have never come across such data in your entire career, I will get it for you. But if this is the case, what have you been doing these past 30 years in the Education field?

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    8. Gail Carnes

      Consultant

      In reply to Christine Nicholls

      Hi Christine,

      Good question, because my own google search turned up nothing. Would very much like some links to substantiating research in this area.

      David?

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  19. John Clark

    Manager

    Christine, On further reflection, I am not sure the 360 AFL perspective is entirely supportable. The focus of all players is the opposing team's goalposts. They constantly move the ball in that direction, albeit being aware of their immediate surroundings. The only games that I recall passing back are soccer, basketball and waterpolo where an offensive move breaks down and the team relieves the pressure, prior to establishing a new offensive phase. May I congratulate you on your efforts to encourage others to work within the spirit and intent of TC?

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to John Clark

      Hello John,
      Thank you for your considered post. I agree that the goal of AFL (pun unintended) is to get the ball through the sticks at the other end of the field, which means that teams are attempting to send it that way by the most efficient route, which is as unidirectional as possible. Nonetheless, the POTENTIAL exists within the game to send it 'backwards' or in any direction (N, S, E, W, covering 360 degrees) in order to achieve that goal eventually. It is rarely a unlinear process, or anything like it, on account of the tackling that can happen. Indeed, some of the boldest moves take place in sending the ball 'backwards', or 'sideways' and upwards too of course, giving the game a balletic air at times. Before writing this piece I watched a lot of AFL games on tv (research!) and noted that everything that I've described here can and does happen.
      For a more informed view from a player of the game (which I've never been) please read Zac Hughes-Miller's earlier post.

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    2. Zac Hughes-Miller

      Student

      In reply to John Clark

      The 360 nature of the sport is more about sensing pressure from behind you than in what direction you can pass, players do pass backwards in AFL but they often turn around to do so (usually easier this way).

      As i said in the previous post, the rules of the game make it integral to try and not be tackled with the ball, the defender has the opposite goal, and because players can be anywhere on the field you must be aware of a potential tackle from any direction. In other contact sports the 'tacklers…

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    3. Zac Hughes-Miller

      Student

      In reply to Zac Hughes-Miller

      Didn't mean that first paragraph to sound snide btw, I was thinking about the 'no-look' handpass behind someone whilst they are facing forward (similar to a back-heeled pass in soccer)

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  20. Ian Davidson

    Retired

    Thank you for your lengthy reply to my post yesterday, which I found a very useful addendum to your article, but I want to challenge you on another point. I was struck by how quickly your article dismisses as 'soft racism' the belief that Indigenous people's spatial awareness could be even partly innate.

    My understanding, admittedly slight, of Noam Chomsky's work on children's language acquisition is that they are born 'programmed' to receive language and match it to the world. If one assumes…

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    1. Zac Hughes-Miller

      Student

      In reply to Ian Davidson

      It is 'soft' racism because of the implications that come with it, just as black athletes (in any sport worldwide) are labelled as having 'natural talent' we see similar numbers of white athletes described as 'gym rats' or 'hard workers' 'first at training, last to leave' etc.

      When Bruce McAvaney describes a piece of play as a bit of magic (a comment almost always reserved for indigenous players, in fact they used to just say black magic) he isn't referring to a complex genetic/environmental…

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  21. Frank Baarda

    Geologist

    Some decades ago, my wife (a teacher) told me that to teach writing the letter N to Warlpiri children they would describe it as a mingkirri (termite mound) next to a karlangu (digging stick). Small children were being taught in the vernacular at that time (none of this 'English only' nonsense).
    One group of children were looking at a blackboard on the east wall of the classroom during writing lessons.
    Subsequently these same children were in a classroom where the blackboard was on the west wall…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Frank Baarda

      There's a lot in highly condensed information in this post Frank, and I just hope that readers will engage with all you'vewritten here thoroughly. Here are a just couple of possible comments. As you say, in all cultures there are children (who usually grow into older people) with soaring intellects and those who are not so bright - and of course, those in between - i.e. a continuum. The same applies to sporting and other physical ability. It needs to be stated that not all Indigenous kids are good…

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    2. David Thompson

      Marketing Research

      In reply to Frank Baarda

      Frank
      “To deny a people an education in their own language where that is possible is to treat them as a conquered people and to deny them respect.” (The Hon. Kim E. Beazley Sr., 1999)
      That is a legitimate viewpoint, but I have encountered a great many Aboriginal parents who do not want their kids trapped out of the modern world. That is why so much energy and fundraising has gone into being able to send these kids to Australian boarding schools. Personally, I think this issue is one that should resolved locally. But if you really think there is reason to cheer when your kid has the cognitive skills in the bottom 5% of the world outside the desert, yet he can play softball really well by his mastery of cardinal directions, then I suppose I'm happy for you. I'd be very interested to see where these kids are when they hit their 30th birthday.

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  22. David Stonier-Gibson

    Electronic Engineer/Small business owner at SPLat Controls - electronic control systems

    One of the most fascinating things I have read for quite a while. I knew that a person's language is a major influencer of their "conceptual life". This show how it can also affect physical skills.

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  23. Peter Ormonde
    Peter Ormonde is a Friend of The Conversation.

    Farmer

    A delightful and thoughtful piece ...

    One of my treasured possessions - perhaps the only one actually - is a very very old piece of gidgee - a boomerang carved by a rock blade... no glass, no steel. Pre us.

    And you hold it up in profile and there in simple wood is a bird wing - the very product of thousands of blackboards of scribbled calculations by Mr Bernoulli ... the thing that keeps 747's up.

    Not bad for a mob with no use for numbers ... no words past three (really - a lot, more than we need, worth the walk). No waste this lot. Professional scientists - professional observers. Great geometry. Great mimics.

    We don't know how lucky we are to have such folks amongst us.

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Peter Ormonde

      Thanks for your post Peter - just one point: it's a furphy to say that Indigenous societies/languages had/have no numbers beyond three...I think that it's simply that that idea has been repeated so many times that people simply believe this to be the truth. For an example of a typical view, "their counting [is not] comparable to our elaborate numerical system. Indeed, it never exceeds 3..."(Von Brandenstein 1970:13).

      In his article John Harris (Australian Aboriginal Studies 1987, number 2, available…

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    2. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Christine Nicholls

      All true Ms N... I should have put it in quotes. But it's the Newtonian physics of gadgetry like woomeras and the geometry of boomerangs that start one on a heretical path of questioning the real value of quadratic equations.

      All in all a most adaptable and observant lot.

      By the way you might be aware of the historical school that believes a large part of the game of Aussie Rules is derived from an Aboriginal game played with a stuffed possum skin. Fewer rules. More biff. No umpire. Like a Collingwood game.

      The locals called it "marn grook" apparently with deep linguistic roots into the contemporary chanting of the hordes - "marn the pies"... well it's a hypothesis innit? There's a bit about us pinching the national sport as well here: http://www2.brandonu.ca/library/CJNS/25.1/cjnsv25no1_pg215-237.pdf

      Genetics or wot????

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  24. Steven Newton

    Teacher, Student

    I read and commented a little on this article from an education point of view and continued to read all responses and am really glad to see some genuine comments from different perspectives. Some very thought provoking comments that at times have both supported and ruffled my own views, great stuff. Thank you to the genuine conversationalists for helping me learn something.

    A little disappointing however to read a few commentors that come across as very thinly veiled racism. I only hope you too have learnt something.

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    1. David Thompson

      Marketing Research

      In reply to Steven Newton

      "A little disappointing however to read a few commentors that come across as very thinly veiled racism. I only hope you too have learnt something."
      Why are you "disappointed"? What do you hope they have learnt that they don't appear to have?

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    2. Steven Newton

      Teacher, Student

      In reply to David Thompson

      It was more a comment pertaining to the link between racism and closed minded people.

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  25. Ian Davidson

    Retired

    In reply to Zac Hughes-Miller

    You are obviously steeped in sport and sports coverage. I am not, and so was unaware until I read your post that expressions such as 'natural talent' are being used as code to play down impressive performances by black sportsmen. The subtext seems to be that black and white sportsmen are not on a level playing field and that it is therefore reasonable to discount the efforts of black players. Given this state of affairs, it is difficult to make suggestions such as…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Ian Davidson

      Hmmm - 'natural' talent - that's a hard one, and there's so much in your response Ian, that I shall only take it bit by bit, and deal with only one aspect of it here.

      Certainly, in my article I have not discounted the role of a person's physiology, body type, etc because clearly they play significant roles in any person's sporting achievement, and the specific sport that they might succeed in (gymnastics; cycling; Rugby, swimming; polo etc etc)- but body types, individual physiology etc etc vary…

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    2. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Ian Davidson

      Ian: thank you for your thoughtful post. I've responded to you and John Clark in one post in considerable depth, although I’m aware that you may not find what I say convincing, but this response is specifically in relation to your final paragraph above, where you cited Chomsky's linguistics. I'm particularly confused by your final sentence, because in terms of his theory of linguistics, Chomsky is in fact a nativist. (For others who may be reading this, ‘nativists’ assert that some concepts, beliefs…

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  26. Mike Puleston

    Citizen

    Great article, Christine, and a reminder that knowledge and skill is often culture-based. I remember reading somewhere of experiments that showed indigenous kids to be whizzes at the "match the turned-down cards" game, compared with non-indigenous kids. This applied especially when the cards depicted natural objects - stones, shells, leaves etc, but also with conventional playing cards. The indigenous kids were trained from an early age to be keen observers of detail.

    As for spatial orientation…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Mike Puleston

      Thanks Mike, and having lived in two cultures very different than my own (on an Aboriginal settlement in northern Australia for many years, and also in Japan) I do agree that knowledge/skills are considerably more culturally based than I might have believed had I not had those experiences.

      For example, not particularly relevant to this discussion, I recall one older Aboriginal man saying something that I will always remember. (The background to this is not there are no words equating to "please…

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    2. Mike Puleston

      Citizen

      In reply to Christine Nicholls

      Yes, Zac's posts are most informative. With the greatest number of on-field players of the football codes, and the possibility that you can get physically hammered hard from all directions, AF must develop a high level of 360 degree awareness. Conversely, a person with a high degree of 360 degree awareness would have an advantage in AFL, being able to get the ball away more quickly, and being better aware of where to put it.

      There are probably implications for geometry, trigonometry, and calculus. AF = speed calculus?

      Where do indigenous girls and women feature in all this?

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    3. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Mike Puleston

      Yes, indeed ref. the implications. I guess that the AFL field is the arena par excellence to demonstrate such skills, but certainly many of the Warlpiri girls/women demonstrate such skills on the basketball (yes, it was basketball, not netball) court - I used to play with the young women at Lajamanu and they were 'deadly' accurate in their throwing not only to one another, but goal throwing. This skill can be demonstrated to some extent in many sports.

      By the way, for all of you AFL tragics, I have received a tweet from Adam Goodes about this article, which he has given me permission to share:

      Adam Goodes
      ‪@adamroy37
      Thanks for sharing “http://theconversation.com/its-time-we-draft-aussie-rules-to-tackle-indigenous-mathematics-15032”: really interesting read.

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    4. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      Christine, nearly 200 posts later, and you still have not provided a scrap of evidence of Indigenous mathematical ability. And your attempts to argue superior spatial ability have in fact revealed the opposite. The Warlpiri (and others) are in fact hampered spatially as reflected in their languages, which are much lighter than just about ever other culture on earth, because the Warlpiri lack the relative directionality, without which, mathematics (such as geometry) becomes impossible.

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    5. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to David Thompson

      Tell that fella who burned and sculpted my treasured boomerang that his geometry is "impossible"...

      It took us a lot of serious arithmetic and physics to work that out. Same physics. Same concept. Offset leading edge, trailing edge, slightly concave lower surface. Not a formula or a blackboard in sight. Not a word written either.

      An expression of eons of watching and doing and refinement and tradition. Empiricism without stats. And a very different way of seeing the world.

      That said, there is nothing new or even novel about Aboriginal sporting prowess - from cricket through to boxing, racing, rodeos, football in various codes - bar soccer (?), tennis, more boxing and athletics.

      I wouldn't rule out genetic potential at all. Nor do I discount the contribution of an equally nurturing sense of place - physically and spiritually.

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    6. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Peter Ormonde

      PS ... I'll bugger off in a tick ... but I tracked down a bit from a paper I read (on real paper) a long time ago... ethnomathematics ... a wonderful notion. I remembered the word and little else ... Now buried in this excerpt is a reference to some academic study - Kearins, 1977 ... demonstrating superior spatial skills by Aboriginal kids. So this difference seems to have been recognised a while back.

      http://www.aiatsis.gov.au/collections/exhibitions/ethnomathematics/docs/m0069594/m0069594_v_p13to18_a.pdf

      It's actually worth a read this.... excellent bit of observation. I remember coming across this when I was looking at Aboriginal economic concepts - and this Yolnu lot are particularly interesting because of their lengthy contact with Macassans, hence trade, markets and the concept and use of money.

