Which is the Best ATSI Elaboration?

Are we trying to stir up trouble? No and, of course, yes. And yes. If we were really stirring up trouble, we’d be asking for the worst Aboriginal and Torres Strait Islander elaboration. But yes, as with our previous competitions,1 the intention is to damn an aspect of the draft mathematics curriculum by making evident the faintness of the possible praise. Moreover, given that there is essentially no tradition of Aboriginal or Torres Strait Islander mathematics, something has to be said about this aspect of the curriculum. We do so.2

First, the competition: prove us wrong. Find the best, stellar Aboriginal and Torres Strait Islanders elaboration in the draft mathematics curriculum. Of course “best” is open to interpretation, but it must be somehow obvious or argued that the elaboration has genuine pedagogical value. (We believe there are at least a few such elaborations that are worthwhile, even if the clear majority are not.) The winner of our competition receives, as usual, a signed copy of the best-selling3 A Dingo Ate My Math Book.

Now, some remarks on Indigenous mathematics and the ATSI “priority” in the curriculum. In our whacking of the draft curriculum we have avoided so far the Aboriginal and Torres Strait Islander angle. It was and is a second order issue; whatever the flaws in the ATSI material, they pale in comparison to ACARA’s central mathematical sins. Still, something has to be said. The current silence is deafening, and dishonest.

The cross-curriculum priorities of the Australian curriculum are

three key areas that need to be addressed for the benefit of individuals and Australia as a whole … [They] give students the tools and language to engage with and better understand their world at a range of levels.

Whatever that means. The three cross-curriculum priorities are Asia and Australia’s Engagement with AsiaSustainability and Aboriginal and Torres Strait Islander Histories and Cultures. The first two priorities feel arbitrary and weirdly specific, but the third is natural and important. It is an intellectual and moral imperative for Australians to learn about the people who got beaten up in the making of modern Australia.4

The cross-curriculum priorities “do not constitute curriculum on their own” but, rather,

the priorities are identified wherever they are developed or have been applied in content descriptions. They are also identified where they offer opportunities to add depth and richness to student learning in content elaborations.

It follows that each learning area, including mathematics, may incorporate more or less of a priority within different topics and at different year levels. If and where a priority does not fit, there is no obligation to force the issue and of course it would be foolish to do so.

How, then, are these three priorities dealt with in the draft mathematics curriculum? Well, to begin,

The cross-curriculum priorities of most relevance and meaning to the Mathematics curriculum are Sustainability and Aboriginal and Torres Strait Islander Histories and Cultures.

Yeah, that makes sense. It’s not like there’s any Asian countries with a strong mathematical culture or mathematical history.5

Sustainability at least exists in the draft, although, for better or worse, it is pretty token. There are a dozen or so elaborations in the draft that might loosely be tied to issues of sustainability. They are ok, but they’re small beer. The big beer is the ATSI priority.

The draft curriculum contains about 130 Aboriginal and Torres Strait Islander elaborations, which, whatever their individual merits, whatever support they provide for the ATSI priority, is, in context, absurd. For better or worse,6 the draft mathematics curriculum is almost entirely devoid of culture and history. There is not a word about Greek mathematics, or Babylonian mathematics, or Egyptian mathematics, or Chinese mathematics, or Mayan mathematics, or Indian mathematics, or Middle Eastern mathematics, or Modern European mathematics. Not a single mathematician is mentioned by name, except for the very few that appear, unelaborated, in a mathematical term.7 In this anti-cultural context, to have such heavy weight on Aboriginal and Torres Strait Islander culture is absurd.

The draft’s introduction to the ATSI priority reads as follows:

In the Australian Curriculum: Mathematics, students can engage with and value Aboriginal and Torres Strait Islander Peoples’ histories and cultures in relation to mathematics. Aboriginal and Torres Strait Islander Peoples have complex kinship systems that connect all people to environmental systems, which is the hallmark of sustainability. They tend to be systems thinkers who are adept at pattern and algebraic thinking, which informs Aboriginal and Torres Strait Islander Peoples’ cultural expressions, ways of caring for Country/Place, and the development of material culture.

Content elaborations in Mathematics have been structured around identified themes in Aboriginal and Torres Strait Islander Peoples’ mathematical thinking, understandings and processes, in contexts that can be taught across the content strands and through the year levels. They provide a rich, connected narrative by returning to contextual examples from all over Australia. For example, within the probability and statistics strands, stochastic reasoning is developed through Aboriginal and Torres Strait Islander instructive games and toys. Spatial reasoning is linked to land/cultural/star maps and proportional reasoning is learned in relation to material culture, such as weaving or strings and cordage.

This is cloying, manipulative, generalising, patronising and, to a large extent, false. Again, there is no mathematical tradition to speak of in Aboriginal or Torres Strait Islander Culture, and it is unhelpful and embarrassing to suggest otherwise.8 What is the purpose, or even the meaning, for example, of the following Year 1 elaboration:

using part-part-whole reasoning to partition the 365 days of the year into the seasons of an Aboriginal and Torres Strait Islander seasonal calendar, saying how many days are in each of the seasons

To teach about Aboriginal and Torres Strait Islander concepts of season is fine and good. To have ten elaborations on this in a mathematics curriculum, to pretend that this is mathematics, is not.

Even if there is no Indigenous mathematics, there can be worthwhile elaborations on ATSI history and culture and technology, with mathematics as a tool of study. A number of ATSI elaborations are along these lines and seem natural and good. Many more, however, are forced. Take, for example, the following Year 7 elaboration:

exploring the relationship between volume and capacity of different sized nets used by Aboriginal and Torres Strait Islander Peoples to catch different sized fish

Similar to the seasons, teaching about Indigenous fishing culture and fishing technology seems worthwhile. But, to try to jam this teaching into a pointless mathematical computation is meaningless, and it will impress no one. Many of the ATSI elaborations are pushy and amateurish in this manner. And, without seeking to venture into Dark Emu territory,9 some are manifestly absurd:

exploring geodesic design in Aboriginal and Torres Strait Islander building traditions and its relationship to Euler’s formula and how this has influenced contemporary housing design

Still, amidst the nonsense there are good ATSI elaborations. Find some. Win a book.

************************************************

1. We haven’t forgotten the previous winners. We’re waiting until it is legal to meet with The Evil Mathologre to sign the books, and then we’ll send them off.

2. So much for not stirring up trouble. 

3. In Polster and Ross households.

4. There is also, of course, the moral imperative to improve the woeful state of the education of Indigenous children. (And Indigenous health. And not being beaten up by cops.) This, however, is distinct from the issue of what Australians generally should be taught of Aboriginal and Torres Strait Islander history and culture. 

5. It’s not by a long shot the main screw-up here, but there is also something weirdly ass-backwards about the curriculum quote on the priorities. The supposed purpose of the priorities is not that the priorities may have “relevance and meaning” to mathematics but, rather, that mathematics may provide meaning for the priorities.

6. Worse.

7. We located reference to Fibonacci numbers, Pythagoras’ theorem, Euler’s (characteristic) formula and, stretching the rules, the Cartesian plane. We could see nothing else. No Euclid, no Archimedes, no Brahmagupta, no Madhava, no al-Khwarizmi, no Pascal, no Fermat, no Gauss. 

8. Readers who doubt this are welcome to debate the point in the comments. 

9. The Dark Emu debate is not irrelevant here, but is also not the main point. We’ll just note that the whacking of Pascoe’s book by Sutton and Walsh is well worth reading and, it seems to us, decisive. 

11 Replies to “Which is the Best