      Curious business this sweeping generalisation lurk.

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    7. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Peter Ormonde

      You are right, Peter - Judith Kearins has made an important contribution to this field, as has Pam Harris (cited in my article). There's real problem with our dominant culture in terms of cultural memory in relation to Aboriginal education - so many worthwhile initiatives - and research either forgotten or ignored. Others I can think of who have contribute greatly in this arena are a number of people in the Yunupingu family group, Holly Daniels (from Ngukurr) Leon White, Stephen Harris and Beth Graham, and there are more, too.

      There is a crying need for a volume on 'Best Practice' in Aboriginal education with contributions from Aboriginal and non-Aboriginal theorists and practitioners.

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    8. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Christine Nicholls

      Now surely there's a bit of funding around for that Best Practice volume Ms N?

      Would seem rather essential as a stepping stone across any gaps I can think of.

      Be interesting to have a piece from you in future about this notion that learning in local language part of the time somehow "imprisons" kids in outstations...either geographically or socioeconomically .. by providing a "second rate" isolationist basic training.

      Given the sort of evidence-based approach you advocate I would imagine that is is perhaps a non-issue, but I have this sort of criticism from several sources now.

      Doesn't appear to be true.

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    9. Frank Baarda

      Geologist

      In reply to David Thompson

      Goodness gracious David! Have you been paying attention?
      "The Warlpiri (and others) are in fact hampered spatially as reflected in their languages, which are much lighter than just about ever other culture on earth, because the Warlpiri lack the relative directionality, without which, mathematics (such as geometry) becomes impossible."
      At first this statement made me angry. Very very angry. It flies in the face of much of what has been written in this forum. How silly of me. It was a joke! (as…

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    10. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Frank Baarda

      I think Ms N is in the running for a Brownlow myself...

      Speaking of running - one of the more interesting things about Adam Goodes style of play is his running - the sheer quantity of it - 20 kms a game + .... and we're not talking a gentle jogging or marathon pace here... we're talking short bursts of anaerobic work that leave you puffed or breathless ... that would leave me flat on my back twitching.

      That is an astounding workrate - a Phar Lap of footy players. The guy must have the metabolism…

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    11. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Peter Ormonde

      My late father was a geneticist, and while knowledge about genetics hasn't (unfortunately) been transmitted to me genetically (parenthetically just as a lot of what Kim Beazley Sr. stood for hasn't been passed on to Beazley the Younger), so therefore I can't claim expertise in the area, there are some things that I do know as a result - the first being that BOTH parents actually contribute to a child's genetic makeup! What I'm saying here (to some extent in jest Peter) is we can't make assumptions…

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    12. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Christine Nicholls

      What a pity genetics isn't inherited Ms N ... a flaw in the system???

      You're right of course both parents contribute to the fertilised nucleus equally... but there's more going on than just the nucleus... there's all this mRna stuff floating about out in the rest of the appalling egg business - hence extra nuclear - which does stuff all by itself ... no help whatsoever from dad ... ever ... any of them .... a straight line from mum ... all of them.... forever.

      One of the things this extra-nuclear…

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    13. David Thompson

      Marketing Research

      In reply to Frank Baarda

      Frank, I have been very clear and direct in responding to specifics posted here, so I have not only taken in what has been written in this forum, I have researched areas that were new to me, and I have responded to several posters and their ideas and claims. And you betcha I have posted 'flying in the face of [some] of what has been written in this forum.' A lot of it is philistine, vulgar, and plain wrong. So what is your problem? If you are very, very angry, you need to look to yourself for answers. All I have done is respond honestly to what's posted.

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  27. Robin Simson

    Retired secondary educator at Environmental education

    Christine
    My experience in education convinces me that much mathematical teaching is boring and rarely relates directly to life experience. Not only indigenous students but all young Australians would enjoy maths classes a lot more if the teaching tapped into the child's interests. As you say AFL is awash with mathematics and you can build in related aspects of science like how wind speed affects the flight of the ball. My sport of orienteering is a wonderful vehicle for teaching maths - direction, distance, timing, speed, performance tables etc. etc. I would hope the implementation of the National Curriculum in mathematics brings about a more imaginative and enquiry learning approach to maths teaching.

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Robin Simson

      All I can say to this is that I strongly agree with your approach, and imagine that you've been a terrific and imaginative teacher...while some kids will always understand subject matter taught via a decontextualised approach, the kinds of activities you're discussing will rope in those kids who don't respond to that...

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    2. David Thompson

      Marketing Research

      In reply to Robin Simson

      Robin, if you were correct, David Beckham would have won the Nobel Prize for Physics by now.

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  28. David Cordover

    logged in via Facebook

    I have a similar belief and wonder if this spatial awareness might also play out on a 'virtual field'... that of a chess board.

    Chess is widely used in schools worldwide to teach various mathematical thinking skills, one of which is spatial manipulation (just try to visualise where a knight can move in 3 moves time).

    I feel that chess would be a highly engaging tool (http://www.winters-flat-ps.vic.edu.au/chess.html) for teaching mathematical concepts to indigenous students. The fact that chess is a game and engages and excites students has also been seen to address issues of school truancy.

    It seems to me there are a number of benefits, both educational and social, to the implementation of a chess program targeting indigenous students. What do others think of this idea?

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to David Cordover

      Thank you for your post.
      It seems to me that your comment makes a lot of sense - i.e. to teach chess to all children, including Indigenous children, but really someone (particularly a maths teacher, I would suggest) who knows more about chess than I, needs to respond to this.

      David - can you cite any examples or research where teaching chess to kids has addressed matters such as school truancy, to which you allude? There may even be some studies outside of Australia that are in existence...over to you and others.

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  29. Frank Baarda

    Geologist

    To paraphrase K.Rudd: If I've veered somewhat off topic..."I'm Sorry!"
    Around 20 years ago the small locally owned company I manage, carried out a multi-client mineral exploration access track contract. Using a front-end loader we 'cleared' over one thousand Km. of access tracks starting from the Tanami road heading west to close to the West Australian border. This was mainly spinifex-country (manangarra). The spinifex had trapped windblown sand and combined with the countless termite mounds (mingkirri…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Frank Baarda

      Great post Frank.

      Just a clarification: I'm guessing that you are referring to Kim Beazley, Senior, here rather than 'son of', i.e. the present ambassador to the US?

      As you know, Kim Senior was an intellectual giant, and the Education Minister for the Whitlam Government, who has many credits, including the introduction of the bilingual education programs in a minority of Northern Territory schools.

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    2. Frank Baarda

      Geologist

      In reply to Christine Nicholls

      Ooops, yes indeed Kim Beazley Senior.
      While I am at it:
      One of the furphys those of us to whom the advantages of 'Teaching in the Vernacular' is self evident are prennially confronted with is 'But they have to learn English if they are to move forward'.
      That is what BI-lingual (BI as in two, both) is all about. I'm yet to meet a Warlpiri parent or carer that doesn't want their child to learn English.
      At a meeting at which the then "4-hours English only" policy was being vigorously debated, one (outside) participant remarked "With Warlpiri you could never send a man to the moon". Japangardi's droll reply: "Why would we want to send a man to the moon?"
      A week later Japangardi said to me "Weren't the Russians first in space?"
      Yes, I told him. I'd recommend to the NT Department of Education they should introduce a "4-hours Russian only" policy.

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    3. David Thompson

      Marketing Research

      In reply to Frank Baarda

      Frank, even better would be 4 hours of Maths/Science. If this thread is to believed even 4 hours per WEEK would be a great improvement.

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  30. Clare Towler

    logged in via Facebook

    Dear Christine,

    Thank you for contributing this interesting article. I want to add some points which came to mind, and I would enjoy any responses.

    The article seems to miss the fact that knowledge is not a thing, but involve ways of knowing – systematised practices that transmit knowledge over time and space. The point is that education is more than content, it is also process, and like any practice it is imbued with cultural assumptions and values, which determine how we can know in the…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Clare Towler

      Hello Claire,

      Thank you for your post. I particularly agree with your points about education needing to be about process, as well as the importance of bearing in mind the diversity of Aboriginal and Torres Strait Islanders, their communities, and in some cases, their practices.

      There's a need to conceptualise Australia, BC ('Before Cook') amd even now, as akin to Europe, an agglomerate of many somewhat but not totally interrelated cultures...and to act on that in education.

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  31. John Clark

    Manager

    Ian Davidson - You have much more eloquently expressed what I initially responded to Christine's post. It would seem now that scientific research is constrained by fear of charges of racism. I have an interest in the inclusion of indigenous Australians, but every time I try to formulate a statement or question, I end up discarding it. I am sure many others have also given up.

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to John Clark

      To Ian - and also John, re your thumbs up to Ian's genuinely considered post, perhaps the following points also need to be considered.

      First - I do think that we need to think a little more deeply about knowledge acquisition, and apply it to this specific situation. In doing so, it's necessary to distinguish between the brain's capacity (and I'm talking about 'any' brain here, regardless of gender, 'race' etc etc) to grasp any kind of subject matter, via mental acts. We are all capable of…

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  32. Ryan Manhire

    Student

    A very interesting and thought provoking article. While being almost proud of being an 'Australian' who has no interest in our unique take on football, I can definitely picture in my head the points you are making about movements over the 360 degree playing field and the constant locational checking that would come into account. I also had no knowledge of the specifics of various Indigenous players' approaches to the game through their - taught - spatial and directional positioning techniques…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Ryan Manhire

      Thanks for this post Ryan, in which you make a number of really valid points, including that of non-Indigenous Australia needing to educate ourselves further about Indigenous Australia, and value perspectives that differ from those of the mainstream. In a sense the only reason the chosen exemplar is AFL here is because, as you note albeit indirectly, Australia is such a sports-crazy country, and that might constitute a good and accessible entree into the differences in mathematical understandings…

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  33. Ian Davidson

    Retired

    In reply to Christine Nicholls

    Thank you for that reply, Christine. What you say amounts to an expanded answer to one of my original questions, namely what grounds there were for classing Indigenous Australians' remarkable spatial skills as mathematics. I now see Indigenous Australians' spatial awareness as their brain's mathematical capacity applied to the circumstances in which they live -- circumstances very different from those that gave rise to our mathematics.

    Your explanation makes it…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Ian Davidson

      Ian, thank you for your generous post. Regarding your post, with respect to the sentence: "Your explanation makes it clear how significant it is that the mathematics non-Indigenous children encounter at school 'ties in' with the world they have experienced beforehand..." nails down several important aspects relating to learning/education generally, the first being that anyone of any age can only ever go from what is 'known' to the unknown, by building on what is already known, in terms of successful…

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    2. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Ian Davidson

      Responding, indirectly, to Eva's post (please see below), and of course, more directly to yours, both this one and an earlier one from you, & in the interests of coming up with a summary of all of this correspondence, one of the threads in the correspondence to this article has been whether or not what I've categorised as 'maths' with respect to what I've described as 'Indigenous maths', is actually 'maths' by the criteria applied by the dominant culture.

      Without repeating my own view (which I think is obvious by now!) I'm wondering whether you could elaborate on your current position - and others may wish to do so, too.

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  34. Ian Davidson

    Retired

    In reply to Donovan Baarda

    Donovan, last night in reply to a post by Christine Nicholls, I wondered aloud whether a non-Indigenous kid growing up alongside Indigenous kids, and being fluent in their language from early childhood, would acquire the same direction sense as his mates. This morning, Christine posted a reply recommending that I query you on this. Your experience certainly fits the bill, growing up at Yuendumu and now working in a big way in the Western numbers realm as a software engineer…

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    1. Donovan Baarda

      Software Engineer

      In reply to Ian Davidson

      As a child at Yuendumu I did have the strong directional sense. I can remember playing mental games sitting in a chair with my eyes closed trying to believe I was facing in some other direction, trying to imagine what it would be like to not know what direction yatijarra (north) was.

      I don't think you'd need that strong sense of direction to converse effectively in Warlpirri, but you'd probably at least have to know the cardinal orientation of whatever you wanted to talk about in any detail, so…

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    2. Frank Baarda

      Geologist

      In reply to Ian Davidson

      And now a reply from someone that has learned Warlpiri as an adult (albeit very far from adequate).... When Google Earth came into existence I did what millions did.... I googled the places of my childhood. Lo and behold the north-south railway line in my memory, turned out to be east-west in 'reality'
      Through living on a place where the mother tongue made copious use of cardinal directions I had added spatial orientations to my memories. Somehow my sub-conscious felt the need to add directions to my memories, an imperative that did not exist at the time the memories were initially formed (in another far less space oriented language)
      " Elke heinnering werd een diamant, en zij sleep er telkens niewe kanten aan" (Dutch) .... Every memory became a diamond, and forever more she polished new facets onto them...

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Gail Carnes

      Thanks for your post Gail, environmental scientist, and I hope that many readers will open up the link that you’ve provided here & read that article thoroughly. It strikes me that the article you’ve suggested ought to be compulsory reading for all Australian volunteer (and of course professional) firefighters, in terms of offering guidance in developing, implementing and managing fire regimes in Australia today. While of course this approach cannot be duplicated willynilly today, because of changed…

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    2. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Christine Nicholls

      Not as simple as it sounds Ms N...

      Take this business... " * knowledge of germination of plants by means of fire; maintenance of biodiversity via controlled burning..."

      Now I've worked with some very clever chaps trying to put this stuff back together using our science and maths. We survey the living daylights out of a place and then start reading up on what was known about fire, seeds, flowering and the like. Some would be killed by fire outright, but needed fire to germinate - provided…

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    3. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Peter Ormonde

      Thank you for this valuable post, Peter - one of the most important aspects of which is the interrelatedness of aspects of (in this case, environmental) knowledge in areas/matters that at first glance may appear to be totally unrelated. I think that the integrated nature of some matters that we often tend to think of as existing in individual compartments is what you're alluding to here - please correct me if this is not a fair assessment.

      Just to clarify my own position, I certainly wasn't trying…

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    4. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Christine Nicholls

      Oh no Ms N ... I wasn't doing this horny handed son of toil lark then ... I was rampaging through the NSW National Parks and Wildlife Service ... playing with botanists and mathematicians and biologists and the like... doing things like looking at fires and long term conservation outcomes for say a patch of some useless, fragile, pathetic plant on a Threatened Species List... how often to burn the place so that those banksias regenerate but not so you'll kill all the baby angophoras... some of them…

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    5. Gail Carnes

      Consultant

      In reply to Peter Ormonde

      Of course, it's not simple, Peter. Dr Nicholls wasn't implying that it is. I think we all agree that traditional knowledge can't be easily codified. The tools for capturing and communicating such knowledge are limited, plus there are IP issues to consider. We can take that as a mutual understanding and then still have a conversation about school curricula, which is what this is about.

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    6. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Gail Carnes

      It's also about what we recognise as "useful knowledge" Gail. There's much more to this than reducing truancy and improving individual educational outcomes.

      To hear some pundit's pronouncements you'd think the only things worth teaching or learning are directly oriented towards employment, skills and earning a quid. But the fact is we actually don't know what is important or useful, or what will become so. It is not our knowledge to teach.

      Certainly not simple but making every effort to nurture and protect what remains of traditional culture and knowledge is surely part of the job - beyond even an exclusive focus on the individual and their future employment.

      And we can't teach that - can't even recognise it when we see it. So no not simple at all.

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    7. Gail Carnes

      Consultant

      In reply to Christine Nicholls

      I'm no expert on traditional knowledge systems, but I do have a keen interest in this area. There's been some work done by CSIRO and the Bushfire CRC towards developing a bayesian belief network model for compiling traditional knowledge, which, as Peter states, is multi-layered and linked throughout. Peter's also correct that burning for ecological reasons is very complex for those who don't have tens of thousands of years of knowledge passed on to them.

      Peter's perspective on "useless, fragile and pathetic plants" on the threatened species list is, I'm sure, meant to be humorous because, considering how little is known about ecological linkages and connections, as Peter himself agrees, we're certainly in a weak position from which to proclaim any particular plant species "useless."

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    8. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Gail Carnes

      Well spotted Ms C ... yes it was a veiled effort at humour - but I have had these discussions with property developers and landholders regarding "useless" plants and animals...

      And a lot of folks - some explicitly others less so - reckon that traditional knowledge and culture - from language through to sense of place and lessons on interacting with the environment - are all useless... irrelevant, backward-looking, politically-correct and "useless".

      From where I sit it's exactly like throwing away 50,000 years worth of field notes... encoded and encrypted in stories, myths, songs and social behaviours - but observations made by serious professionals ... watching stuff for a living. Like burning down the library at Alexandria again.

      I sincerely hope that you clever lot can find some way of keeping this stuff about - maintaining our resilience as a species if you like.

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    9. David Thompson

      Marketing Research

      In reply to Peter Ormonde

      Ah yes, the old 'Aborigine as museum piece' trope. Second only to its cousin, the 'Aboriginal zoo'. Sometimes, getting rid of old ideas (like these two) is an ethical priority that trumps your own acknowledged ignorance of 'useful' knowledge.

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    10. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Peter Ormonde

      Peter - I have to agree wholeheartedly with your philosophical position on what actually constitutes 'useful knowledge' - and that we don't know how much we're losing out by placing tight parameters around what's generally socially classified as 'useful knowledge- sleepers, awake!

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    11. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Peter Ormonde

      I took that comment as tongue in cheek! On a more serious note, could you please provide us with some information about what you're working on in terms of your work as a farmer, that has a direct bearing on the current discussion?

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    12. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to David Thompson

      Excellent - a trope!

      Nope David ... a straw trope I'm afraid.

      As for the ignorance of what in the end turns out "useful"... I plead ignorance along with the rest of us not gifted with prophesy.

      It is inevitable - desirable - that traditional life of scattered homelands and isolated communities change. Particularly on health, education and opportunities. No static museum exhibits at all... but a knowledge of what has gone before might be rather handy at times.

      For example - one of…

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    13. Frank Baarda

      Geologist

      In reply to Peter Ormonde

      Peter,
      In case you haven't come across it:

      “Cultural survival is not about preservation, sequestering indigenous peoples in enclaves like some sort of zoological specimens. Change itself does note destroy a culture. All societies are constantly evolving. Indeed a culture survives when it has enough confidence in its past and enough say in its future to maintain its spirit and essence through all the changes it will inevitably undergo. ”
      ― Wade Davis, The Wayfinders

      An excellent book (subtitled "Why Ancient Knowledge Matters")

      Being enmeshed in our ("western") culture which includes such bizarre concepts as "time is money"
      I can't elaborate, even if I'm finding this a scintillating discussion.
      So here's my latest two bob's worth (ha ha ha 20 cents, wonder how much that is in minutes and seconds, and how can I explain this to my Warlpiri friends?!)

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    14. David Thompson

      Marketing Research

      In reply to Frank Baarda

      Frank, you raise a very important issue re 'time is money'. This thread is about Aboriginal exceptionalism in spatial cognition. I am no expert myself, but I have read and heard much about Aboriginal difference when it comes to understandings of "time" as well.

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    15. Frank Baarda

      Geologist

      In reply to David Thompson

      To get an inkling as to the different conceptualisation of 'Time' in different cultures you can't go past Steven J. Gould's book 'Time's Arrow Time's Cycle'.
      After I read it, I came just that little bit closer to understanding where my Warlpiri friends and neighbours were coming from.
      Another two-bob's worth:
      I've come to realize for instance that an English sentence such as "A long time ago in the Dreamtime" is a bit of a nonsense.
      Not that Warlpiri doesn't have words related to time. Most Warlpiri people are bicultural in a sense they can function in the 'western' time's arrow environment.
      To get your head around time's cycle just ask yourself what will it be two seasons from now. Then ask yourself what was it two seasons ago. Presto! Go back in the past and sally forth into the future, you arrive at the same destination....

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    16. David Thompson

      Marketing Research

      In reply to Frank Baarda

      Oh good god Frank, I am more than sensitive to the nuances and contradictions of 'time's cycle'. Come on, I am a denizen of the 'dominant culture', the very culture built on the thoughts/works/teachings of Homer, Herodotus, Aeschylus, Zeno, Thucydides, Polybius, The Bible, Ptolemy, Roman Catholic Church, Newton, Einstein, and postmodernism.
      Please, I'd tell you all about time, alright, except I haven't got the time.

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    17. David Thompson

      Marketing Research

      In reply to Frank Baarda

      In other words, just as this thread worked out how differences between traditional Warlpiri spatial understandings and those of the 'dominant culture' are relevant to understanding the challenges the Warlpiri currently face, perhaps differences in temporal cognition might shine even more light on how to approach those challenges.

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    18. Frank Baarda

      Geologist

      In reply to David Thompson

      David,
      I wasn't having a go at you.
      I merely used this space to address the multitude in case they hadn't heard of Steven Jay Gould's book.
      I found it so illuminating that I wanted to share it with those that hadn't stumbled on it.

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    19. Frank Baarda

      Geologist

      In reply to Peter Ormonde

      Peter,
      This isn't really a reply or a comment, just couple of anecdotes (yimi-jarra) that your comments make me think you may enjoy:
      A white-fellow friend (F) went out "bush" with a mutual Warlpiri friend (WF) on a bright sunny day. WF told F "This is perfect roo hunting weather". On a subsequent trip on a miserable cold drizzly day WF told F "This is perfect roo hunting weather". "Aha!" said F, and pointed out the contradiction to WF. WF then proceeded to tell F at length and in great detail how kangaroos behaved in differing places under different weather conditions. In short, ALL weather conditions are perfect for roo hunting, providing you know how the kangaroos behave.

      In my wife's ESL class a drawing of a speeding kangaroo with the caption "Marlu ka pangka-mi kakarara pura" (again E.&O .E.) (the kangaroo is running towards the east), a little girl rendered the following English translation: "A meat running away"

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    20. Gail Carnes

      Consultant

      In reply to Peter Ormonde

      Traditional knowledge itself is one thing, but knowledge systems, or ways of thinking, are another. There are, of course, different ways of viewing the landscape and taking in information from it. There are different ways of sensing the orientation of one's body in three-dimensional space. These ways are teachable because they are taught. They're taught to children every day, and will be for as long as a particular body of knowledge exists and there are people around to teach it.

      As for how useful traditional knowledge is, it's fairly clear that far more useless was the ecological knowledge Europeans brought with them to this continent, now the most desecrated on earth.

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    21. Gail Carnes

      Consultant

      In reply to Peter Ormonde

      "From where I sit it's exactly like throwing away 50,000 years worth of field notes... encoded and encrypted in stories, myths, songs and social behaviours - but observations made by serious professionals ... watching stuff for a living. Like burning down the library at Alexandria again."

      Very well said, Peter. Yes, serious professionals, indeed, and whose lives depended on their knowledge.

      The perspective of a farmer is an interesting one. How do you reconcile the destruction of habitat with the need to feed the current inhabitants? Obviously, you'd want to do it as sustainably as possible. How do you keep "sustainable farming" from becoming an oxymoron?

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    22. Gail Carnes

      Consultant

      In reply to Frank Baarda

      That's a funny story! I have a similar one. I was a with a group of Cambodian orphans who were visiting Australia, and for one afternoon's outing we took the to the zoo.

      The kids were amazed by the specimens on display: kangaroos, giraffes, zebras. "What kind of meat is that?"they asked, pointing here and there excitedly...

      Yes, on one level we're all just meat, either running away or placidly existing in our enclosures.

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    23. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Frank Baarda

      No such thing as a "useless" animal there then! How delightful! I will file it away under youthful utilitarianism.

      I remember watching a couple of kids up a tree helping themselves to a hive of honey - absolutely smothered in the stuff ... hair, eyes, noses, ants ... and grinning like they'd just walked into a chocolate shop to find it unattended. What a life.

      One of the things that has always confounded me is related to food preparation. Now I'm a bit of a botany buff and some of the…

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    24. David Thompson

      Marketing Research

      In reply to Gail Carnes

      What makes knowledge 'traditional'? It smells a lot like dismissing that knowledge as second-rate or even not knowledge at all, but too coy to own up to what they really mean.

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    25. David Thompson

      Marketing Research

      In reply to Frank Baarda

      Oh Frank, I didn't think you were having a go. I was just being flippant about me and my fabulous omniscient "dominant culture". ;)

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    26. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Gail Carnes

      I've spent a lot of my time looking at "sustainability" as a concept and I'm pretty sure it doesn't need the addition of farming to become an oxymoron.

      Closest thing we've seen to anything "sustainable" long-term - is the locals I'd reckon. Pretty basic by our standards but given the name Manly in Sydney, seemed they had a healthy if spartan life. Not for me though. Or any of us I suspect.

      Once you start burning stuff for a living - beyond patchburning and firestick farming - you run into…

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    27. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Gail Carnes

      Yes, indeed! And we are all part of the food chain - a fact which the crocodiles occasionally remind us, although in our cotton wool existence it can be easy to forget...

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    28. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Peter Ormonde

      Examples abound: e.g, if I may quote from a book I've written:

      "Clay’s efficacy as a means of adsorbing toxins meant that it was widely used as a cure for diarrhoea and other gastro-intestinal complaints. Clay also made it possible for Aboriginal people to eat a number of toxic Australian plants which would have otherwise been inedible, causing severe illness or even death, thus expanding the repertoire of available food on this continent and its surrounding islands.
      The role of clay in Indigenous…

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    29. Gail Carnes

      Consultant

      In reply to David Thompson

      I agree with you, David. I use it as a term of art, but am always tempted to put it in quotes. The other phrase that bothers me is "Western science" or "contemporary science." I think "traditional knowledge" is just as contemporary as "contemporary science". Thanks for bringing this up!

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    30. Gail Carnes

      Consultant

      In reply to Peter Ormonde

      Thank you, Peter, for such a thoughtful reply. Your idea about patchworks makes perfect sense. I'm a big fan of permaculture and hydroponics, but don't know where they meet... Would be very interested in learning more!

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    31. Gail Carnes

      Consultant

      In reply to David Thompson

      "For folks who really seem to be culturally if not genetically challenged when it comes to cooking - only the Italians run a very lacklustre second compared to the locals when it comes to their obsession with food ... running meats in particular."

      What a lovely experience.... thanks for sharing it!

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  35. Eva Cox

    Professorial Fellow Jumbunna IHL at University of Technology, Sydney

    There is so much valuable debate and information on this site that I'm stuck in trying to work out how it could be usefully disseminated and considered as part of re-framing the closing the gap issues this relates to: from an Indigenous deficit model, to one of working to close the mutual lack of understanding of different ways of seeing and explaining. This shift would make it easier for all of us to devise mutually informative educational programs and to learn other ways of seeing and describing based on mutual respect for the differences rather than assuming superiority and ignorance.

    This shows up in areas like early literacies where Aboriginal parents are wary of programs that ignore different types of literacies their children may have, and assume their children are empty vessels to be filled.

    It would be good to have a summary of the serious debates and ideas raised!!

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    1. David Thompson

      Marketing Research

      In reply to Eva Cox

      Yes, I must agree. Despite my exasperation at times, the thread is hitting 200 posts, which end up coming at the issue from every corner possible. Yes, the thread would be the perfect material for a damn fine guide to the issues. Well done Christine!

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    2. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Eva Cox

      This is an excellent suggestion, and my reason for not answering immediately is that I've been thinking about possible courses of action leading on from this very broad discussion, with the key point (as you've put it so well) being to work together on creating "mutually informative educational programs and to learn other ways of seeing and describing based on mutual respect for the differences rather than assuming superiority and ignorance."

      You are also quite right about the question of literacy…

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  36. Adele Pring

    Educator

    Thanks Christine for your article on Aussie Rules and Aboriginal Maths
    What a great way to educate football followers about Aboriginal culture.
    I forwarded it to some colleagues in the education department and they're forwarding it.
    I referred to the Harris quote some years ago in some advice for teachers about Aboriginal people and mathematics and in a paper I called ‘Astronomy and Australian Indigenous People’. Some extracts follow.
    Warm regards,
    Adele Pring
    FINDING DIRECTIONS DURING THE…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Adele Pring

      Hello Adele,

      Thank you so much for this detailed and information rich posting, which is important in this discussion in many ways, not least because it's an outcome of your own long-term successful background as an educator in the field, and shows that educators have been aware of the significance of such knowledge for quite some time, and how it's imperative that such knowledge become part of the national curricula in both science and mathematics - there's a real opportunity there to right some…

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  37. Warren Beckwith

    Mathematics Teacher

    Thank you for the article Christine. I'm a Maths teacher from Perth and a passionate AFL fan (I have umpired the game for many years). I have tried to incoroporate Australian Football into my lessons, when appropriate.
    Obviously there are some simple examples, such players' statistics (heights, game stats etc), or the scoring system and the patterns that arise from this. Another significant aspect of the game is that players must make quick decisions. If they have possession of the ball, they must…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Warren Beckwith

      Many thanks for this interesting post, Warren - the perspective of maths teachers currently working in classrooms around Australia is obviously incredibly important in relation to the current discussion, and it's great to hear of teachers' often very creative initiatives to engage kids in the classroom. I imagine that applications this approach would be very successful, both for Indigenous and non-Indigenous kids - especially boys.

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  38. Stephen Ralph

    carer at n/a

    I'm reading a book called "Brainsex" by Moir & Jessel which explores the differences b/w the sexes. Admittedly it was published in 1992 so it would be interesting to know if the data/information is still relevant.

    The book quotes a study by Stanley and Benbow that says in regard to mathematical excellence the beast boys eclipse the best girls by 13:1.

    It also states that boys have superior eye-hand co-ordination necessary for ball sports.

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    1. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Stephen Ralph

      I'd be taking those stats with a toxic load of salt Stephen ... check under the hood and see where the sample comes from...

      Over the last decade I have become an avid TV netball watcher. Tell any of those women their hand-eye co-ordination is wobbly... then duck ... really quickly. Revolutionised the game Australia has.

      I know these women would be "outliers" - exceptions that prove the rule... or, when we are looking at such numbers of educational "achievement" are we really looking at…

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    2. Stephen Ralph

      carer at n/a

      In reply to Peter Ormonde

      Ironically Peter the book also went on to say that b/c of superior spatial cues, men are better map readers.

      Dr Camilla Benbow & Dr Julian Stanley - google them.

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    3. David Thompson

      Marketing Research

      In reply to Stephen Ralph

      Stephen, sex differences in spatial ability are well established, especially at the extremes, which is why you find relatively so few women Mathematicians, let alone Theoretical Physicists.

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  39. Katherine Ingram

    ESL teacher

    Thanks Christine for fascinating insights into AFL skills and intensely different world views. Having grown up in a football-mad household (and therefore joining the Anti-Football League) I have only recently come around to considering what makes Australian Rules unique. I now know another little gem.
    But I have long been thinking about what knowledge we miss out on when language dies. I think your original article pointed to a very precise example. Nicholas Evans’ ‘Dying Languages’ 2010…

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    1. Frank Baarda

      Geologist

      In reply to Katherine Ingram

      This from a transcript (4th.April 2012-Alice Springs)- The Parliamentary Inquiry into Language Learning in Indigenous Communities:
      A Warlpiri man (here not identified for privacy reasons):
      "I grew up in Yuendumu, learning both in Warlpiri and English. I work in the language centre in Yuendumu, and my main work is translating and recording stories for new books. I have brought some of them here for you to maybe check out later. They are in language. When I was growing up, since I was in preschool…

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    2. Katherine Ingram

      ESL teacher

      In reply to Frank Baarda

      I enjoyed that little cross cultural indulgence Frank - similar to my own occasional fantasy about language loss, which of course is very difficult for native English speakers to get their heads around.

      The enforcement mentality vs the facilitative mentality - what a waste of an opportunity. Why do we not listen to the people like the Warlpiri man you have quoted, and do what works? There's so much evidence about best practice and what works in successful education systems. But we seem to have a special talent of ignoring all that and going for the mediocre. Our slipping down the ranks of international education outcomes shows that clearly enough.

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    3. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Katherine Ingram

      Katherine - your eloquent 'what if' scenario really spells out the reality of the situation today with many Aboriginal children in places where Aboriginal languages are still spoken as the community's first language who, like other Australian kids, enter school (mostly) unable to read and write but are beset from day one with an even greater obstacle to real learning - of not being able to use the strongest string to a young child's bow - their own language skills. And worse still, having that linguistic skill regarded as an encumbrance to their learning...

      It is difficult enough for many 'mainstream' children starting school to master reading and writing, and as we know, many don't, but imagine the triple jeopardy situation of also having to start learning a new language on your first day of school...that is a recipe for failure except for the few brilliant kids who will cope...

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    4. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Katherine Ingram

      Do not despair Ms I - place not your faith in glib statistics.

      What are they measuring these global educational comparators? What skills and capacities are identified and weighted? More important - which "educational outcomes" are ignored? What's more educationally significant - 12 times tables or learning how to protect you little sister? Does enthusiasm count? Curiosity? How about character? How about a 12 year old with 7 languages under his belt? An insatiable appetite for reading? Chess…

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    5. David Thompson

      Marketing Research

      In reply to Peter Ormonde

      Peter, they are measuring the skills, knowledge, and aptitudes needed to thrive in a modern, post/industrial, polyglot world of 5 billion plus. They are not measuring the skills, knowledge, and aptitudes that might have been important to thrive in a pre-agriculture world of bands of a few hundred people or so.

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    6. David Thompson

      Marketing Research

      In reply to Peter Ormonde

      "learning how to protect you little sister" is not the job of school teachers. It is the job of the family and community. All this passion for turning children over the functionaries of the State is offensive. And scary.

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    7. Katherine Ingram

      ESL teacher

      In reply to Peter Ormonde

      Peter, I'm interested to know what you think about a full-time truancy officer versus a full-time linguist at Yuendumu?

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    8. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Katherine Ingram

      Can this truancy officer speak a few useful languages then?

      Depends what a truancy officer does really. And maybe what a linguist does too. Either or both could be useful - or neither.

      One looks to some sort of future - one is some sort of insurance for the past. Don't have problems with either.

      If they contribute to building and strengthening the local community - leave something useful and lasting - then they've helped. And that can come from a copper, a school teacher, a road worker, a half-decent boss or even a half decent cook. Anything that gets people talking and working together ...

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    9. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to David Thompson

      Thrive??? Wot - like Rupert Murdoch? Not quite that thriving? So what does thriving look like ... being part of a functioning community for a start. Having opportunities available and knowing how to take them on.

      But given the sort of market around some of the great Aboriginal painters, I'd be most wary of lecturing folks about what is needed to thrive... what the hell would we know?

      Not everyone wants to be an accountant. For some the best "career opportunities" they'll be able to get…

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    10. David Thompson

      Marketing Research

      In reply to Peter Ormonde

      Peter, don't tell me. Tell the OECD Education types.

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    11. Frank Baarda

      Geologist

      In reply to Peter Ormonde

      The mooted truancy officer is part of a multi-million ($95M from memory) "improved attendance" initiative announced by Ministers Macklin and Garrett as part of the euphemistically named Stronger Futures- The Intervention Mark II.
      Apart from the gratuitous punitive aspects of this initiative (a threat to withhold Family Assistance Benefits if children don't attend school), the flaw as I see it is that improving attendance is futile if the children don't learn anything. This is particularly so for…

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    12. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Frank Baarda

      A great - and important - contribution to the debate Frank.

      In further response to Katherine's succinctly phrased question "about [whether or not there should be] a full-time truancy officer [or] a full-time linguist at Yuendumu", apart from your entirely valid point about the likely alienation of little children from day one of their schooling when that schooling is conducted in what is essentially a foreign language to them (and let's remember, these are little kids in their own 'country…

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    13. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      Christine, given there is an actual real Warlpiri woman in the current NT Parliament (in government too, not opposition) - born/bred/speaks Warlpiri - shouldn't these issues be able to be resolved, rather than getting bogged down in the largely whitefella world of the Aboriginal Industry bureaucracy?

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    14. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to David Thompson

      Ohhh David - of course I know that. Bess Price Nungarrayi is someone I first met over 30 years ago and I know her to be a good woman doing a difficult job. I also know most of her family members, some very well indeed - and in some cases (the older family members) I've known them for 30+ years, too.

      However, I'm afraid that your assumption in this post is fatally flawed: Bess Price Nungarrayi, part of the Territory's CLP government, does not speak for ALL Warlpiri people any more than you speak…

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    15. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Christine Nicholls

      Aw heck Christine - we've even got one in parliament now ... what more could they possibly want??? You want a go at Prime Minister next turn?

      I recall that we've recently had an atheist running the show for us and I've been sitting here for almost 1,000 days waiting eagerly for an outpouring of godless legislative reforms and edicts with very little joy. When will we heathens get the calibre of political representation we deserve???

      Where are all these simple answers we know are plain as the nose on your face? Why do we have to worry about this sort of thing now that there's a real one in parliament?

      Truly that is a very strange thing to say David.

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    16. Katherine Ingram

      ESL teacher

      In reply to Frank Baarda

      Great analogy. Schools worth attending and worthwhile experiences at them and maybe no-one needs old-fashioned truancy officers.

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    17. Katherine Ingram

      ESL teacher

      In reply to Frank Baarda

      Frank - I think it was you who told about children learning to write the letter N as a termite mound with a digging stick?? I've been thinking about the skill involved in producing the mirror image when reoriented in the opposite direction. I guess in most cases those children would've been corrected, made to feel they'd made a mistake and thus what Chris Sarra refers to as the 'toxicity of low expectations' becomes more firmly entrenched. The dominant culture has a very limited if powerful world view and it's a great shame we do not address this in our education systems.

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    18. Frank Baarda

      Geologist

      In reply to Katherine Ingram

      The anecdote of the letter N refers to a period in time when "toxicity of low expectations' didn't apply.
      It was at the height of the much maligned self-determination policy. Most Warlpiri school pupils were subjected to 'team teaching'. A Warlpiri teacher and a non-Warlpiri one working as a team each bringing different skills and knowledge that resulted in effective teaching in a cross-cultural setting.
      The Warlpiri teacher contributed an ability to communicate with the students and his or her…

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  40. Katherine Ingram

    ESL teacher

    This is off on a tangent, but I wonder if anyone can tell me what the current status of bilingual education in NT is? I've made a couple of inquiries through official channels but been stonewalled.

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    1. David Thompson

      Marketing Research

      In reply to Katherine Ingram

      Katherine, I'm sure if you put a call into the MP for Sturt - Bess Price - her office would gladly assist. I'm sure an email would be just as effective.

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    2. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Katherine Ingram

      I don't think that this is off-topic at all - what we're discovering via this extensive discussion is that there is a whole bunch of interrelated ideas/issues that are brought into play in this field.

      My feeling is that you should approach your OWN local federal MP, especially as an election looms, and ask them to find out the answer to your significant question. This will be a particularly efficacious approach if you are living in a cliff-hanger electorate - of course.

      There is also an organisation called 'Friends of Bilingual Education', and perhaps one of their members will know the answer to this question & post it up on to this site.

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    3. Frank Baarda

      Geologist

      In reply to Katherine Ingram

      I'll digress first and then answer your question as best I can. To the extent that I tell you things you already know, it isn't my intention to "teach you how to suck eggs"
      The "4 hours English only" policy (4EOP) a few years ago effectively closed down the few remaining bilingual programs in the NT that had survived a decade of attrition. There are rumoured to be one or two schools that didn't throw in the towel, but I think if so they are better off remaining under the radar. When 4EOP was first…

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    4. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Frank Baarda

      Thanks for that detailed explication Frank.

      I still reckon it would be worthwhile for people like Katherine, Sally (who's just recently posted) and others to put the same question to their local members, asking them to find out from the NT Govt./N.T. Education Department what the "official" government line is on bilingual education at present, especially in the lead-up to the election, during which time people may expect to receive quicker-than-usual answers.

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    5. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      Christine, it is very telling that you are so keen to fob this issue away from an actual Warlpiri woman in power in the NT (the very people who run the education system remember). It just smells yet again of the gubba-run Aboriginal Industry wanting to control all flows of information about these issues.

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  41. Sally Baker

    Artist

    “Too right” the Australian Curriculum can foreground independent existence and coexistence of Indigenous Knowledge Systems, - with new systems of teaching and planning for learning. Australians can expect teachers to develop a national community of practice across the country, skillfully embedding Indigenous Australian knowledge and practices into the Australian national curriculum. The teams’ consciousness’s are drafted through The Australian National Professional Standards for Teachers, comprised…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Sally Baker

      Sally, many thanks for your comments here.

      Do you, or anyone else reading this, know how do classroom teachers living a long way away from metropolitan areas or so-called 'ordinary people' (eg parents, Indigenous and/or non-Indigenous) who might want to influence the curriculum, are able to become involved in this process? Can they contact project teams directly?

      I know that AITSL has a website, with Illustrations of Practice, and Pilots and so forth that people may access if they wish, but beyond that, how can others provide input in the way you suggest, if they wish to assist the process of embedding Indigenous Australian knowledge and practices into the Australian national curriculum?

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    2. Sally Baker

      Artist

      In reply to Christine Nicholls

      The National Digital Learning Resource Network

      Teachers, jurisdictions, associations and publishers can select and prepare digital resources for sharing at the national level through the National Digital Learning Resource Network (NDLRN).

      The criteria for quality digital resources are outlined in the Education value standard for digital resources. Education Services Australia provides an infrastructure through NDLRN to facilitate distribution of digital resources to all educational jurisdictions and sectors in Australia.

      http://www.ndlrn.edu.au/developing_digital_resources/sharing_digital_resources/sharing_digital_resources.html

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    3. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Sally Baker

      Once again, thanks Sally - I've just checked out their website and I guess others have, too. Do these digital resources directly inform the national curricula, or to phrase this differently, what's the conduit between the digital network and AITSL/the national curriculum?

      You seem to have some personal experience of this group and its activities/scope, so if you could please provide a little more info. on it, that would be great.

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    4. Geoffrey Harold Sherrington

      Boss

      In reply to Christine Nicholls

      Christine,
      There are many concepts that have both an old traditional view and a modern view in conflict. There is a delicacy in the transition.
      Here is a rock painting in situ that is likely to be there for many more years.
      http://www.geoffstuff.com/WomensBusiness.jpg
      The theme as explained decades ago was that the rainbow serpent on some nights would bite a mature woman in the genital region, as shown. If no blood appeared, then the woman had cause to think she might become a mother. Nowadays…

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  42. John Clark

    Manager

    The degree of interest in this post indicates the level of interest and concern of the topic, but the it's time for a reality check, since the comments are broadening beyond reasonable bounds, attributing all sorts of benefits to the inclusion to mainstreaming indigenous languages, cultures and learning processes. It is further degenerating in to "we should, they should" solutions to an intractable problem. As stimulating as the discussion is, it ignores the imperatives of our time. Australia…

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    1. Frank Baarda

      Geologist

      In reply to John Clark

      John you're absolutely right in that the comments are broadening "beyond reasonable bounds" and that we are dealing with an intractable problem. I don't expect a forum such as this would offer silver bullets, but the broadening of the discussion in itself may not be a bad thing in that it may throw some light on the nature of what many define as a 'problem'. It reminds me of what I heard Rosalie Kunoth-Monks start a speech with: "In Australia we don't have an Aboriginal problem. We have a white-fellow…

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    2. David Thompson

      Marketing Research

      In reply to Frank Baarda

      Frank, if one there's one thing this thread has clarified is that the Warlpiri issue is a completely separate issue to any "Aboriginal/Indigenous" issues, and that we should we not conflate them.

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    3. Frank Baarda

      Geologist

      In reply to David Thompson

      Not sure what you mean David.
      It's a bit like saying 'The Dutch issue is a completely separate issue to any "European/Caucasian" issues.
      The reason I use 'Warlpiri' is because these are my friends and neighbours and because I am aware of the great diversity within Indigenous Australia. I suspect this is also the case with Christine.

      Similarly I might talk about Dutch people (I'm Dutch born) and not use European in recognition of the great diversity among peoples in that part of the world.

      Really I must go, the European imperative to turn up somewhere at a certain time on time beckons.

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    4. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to John Clark

      Evolution is it? A sort of linguistic misunderstanding of survival of the fittest?

      You are of course correct that these kids need to learn English - amongst other things. We should probably be learning Chinese.

      See the thing is John this bilingual stuff actually works - unlike any sort of tough love, exhortation and incentives. The schools using a bilingual program were pulling 90% attendance rates... even during the honey season.

      There's some nasty history to all this stuff - and being…

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    5. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to John Clark

      John, I know this to be a thoughtful post on your part, but I must differ on certain points you've made here. Frank has already commented on your statements about Australian languages (the linguistically accurate name for Australia's Aboriginal languages), but I'd like to add to that critique, especially because this article has appeared in the science and technology stream of The Conversation.

      It's simply not valid to attempt to apply scientific principles to the dramatic Indigenous language…

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    6. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Christine Nicholls

      Excellent point re the Welsh Christine ... the revisited concern to recognise and restore the language (and by implication the culture) follows hundreds of years of active legal suppression.

      The bloody Tudors started it back in 1535 ... Henry VIII - himself a welshman... decided to do to Wales what he was doing to any female in arms' reach in Court ...

      Section One:
      ""...because that the People of the same Dominion (Wales) have and do daily use a speche nothing like, ne consonant to the…

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    7. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Peter Ormonde

      Great post, Peter. A terrific, very telling background narrative highlighting the injustices meted out to the speakers of Welsh over such a long time..

      I'm reminded of another historically-verifiable anecdote that I believe is equally telling in this context:

      In 1492, Antonio de Nebrija completed a Castilian grammar book, the first ever completed of a European language. When he presented it to Queen Isabella she asked, "What is it for?", and the Bishop of Avila answered for de Nebrija: "Your…

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    8. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      Christine, actually it is precisely about evolution. Evolution is about adaptations to an ever-changing environment. As all the recent research has shown, scientific literacy amongst this country's school kids has declined - both absolutely and relatively - along with verbal and quantitative literacy over the past 15 years. And here you are wanting to shove dreamtime lore into the space where evolution, mechanics, and chemistry should be taught!

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    9. Frank Baarda

      Geologist

      In reply to Christine Nicholls

      For those interested in this sort of thing, I recommend you look up the history of Guarani. Guarani survived ironically in part due to the Jesuits that used it to communicate (written and spoken) between 'outposts'. A few decades ago Dictator Stroessner (spelling?) declared Guarani and Spanish to be Paraguay's national languages. Today Paraguayans are proud of their native language and I read somewhere that Paraguay is the only country in the Americas where the Indigenous language is spoken by a majority of the non-Indigenous citizens.

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    10. David Thompson

      Marketing Research

      In reply to Frank Baarda

      Frank, 3,000 people speak Warlpiri. 22 million speak English. English is the indigenous language of Australia.

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    11. Frank Baarda

      Geologist

      In reply to David Thompson

      I have to repeat it:
      "... All societies are constantly evolving. Indeed a culture survives when it has enough confidence in its past and enough say in its future to maintain its spirit and essence through all the changes it will inevitably undergo. ” ― Wade Davis, The Wayfinders
      It's the "enough say in its future" bit that I find the most relevant to the current situation remote Aborigines find themselves in.
      To dismiss Warlpiri 'Weltanschauung' as mere 'dreamtime lore', that should have no space in our education system, is not doing it justice. It is just another subtle way by which our dominant society denies Aboriginal society a say in its future.
      As this forum has clearly shown incorporating Aboriginal knowledge etc. into the national curriculum is no simple matter. If we don't succeed in doing so we will all be the poorer for it.

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    12. Frank Baarda

      Geologist

      In reply to David Thompson

      As Manuél from Barcelona would say: ¿Qué?
      'Dominant' I'll accept, but Indigenous?
      In Richard Trudgen's book 'Why Warriors Lie Down and Die', there is a beautifully named chapter:
      "What Language do you Dream in?"
      At the time I read it I pondered how this applied to me. My more than half a century in Australia resulted that I dream in English. Did it bother me that I no longer dreamt in Dutch (my mother tongue) or Spanish (my childhood language). No it didn't one bit. Millions of people dream in those languages. There are only 3,000 people that dream in Warlpiri. That is a worry to me.

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    13. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Frank Baarda

      Strongly agree with this post, Frank, although I can't agree that such language use is as subtle in its undermining effect as you’ve suggested here, in terms of describing Indigenous religion.
      The ideological intent of such deliberately derisory use of language - “dreamtime lore” - gives the game away I'm afraid.

      Why not use the terminology of the local language, in this instance, ‘Jukurrpa’, the semantic scope of which is far more comprehensive than such impoverished and inadequate English translation as connoted by 'dreamtime'.

      And as for the word 'lore' - Law is the mot juste, surely...bringing to mind the celebrated Pope Gregory quote “Non Angli, sed angeli…” – and the social context of that statement wasn’t so very different from this one, really…

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    14. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      Christine, given your low opinion of actual, real Mathematics and Science, naturally your lessons on Jukurrpa, shall be followed by lessons on the sorcery and magic still rife in remote Aboriginal communities today?

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    15. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to David Thompson

      Argumentum ad absurdum...reductio ad absurdum.

      You are not engaging with anything that I have actually written David, in either the article or in my subsequent posts. In future, if you wish to make comments, you will need to back them up with actual quotations taken directly from my article, or DIRECT QUOTATIONS (and not merely selective two or three word 'quotations' taken out of context) either from my responses or from the posts and responses of others, David.

      The Conversation is a serious discussion platform, which requires thoughtful and reasonable responses. It's not Facebook, or some kind of social media platform that gives rise thoughtless slinging matches between teenagers, so please don't treat it that way.

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    16. Frank Baarda

      Geologist

      In reply to David Thompson

      David, what do you base: "on the sorcery and magic still rife in remote Aboriginal communities today?" on?
      Next thing you'll tell us that cannibalism is commonly practiced in remote Aboriginal communities.

      As for your allegation that Christine has a "low opinion of actual, real Mathematics and Science" again I fail to detect any evidence of this in this wide ranging and fascinating discussion. And what do you mean by "REAL Mathematics"?

      Remote communities suffer enough from stereotyping and stigmatization for your prejudiced generalizations to remain unanswered.

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    17. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to David Thompson

      David,

      There is nothing unactual or unreal about the science and mathematics embodied in my ancient old boomerang over there on the wall. It is a real, three dimensional, concrete fact.

      It is worth wondering surely how a "stone age culture" managed to "stumble across" the principles behind Bernoulli's equations governing lift and thrust don't you think? Makes "stumbling across" the wheel look rather crude and unsubtle don't you think?

      Took us a long time, a lot of blackboards and squiggles…

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    18. Geoffrey Harold Sherrington

      Boss

      In reply to Peter Ormonde

      Peter,

      "a smart articulate AFL star or two..."
      Like the coach who said on radio "There's always doubt. No doubt about that."
      Or his mate who mentioned "A good-sized quarter acre block". I have a collection of these.

      You are a little way out of the bad corner, Peter, because you've displayed some signs of scholarship and original sources above. But please, don't mention AFL. It is one of the least sustainable mass pursuits of Melbourne. Indeed, I used it to illustrate a couple of lead articles on Jo Nova, whose reading is encouraged as part of your continuing education, not because of the choice of authors or topics, but because of the diligence of selection of relevant articles and papers. There is a lot of raw data there. Sure, some of the respondents get it wrong, as do I, as examinees do, but that is a feature of many blogs. Diversity makes one think harder.

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    19. Frank Baarda

      Geologist

      In reply to Peter Ormonde

      Peter, great stuff you've been digging up and harvesting.
      By contrast to those enlightened first fleeters, in Malthus’ An Essay on the Principle of Population' you find this:
      “A native with his child, surprised on the banks of the Hawksbury river by some of our colonists, launched his canoe in a hurry, and left behind him a specimen of his food, and of the delicacy of his stomach. From a piece of water-soaked wood, full of holes, he had been extracting and eating a large worm. The smell both…

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  43. Geoffrey Harold Sherrington

    Boss

    If you came to melbouren with no prior knowledge of its activities, you think the people were partly mental. Here we are, crying our eyes out at the need to shut down fossil fuel plants then bingo! the lights come on at the MGC and a few other play pits. Hundreds of thousands of people travel to these sites each weekend in the season. There is a huge production per capita of the deadly CO2, just for entertainment. Foopball must be about the first activity to be closed down by the CAGW people, if…

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    1. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Geoffrey Harold Sherrington

      Ah yes the good old days eh Geoffrey Harold?

      They'd be the good old days of trachoma and mass child deaths and missions ... and the days of working for rations on cattle stations... of having your wages confiscated by the State Government, of having your kids pinched by the State... of not having a vote, of having to ask permission to move or get married, of not getting to have a swim in the local pool or sit in a seat at the local cinema, or get a drink in a pub, ... when they were classified as fauna... yep... nostalgia just ain't what it used to be.

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    2. Frank Baarda

      Geologist

      In reply to Geoffrey Harold Sherrington

      "There is a dominant factor that will improve the lot of unhappy aborigines and that is the gaining of self esteem over time." That is one important nail you've hit on the head Geoffrey. Esteem or respect from others is also necessary. To categorize everything that has happened in remote Aboriginal Australia the last half a century as failed social engineering experiments is however unfair and doesn't give credit where it is due. There have been many positive things happened out here, this is especially…

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    3. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Geoffrey Harold Sherrington

      Thank you for your post, Geoffrey. You're absolutely right about footie (ie AFL, especially) fever taking hold of so many Australians of all backgrounds during the winter months, and this is why I do believe that using it as an exemplar in maths and other classes is such a good idea, potentially.

      And not just potentially - teachers like Warren are already using the idea productively in classrooms, as you'll see from previous posts.

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    4. Geoffrey Harold Sherrington

      Boss

      In reply to Christine Nicholls

      Christine,
      AFL is better than South Park, is it?
      Have you considered if you are demoralising many people by promotion of elementary concepts?

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  44. Beth Graham

    logged in via email @netspace.net.au

    Great Article Christine. The focus on AFL was brilliant. We had written all that spatial stuff into the Transition Curriculum but those books have been long gone.

    My favourite story to illustrate what the kids knew about spatial orientation came from an incident that occurred at Yirrkala in the 70's. A grandmother was in the bush with 2 small chn. She had some kind of a mental breakdowm, left the chn and returned to Yirrkala on her own. There was a great fuss and people set out to…

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    1. David Thompson

      Marketing Research

      In reply to Beth Graham

      " I looked at my own chn and realised that in similar circumstances they would have died."
      OTOH, your own children will grow up able to comprehend and learn geometry, algebra, and calculus, train as engineers, bionformatics, economists, or doctors. They will be able to pick up, move to any society/culture on the planet, ply their trade, and thrive. What future do you think your 5 old tracker has?

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    2. Frank Baarda

      Geologist

      In reply to David Thompson

      If the 5 year old tracker hadn't known how to track, he would have had no future at all.

      The world would be a sad place if a person's quality of "future" was defined solely by an ability to comprehend geometry, algebra and calculus and train as engineers, bionformatics (what are they?), economists or doctors.

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    3. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Beth Graham

      Thank you so much for these comments Beth, and especially for the story about the little kid successfully navigating his way back towards home, not to mention his common sense approach to his little brother. This anecdote encapsulates so much information about the superiority of even very young children in terms of their mathematically-based spatial understandings, counterpointing the large number of 'lost white' children narratives in Australian literature and film (for example, Walkabout…

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    4. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Beth Graham

      P.S. Beth (and important).

      Could you please say a little more about the ***specific ways*** in which you incorporated spatial relationships into the curriculum at Yirrkala in the 1960s and 1970s? That would be great, especially as I'm collating all of these ideas and will put them into a larger paper, so it's important to collect them all right now.

      A paragraph or two in reply to this request would be terrific, so please post it on this site.

      Thank you, Beth.

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    5. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      "***specific ways*** in which you incorporated spatial relationships into the curriculum"
      Pssssttttt...in the dominant culture, this is known as "geometry", "geography", "calculus" and so on. It has been the foundation of school curricular for around 2,000 years now.

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    6. David Thompson

      Marketing Research

      In reply to Frank Baarda

      If I had as much confidence of folks here is the reality of these spatial abilities and superiorities, the first place I would be looking at is genes. Populations who evolve in environments highly isolated and/or markedly different than other populations will see different results of natural selection; especially over the tens of thousands of years we are talking here. Has any DNA sampling been gained from the Warlpiri so such analyses could be undertaken?

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    7. Christina Davidson

      CEO at ANKAAA - The Association of Northern Kimberley and Arnhem Aboriginal Artists

      In reply to Beth Graham

      Thanks for sharing this great story

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  45. Colin Farrelly

    Consultant

    Loved your article Christine - and wow what a discussion that follows!

    Many years ago I picked up a book at a second hand bookshop called “The Psychology of Aboriginal Australians” (Kearney, de Lacey and Davidson, 1973) and I was impressed by the research that demonstrated how indigenous Australians performed significantly better than other groups at tests involving spatial ability, despite doing badly at most of the classical intelligence tests.

    So it was a delight to read your article about…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Colin Farrelly

      Many thanks Colin for this terrific and informative post, and your point about “situational awareness” is well taken - it really adds something to the discussion. In fact, it's no doubt possible to construct a Venn diagram of some sort around “situational awareness” and "spatial awareness" although they're not 100% synonymous of course.

      Although you're hesitant about entering the educational curriculum debate, your post had left me with an appetite to hear more of your ideas, so please go for it!

      At a later date I'll be collating all of these comments (well, the sensible and constructive ones like yours) and I'd like to add your curriculum ideas into the mix. Thanks again, Christine

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    2. Colin Farrelly

      Consultant

      In reply to Christine Nicholls

      Christine – happy to expand on my last point, but I’ll try to restrict myself to areas I know something about.

      I spent the early part of my career (in the 1980s) developing software for minerals exploration and consulting in mathematical geology. This was mainly to do with the collection, management, analysis and interpretation of spatially located geoscientific data.

      The existing commercial software could do all sorts of number crunching, but handling the spatial aspects required purpose…

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    3. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Colin Farrelly

      Thank you for this response Colin, which I find interesting and thought-provoking, and which I'll be factoring in when I come to summarise this discussion and write it up. Your point about changes in mathematical requirements over time is well taken, and the need for better skills in identifying patterns and relationships in spatial data (including changes over time). One of the points made in my article was about the number of fields today in which such knowledge might play a significant role. And…

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  46. Frank Baarda

    Geologist

    One more anecdote regarding how Warlpiri spacial thinking can manifest itself.
    When we carried out a soil geochemical survey we took an old man with us to avoid areas of cultural sensitivity. A little bit akin to applying for a planning authority permit.
    We were taking soil samples along south-north lines every 250metres. The lines were one kilometre apart. We covered a hilly area of sub-cropping metamorphic rocks. To the south of the survey area there was a diagonal range which was a no-go area…

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    1. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Frank Baarda

      One really need look no further than the current explosion of art Frank - particularly the Central Desert dotty stuff from out your way - and it's more sophisticated innovators such as the wonderful mind-altering Emily Kame Kngwarreye. Like the Central Mapping Authority has been invaded by Jackson Pollock.

      I had the great - if difficult - delight of having an old lady from up around Tea Tree explaining her yam painting I'd just bought. Bit like having a conversation with a wheezing cement mixer…

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    2. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Frank Baarda

      Great anecdote, Frank. If you have any more exemplars relating to this topic, please keep them coming in because they'll all go into the eventual written article.

      My feeling is that this aptitude should not be written off as genetic endowment, but rather be recognised as having the status of 'mathematics'. To call what 'we' do 'maths', but what 'they' do as an unearned gift delivered at birth, seems unfairly ethnocentric and also, a tad hypocritical.

      There's a converse side to this as well…

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    3. Geoffrey Harold Sherrington

      Boss

      In reply to Frank Baarda

      Frank,
      One time in Arnhem Land, the official map endorsed by Canberra had a "no-go sacred" site. When I asked Big Bill about this, he laughed and said it was just a place where it was easy to hunt for flying foxes. Give him a pencil and he'd change it, there were many such places.
      This is a non-trivial example. It goes to the point of how not only the stories, but also cultural matters like painting and trendy language expressions have been altered by whitey versions of correctness. There is not…

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    4. Frank Baarda

      Geologist

      In reply to Geoffrey Harold Sherrington

      Geoffrey, "the us and them" paradigm is indeed very hard to avoid. It is also nigh impossible to be entirely devoid of ethnocentricity. It is when ethnocentricity slides into ignorance driven xenophobia that a lot of damage is done.
      I agree that equal pay for stockmen was a mistake, if not in principle, certainly in its execution.
      There is a lot of truth in "the road to hell is paved with good intentions".
      With the exception of those odd-ball denialists, it is also now widely accepted that the…

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  47. Stef Rozitis

    logged in via Facebook

    This is very interesting, but as you point out a challenge to white teachers who may know very little about Indigenous knowledge. Do you know if anyone is running professional development in this area? Because to make something main-stream a lot of people need to know it very well!

    If someone who knew about this picked it up and developed it now, it could become the way things are done, otherwise it will just all turn out to be lip-service

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Stef Rozitis

      Stef, you are 100% right about this need for professional development/inservice in the area, and it's what needs to happen if these aspects of the national curriculum are genuinely going to be implemented. Not knowing which state you live in, it's hard to know how to advise you on this, but if you're in the public school system I would start by getting in touch with the Education Department, or if in the Independent system, but getting in touch with the specific local authority, be that Catholic Ed. or other relevant education body.That way such thinking can be developed and incorporated into the curricula of the future, and as you say, become the way things are done.

      But it WILL also, as you say, wither on the vine if it's simply left as it is.

      Please post again if you have some success with carrying this forward in your own region, and thank you for your post.

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    2. David Thompson

      Marketing Research

      In reply to Stef Rozitis

      Interesting that you assume all Australian teachers are white. I am more worried about white teachers who know little of mathematics, science, and English literacy.

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    3. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to David Thompson

      David: with the greatest respect, there you go again!

      To write that including such perspectives may present a challenge to white teachers is NOT, by any means, tantamount to the assumption that "all all Australian teachers are white".

      It's important in this kind of discussion not to attribute comments and ideas to people unless they have advanced those specific ideas/comments.

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    4. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Christine Nicholls

      Do not be dissuaded or distracted by David's heckling Ms N. No real interest in the issues or in a solution. Or even in exploring same.

      I have this curious notion Ms N ... about teaching - or more precisely, about learning. And that really everything we learn we learn for ourselves, we permit ourselves to keep. That the only thing we really learn from our teachers - or more precisely initially learn from our teachers - is enthusiasm... curiosity and interest. But once you've got that sparked…

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    5. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      If that is the case, Christine, then my apologies. And I look forward to the evidence of Asian, Arab, African, Hispanic teachers who do not face the same challenges as "white teachers".

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    6. Frank Baarda

      Geologist

      In reply to Peter Ormonde

      Peter, yet another sparkling and inspiring contribution from your good self.
      What you say about enthusiasm is oh so true.
      What you say about mechanical nous and the local wrecking yard is also on the money.
      You may be familiar with the Bush Mechanics videos that were created here.
      Mind you these are more about the Warlpiri sense of humour that about mechanical wizardry. The clutch plate carved out of mulga wood never happened. Mind you the person (from Papunya) that had lost the little screw…

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    7. David Thompson

      Marketing Research

      In reply to Frank Baarda

      Too much welfare and not enough Mathematics, eh, Frank?

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    1. Claire Bockner

      logged in via email @bigpond.com

      In reply to Christine Nicholls

      Yes, there were many points in common with your observations from Lajamanu and the ‘learned cognitive factors routinely brought into play by some Indigenous AFL players’ that you talk of, in the part of this All in the Mind broadcast ‘How Language Shapes Thought’

      http://www.abc.net.au/radionational/programs/allinthemind/how-language-shapes-thought/4329212#transcript

      dealing with spatial concepts in Indigenous communities on Cape York. In this program Lera Boroditsky, assistant professor of…

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    2. David Thompson

      Marketing Research

      In reply to Claire Bockner

      Claire
      My 9 year old uses cardinal space (NSEW) over larger spatial terrain, left/right upclose, as well as 3-D straight/behind/above/below, as well as orient to the spatial perspective in different locations facing different ways. It seems a real shame the Warlpiri are trapped in their world, with access to only cardinal directionality. This is one reason we contribute to funds to send such kids to urban Christian boarding schools.

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    3. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Claire Bockner

      Claire: thank you very much for this very clear elucidation of the major points made/ideas expressed in this broadcast. A good deal of the outline you've so thoughtfully provided does seem to accord very closely with my understandings of the subject. You've also whet my appetite for reading the radio transcript very closely - and I'm sure that the same applies to others reading your post - well, I should say those people whose interest in engaging deeply with this topic is serious...

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    4. Claire Bockner

      logged in via email @bigpond.com

      In reply to David Thompson

      David,

      Great that your child knows the cardinal points and could therefore orientate herself in the desert.

      I don't see what Christian boarding schools have to do with the subject under discussion.

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    5. David Thompson

      Marketing Research

      In reply to Claire Bockner

      To teach the Walpiri about other dimensions of space and spatial orientation, apart fromm just cardinal directionality.

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    6. John Clark

      Manager

      In reply to Claire Bockner

      Claire,
      The reference to boarding schools is that indigenous children are given the opportunity to participate in the real world. This initiative looks forward rather than back, by inclusion. Clinging to the past will hinder rather than help.

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    7. Frank Baarda

      Geologist

      In reply to John Clark

      I have an indigenous grand daughter that is going to boarding school in Victoria. We are all grateful for the opportunity she is given.
      I can assure you however that when she was living out here on a remote community she and other Warlpiri children were not clinging to the past and their world was no less real than the one she is in now.

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    8. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to John Clark

      John,

      Again - with the greatest respect, because I acknowledge the sincerity of your position - the terminology 'real world' is a misnomer here.

      The 'real world' is comprised of many human cultures, languages, ways of thinking, ways of seeing and ways of being-in-the world. Perhaps those people who do not or can acknowledge this reality are those who are living in the past, harkening back to a time (not so long ago historically) when most people lived in small villages (etc) fairly isolated…

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    9. Frank Baarda

      Geologist

      In reply to David Thompson

      The reason some of us have emphasised cardinal directionality is that Warlpiri (and other indigenous groups) are so exceptional at it. In a different context one might discuss for instance why Russian people are so good at chess.
      It doesn't follow that the Warlpiri are trapped in a world with access only to cardinal directionality. The Warlpiri world is just as multi dimensional and fascinating as ours, and has more in common with ours than is often realised. It is just that the differences (cultural/linguistics diversity) should be celebrated and encouraged rather than disparaged and seen as a problem.
      The Warlpiri are however trapped in an ethnocentric, assimilationist, oppressive, neo colonial world, that by not seriously thinking about the sort of thing discussed in this forum, by ignoring the strengths inherent in Warlpiri culture, are denying remote Aboriginal Australians an effective education. Another form of 'Stolen Generations'.

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    10. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Christine Nicholls

      It's actually harder for Aboriginal families to be packing their kids off to town Christine. In many cases they are sending the kids off to somewhere they have never seen, do not feel a part of, don't understand and they fear they will in fact lose their kids.

      At least we know what is involved, know the place, know the kids will be safe and will come back better and with plummy accents and good address books. Buying in is easier for us. We run the show more or less.

      I reckon a large part…

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    11. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Peter Ormonde

      You're quite right about its being much harder for Aboriginal families to send their children off to boarding schools, Peter. It can also be extremely hard on the kids themselves.

      I worked at the other major Warlpiri school (Yuendumu School being the other largish Warlpiri school, but there are other smaller Warlpiri schools, too) - Lajamanu School to the north of Yuendumu on the northernmost fringe of the Tanami Desert, for 10+ years from the early 1980s and into the following decade, for most…

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    12. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Christine Nicholls

      Yes it's bad enough to be told you can't do things but the really tragedy is when you start to believe it. All becomes a self-fulfilling prophecy really.

      And some teachers actually teach this I'm afraid... intentionally or not.

      I wonder if the deodorant helped the lads run better or something. How odd a notion.

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    13. Frank Baarda

      Geologist

      In reply to Peter Ormonde

      Peter a propos that real tragedy ("when they start to believe it"):
      Am told that there is ample research (worldwide) that societies that are disempowered end up behaving the way they are expected to by those that are controlling them. The history of the British Raj in India comes to mind.
      An example of this is that Yuendumu people often tell visiting bureaucrats and politicians that what they want most are jobs, whereas what they really want is to be allowed to run their own lives (the jobs come…

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    14. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Peter Ormonde

      Hello Peter!

      You're right about teachers 'teaching this', albeit not directly, usually, but more often by evincing via their attitudes towards kids (and others) their not-so-undisclosed inner thoughts on these matters.

      Regarding the matter of the antipodean (i.e. deodorant use on feet) - yes, v. v. strange indeed, but unfortunately not as benign as you've suggested (or perhaps all sports people would use it for performance enhancement and not have to use EP 47 or AK 22 or whatever it is that people are using to heighten their performances - memo to relevant sports).

      And for the rest of us, of course - naturally, even genetically - we smell just as sweet straight after extreme exertion as immediately before - and the Pope's ****doesn't stink** - if you'll pardon the dysphemism - it's certainly not French! (cross to Monte Python clip).

      Humans can be self-deluding, and illogical...but this gives rise to serious discrimination and truncated lives, as you understand...

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    15. Frank Baarda

      Geologist

      In reply to Christine Nicholls

      Christine and Peter,
      Surely sometime in your life you have put deodorant on your feet and run like the clappers!
      Wonder what deodorant Kathy Freeman used at the Olympics?
      Christine, looks like you were wrong all along. All this discussion regarding Warlpiri footy skills, mathematics, curricula, spacial and directional skills and concepts, language, learning etc. and it turns out that the secret lies in how they apply deodorant!

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    16. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Frank Baarda

      I had a similar tale from a young mate who grew up with his grandmother out around Bourke in NSW. He would take his sandwiches to school - great huge door stop slabs of things they were - he'd swap them for the devon and sauce on bought bread with the crusts cut off. The white kids really liked his roast pork sandwiches. They might have been less impressed if they'd known it was roasted echidna... yummy by all accounts. Scurrying spiny meats. His grandma was apparently very good at them…

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  48. Frank Baarda

    Geologist

    Throughout this thread, 'nurture vs. nature' pops up from time to time.
    Is the superior spacial consciousness of Warlpiri (and other societies) genetically inherited or is it purely a result of the circumstances of early learning. Undoubtedly 'nurture and nature' are both contributing factors, but my own experiences make me believe that early learning, language, world-view etc. are by far the greater contributor in this instance.
    Please don't interpret the following as an expression of narcissism…

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    1. David Thompson

      Marketing Research

      In reply to Frank Baarda

      "Is the superior spacial consciousness of Warlpiri (and other societies) genetically inherited or is it purely a result of the circumstances of early learning."
      Neither, because there is not a jot of evidence to support this claim, even after 300 posts. In fact, the evidence we do have - including dramatically inferior Mathematics results compared to j every racial/ethnic group on earth - suggests an underdeveloped/restricted spatial ability.
      Frank, as a scientist, using your own perception of your experiences is pretty weak tea. Surely, you are not already unlearning the whole scientific real of human experience which distinguishes modern mankind?

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    2. Geoffrey Harold Sherrington

      Boss

      In reply to David Thompson

      Why do you persist with looking for differences? These are not specimens preserved in ethanol in Bell jars on lab shelves. They are
      People.
      Like others writing here, I've seen quick adaption to reading of air photos, but science needs double blind standards, not hearsay.

      Data trumps belief. But first, estimate the benefit:cost of doing the experiments before you start.

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    3. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Geoffrey Harold Sherrington

      I don't think anyone is actively 'looking for' differences, Geoffrey Harold, but cultural differences do actually exist - and these result in certain different emphases in different areas, in terms of what knowledge is socially and culturally valued within a specific culture. One of those different emphases has been discussed in this article.

      And ***of course*** we're all human cultures, i.e. people. Our differences should be a matter of celebration, mutual respect and recognition, and most certainly should not based on any kind of deficit model, or sense of cultural superiority which I think that you may be getting at here.

      But trying to erase those very real differences is not an option either - because that approach can actually lead to cultural/social superiority/ or deficit models. May a thousand flowers bloom!

      PS quite definitely no experiments having taken place/are taking place...

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    4. Geoffrey Harold Sherrington

      Boss

      In reply to Christine Nicholls

      What a mixed answer, Christine. If you do not have experiments, how do you get clean data?
      We used to experiment with mathematics in the outback. If you drank 24 cans of beer in 24 hours you qualified for membership of the carton club.
      Why all the talk about pigskins when blind Freddie can see a bigger topic with grog. Some undesirable secondary matters will persist until the solution to grog is found. My solution was to stop - in 1983.
      May a thousand Fosters bloom.

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    5. David Thompson

      Marketing Research

      In reply to Geoffrey Harold Sherrington

      "What a mixed answer, Christine. If you do not have experiments, how do you get clean data?"
      Sightings of Biame in the constellations, and directions to the nearest bunyip.

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    6. David Thompson

      Marketing Research

      In reply to Geoffrey Harold Sherrington

      Geoffrey, I, personally, do not hunt for 'differences'. My make-up is more to look for 'patterns' and 'associations'. But epistemological ruptures do happen; as do political, and personal experiential ruptures. And even without 'rupture' per se, gradual change/evolution can eventually reach a place where it is revolutionary compared to a previous place. And while I share some of the skepticism around the discourse of "revolution" associated with the appearance/development of natural experimental science in the 16/18th centuries, I will confidently insist on a difference between 21st century experimental physics, astronomy, chemistry, molecular biology, mathematics, and computer modelling on the one hand, and 'personal experiences' and dreamtime lore on the other.

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    7. David Thompson

      Marketing Research

      In reply to Christine Nicholls

      "But trying to erase those very real differences is not an option either - because that approach can actually lead to cultural/social superiority/ or deficit models."
      Christine, those models are already ubiquitous. Without them, humanity would have no sense of progress, let alone hope, and aspiration.

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  49. Molly Gabbard

    Artist and Art Projects Manager

    Hello Christine,

    Excellent article! I enjoyed your perspective. I would love to read more ellaboration on the connection between Indigenous mathematics and Indigenous art. Have you looked into other Indigenous Australian foundational ideas of ethnomathematics? Ethnomathematics being the relationship between mathematics and culture and more so mathematics that is practiced by identifiable cultural groups.

    Your analysis of Aboriginal spatial abilities in AFL connects well and is represented…

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    1. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Molly Gabbard

      Many thanks for this post, Molly. You’ve packed so much into it that I may need to respond to the various matters you’ve raised over several posts, owing to other pressing time commitments!

      This is a general, rather than specific response to what you've raised but it will frame my more specific response later.

      To begin, all cultural groups, no matter how diverse, bring their mathematical understandings into play in their artworks at some level, some more explicitly than others. In the…

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    2. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Molly Gabbard

      Hi Molly:

      this is the second of my three-part response to your post, and here I'll discuss the concept of 'ethnomathematics'. I suppose that a number of people who've read this article would view its subject matter, in part at least, as being 'ethnomathematics'. One of the most informed respondents on this site, Peter Ormonde has used the terminology, and of course, you.

      As you say, the broadest definition of ethnomathematics is that it concerns itself with the relationship/s between maths…

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    3. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Christine Nicholls

      problematising!!!!????? Is that making a problem out of something? People should be fined or even gaoled for words like that!

      a shockingly mangled word.... up or down there with incentivise, envisioning, privatise and all those other dollops of consultant-speak that demean meaning. I am appalled and aghast. My gob is smacked.

      Back to the business at hand... Ms N - please don't saddle me with some eurocentreric arithmetical anthropologism... I just remembered the word and tracked down a thing…

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    4. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Peter Ormonde

      That's a fair cop Peter - yes, that word is a shocker! I must have been having a 'junior moment', as I normally eschew such lingo, but there's so much of it about on a daily basis one occasionally succumbs (the one that I most detest is the fave. corporate board-speak of 'leveraging' something or someone, which really just means prising their $$$ out of them to the max., as far as I can make out).

      On a more serious note, having taken that one on the chin, I wasn't having a 'go' or crack at either…

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    5. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Christine Nicholls

      One of the most disturbing features of watching a new government "settle in" is hearing the creeping encroachment of what Don Watson so aptly tags "weasel words" ... fed by a smorgasbord diet of dreary briefing notes and technical discussions and a free bar of bureaucratese and acronyms. Peter Garret leaps to mind. Eternal vigilance Ms N!!!

      I look forward to Midnight Oil reforming - suited - and a whole swag of punchy new songs devoted to Expenditure Review Committees, Key Result Areas and Outcomes Evaluation, in the fullness of time. Buggers to rhyme though.

      Back to the serious stuff... has any of this spatial awareness/conceptual framework been analysed systematically? Way out of my turf so I am not aware of any work from a psychological or pedagogical angle looking at Aboriginal sense of place. Be very interested if there is. There should be. There's another project going begging.

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    6. Frank Baarda

      Geologist

      In reply to Christine Nicholls

      Somebody Watson wrote a book "Bendable Learnings" which quite likely has the word 'problematising' in it. I recommend it.
      Not all that long ago the local education services delivery agency (Yuendumu School) had what they call a 'pupil free day'. All teaching staff descended on Alice Springs to attend a workshop. Do you think they were going to discuss the Warlpiri worldview and Warlpiri language so as to better capacitate them to deliver to their clients? No Sir! The workshop was titled "Bendable Visions"

      "Junior moment".... ngurrju, ngampurrpa kana.

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    7. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Frank Baarda

      "Bendable Visions" indeed - ha! But apart from the ungainliness of the language use (it's not exactly a euphonious appellation!) it seems that therein lies a certain truth.

      "Bendable Visions" is no doubt noughties-speak for "No Core Values" - that's what the expression immediately brings to mind, no doubt accurately in this instance.

      On a serious note now, your earlier point of providing a linguist to such schools who are able to deliver inservice to teachers locally - about Warlpiri language…

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    8. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Peter Ormonde

      Regarding your final paragraph here, Peter - there are certainly quite a few individual articles and some books written on related matters, but I haven't come across anything systematised in the manner or to the degree that you suggest.

      In terms of making some inroads in terms of the National Curriculum (which is still a work-in-progress) however, I honestly don't think that what's needed is necessarily another research project or book, although both would be welcome additions - it's to a much…

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    9. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Christine Nicholls

      A few years back SBS carried a weekly TV broadcast of an wonderful Koori/National NRL competition held up on the NSW North Coast somewhere. I used to watch it with my son after he finished school... went on for weeks.

      Funniest thing I've ever seen. All these lanky Warlpiri fellas and similar from all over the place - all AFL hotshots - who might have seen a league game on TV once or twice - having a go at playing this alien rugby league business. Kept the refs busy I can tell you. Very…

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    10. Frank Baarda

      Geologist

      In reply to Peter Ormonde

      Erratum: The Alice Springs 'workshop' wasn't titled 'Bendable Visions' but my wife thinks it was 'Visible Learnings". Never mind, the point I was making (and fully grasped by Christine) remains valid. I suppose the corollary of 'Visible Learnings' is 'Invisible Learnings' which brings to mind 'Hidden Agenda' A friend of mine was asked by a Warlpiri man "What is a hidden agenda?". My friend couldn't explain it.
      And yes Peter the 'somebody Watson' that authored 'Bendable Learnings' was indeed the…

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    11. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Peter Ormonde

      The really sad, nay tragic, aspect of this Peter (tragic in the true sense of that word - not the media-mangled weasel usage whereby ***not*** winning an Olympic gold medal has been described as 'tragic'), is that many of the ideas that you've mentioned towards the end of your post HAVE actually been tried in the past and in an impressively large number of cases they have really worked well and been successful, no matter what criteria of success are applied. For example, the idea of having input…

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    12. Molly Gabbard

      Artist and Art Projects Manager

      In reply to Christine Nicholls

      Thank you for all the information. I have spent the last week delving into and familiarizing myself with these artists a bit more and their ideas. Lot's too review and wrap around.

      The connection between art to science, math and onward to spirituality immediately reminds me of the Egyptians, Mesopotamians and again Native Americans. The aforementioned 'western artists' conveyed their obsession, faith and spirituality through their art that doubled as their scientific/mathematic experimentation…

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    13. Eleonore WIldburger

      scholar

      In reply to Christine Nicholls

      I am a newcomer to this forum and a latecomer to his debate. But let me comment in a few lines on your brilliant article, Christine.

      I’d like to take up the ethnomaths strand in this discussion. I wholeheartedly agree that a comparative approach to mathematics, as well as to ALL subjects of the curriculum is needed when ALL Australian students are addressed. Also mainstream students can learn a lot from comparative approaches to mathematics, science, arts, and so on. I do not think the question…

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    14. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Molly Gabbard

      Good evening – or morning - Molly. Thanks for your very deeply considered response to mine, and you are definitely not ‘off topic’ but engaging with the issues at hand, which have equal implications for visual art deeply and at a structural level - as they do for Australian football, or more.
      Yes, I’m in agreement with you with regard to the mathematical sensibilities evinced in the visual art of contemporary artists/sculptors like Anish Kapoor et al, but would also add that it is important to note…

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    15. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Molly Gabbard

      Molly - regarding your final paragraph on the above post, about Indigenous maths elsewhere in Australia, I have recently found out that Michael Christie of Charles Darwin University has been working with Yolgnu Matha speakers (from Arnhem Land in northern Australia) in precisely that area. Some of this work is available on the following link, and may be useful to you:

      www.cdu.edu.au/macp

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    16. Molly Gabbard

      Artist and Art Projects Manager

      In reply to Christine Nicholls

      Good morning Christine and all,

      I am in agreeance with you on the overarching definition of ethnomathematics in all cultures, indigenous and western. Especially after reading Hickman's article on logorithms and a discussion with my sister who is working on her Phd in Epidemiology - ethno at it's best. It is indeed relative to all cultures.

      I would like to see the discussion of ethnomathematics opened and ideas shared cross-culturally. I am aware this has been a tried topic. Looking within…

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    17. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Eleonore WIldburger

      Thank you so much, Eleonore, for your timely intervention into this debate - and it is definitely not too late to comment – others have in fact commented more recently, and your comment is very welcome indeed (please accept my sincere apologies for taking so long to respond to your post).
      From this article’s inception, the ideas underpinning it have been aimed at all interested parties, regardless of background; all persons, that is, with a genuine desire to understand this place, now called Australia…

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    18. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Molly Gabbard

      Hi Molly - good morning or good afternoon - not sure of the current time in Indiana!

      Good to hear that you agree with the idea that if it's described as 'ethnomaths' for one, that it's a more level-laying field approach to describe ALL mathematics as 'ethnomaths' for ALL (groups, peoples, cultures, individuals). And it is equally true that certain fields of western science have their own highly specialised and often abstruse, practically "secret ethnomathematics languages". In addition (and I…

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    19. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Christine Nicholls

      Gee this is an interesting bit of a chat ... sorry, can't help throwing in another tuppence worth...

      I met a young bloke during one of my stints developing my coffee palate at university. Turned out he was a Koori who'd grown up in and all over western NSW. Essentially self-taught.

      His school experiences were nearly invariably dreadful and disheartening. As he put it, all he learned was that history and progress didn't include people like him and his gran. That they had achieved nothing…

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    20. Frank Baarda

      Geologist

      In reply to Peter Ormonde

      Peter,
      Somewhere in this discourse you described yourself as a refugee economist, and you write under the 'title' farmer. I think carpenter best describes you. You keep hitting so many nails on the head.
      All the discussion about curricula (is this the plural of curriculum?), ethno mathematics, bilingual education etc.usually leaves out the pernicious side effect of an ethnocentric assimilationist education programme. As Wayne so well put it: a hidden curriculum... a dispossession story......
      Not…

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    21. Peter Ormonde
      Peter Ormonde is a Friend of The Conversation.

      Farmer

      In reply to Frank Baarda

      Thanks for the nice words Frank ... would that I could do something - anything - as useful as carpentry.... been a lot of things over my time but I still have trouble with bookshelves.

      It's pathetic isn't it that this token effort of ours of 'keeping culture alive' with a warlpiri room seems deliberately designed to do the opposite, Ministry of Truth style. Tragic really all those 'good intentions' paving the way... as ever.

      So here's a positive suggestion about how our schools can help keep…

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    22. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Peter Ormonde

      I too thought that this was a great post, Peter, and very telling in terms of Wayne's story. Your following post, about giving kids a camera and recording the stories of older people, is equally spot-on, and in fact the Warlpiri media have actually been doing this for some time, up in Warlpiri country.

      But to take up Frank's point, and perhaps take it a little further, it's important that we also engage with the present, rather than simply record for posteritythese remarkable stories of older…

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    23. Gail Carnes

      Consultant

      In reply to Peter Ormonde

      Hi Peter,

      I did just a quick Google search and found quite a few reports, including this one on Indigenous numeracy that summarises much of the research in this area: http://ab-ed.boardofstudies.nsw.edu.au/files/evaluation-maths-indigenous-k-2.pdf

      The section titled "the development of numeracy by Indigenous children" (page 18) is particularly interesting, especially the notion of mathematics as a form of social enculturation.

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    24. John Clark

      Manager

      In reply to Christine Nicholls

      I have been following the discussion now for some time without comment, but the implied criticism of Noel Pearson struck a nerve. As reluctant as I am to be critical of someone so obviously well meaning, it may be time for a reality check. The proposition of using cultural anecdotes to somehow justify the inclusion of obsolete dialects in the national curriculum trivialises attempts to assist indigenous Australians to participate in society in the modern world is fanciful and potential harmful, as a distraction from the efforts of Noel and his supporters. There is a clear and present need to put the past behind us and plan on a future of equality and inclusion. Indigenous Australians should continue to excel in AFL and other endeavours, but be given every opportunity of absorbing the skills and knowledge to fully participate in society as it is, and will be. By all means, maintain cultural links to the past, but all such effort must be extracurricula.

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    25. Frank Baarda

      Geologist

      In reply to John Clark

      Just as the implied criticism of Noel Pearson struck a nerve with you, so did your "the inclusion of obsolete dialects in the national curriculum trivialises attempts to assist indigenous Australians to participate in society in the modern world" struck a nerve with me.
      The Warlpiri language is not an obsolete dialect by any stretch of the imagination. For people in Yuendumu it is not a link to the past, but very much a part of the present (and hopefully the future).
      Warlpiri is a beautiful highly…

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    26. Molly Gabbard

      Artist and Art Projects Manager

      In reply to Christine Nicholls

      Good evening in over in Adelaide Christine!

      Thank you for the extensive reply and thoughts.

      First, I apologize for my degrading remarks on the linear scale...I forget the impact and multiple meanings of heavy words such as 'primitive' and 'evolution'. As a visual artist, I have minimal experience investigating topics in a well thought out and non discriminatory manner. During my undergraduate I took courses in human sexuality and I was too simply regarding the university Kinsey Scale…

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    27. Christine Nicholls

      Senior Lecturer at Flinders University

      In reply to Molly Gabbard

      Hello Molly,

      Thanks for the Sim Luttin link, which I'm sure many will read, like me, with considerable enjoyment.

      It’s our national election today, here in Australia, so I’m taking a little time out from thinking about that (although the result is pretty well a foregone conclusion, and by the time you read this we will almost certainly have a new government; perhaps even before I finish writing this) to respond to your most recent post.

      Thank you for your post, which is, as usual, thoughtful…

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  50. Geoffrey Harold Sherrington

    Boss

    I''m not sure that your methodology is good when you describe differences, however interesting they migjt be, then ascribe deep meaning to them. A s;tory -
    One of our children at kindy age started to bring home paintings that used more and more black paint. Some social medico friends gently suggested psychiatry of depression be tried. Armed with reports, we approched the kindy teacher who replied :That's easy. W!e ran out of piaints in all but black.paint.
    Proper experimental design is more important than phenomenology.
    Maybe the air photo painter style arose becase so mny people had seen so mny originals.

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  51. Adele Pring

    Educator

    My reason for providing information for teachers about Aboriginal astronomy and mathematics several years ago but was so much to have all students learning all of it but teachers being aware of the quite sophisticated knowledge and skills of many Aboriginal people, so the teachers wouldn't have such a deficit view. Having learned quite a bit myself in doing the research I now have a quite good sense of direction during the day and night. I was already quite good at map reading which I put down to…

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  52. Adele Pring

    Educator

    Regarding how Aboriginal people know - I read that when asked they didn't know how they knew, they just knew and I suspect this is because they learned much of it, according to the research, before they could walk and soon after with ongoing lifetime reinforcement.

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  53. Brian Wicks

    Secondary Maths Teacher

    One of the key things about this article is the way in which it encourages us to think outside of the box in terms of the way that teachers present mathematics and utilise existing strengths and understandings.

    As someone who has regular contact with a remote SA Aboriginal community it soon becomes obvious in a class setting that paradigm is everything. It is one of the first features that the mainstream suburban students I take on exchange notice when sitting in class with their Aboriginal friends…

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    1. Geoffrey Harold Sherrington

      Boss

      In reply to Brian Wicks

      "If we are to have success with developing Indigenous literacy and numeracy"

      Better think up some ideas fast, eh?. Nothing that has been tried over 150 years or so has worked all that well for at least a segment of the people.

      Football and the buzz it gives? Might as well go the whole hog with free sex, with the bigger buzz that it gives.

      You educators, having failed so badly so often, are still heading to the absurd. Pig skin cures. ROTFL.

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    2. David Thompson

      Marketing Research

      In reply to Brian Wicks

      Sadly, as Christine has repeated over and again, for some reason 'numeracy' is not part of the Aboriginal cognitive system.

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    3. David Thompson

      Marketing Research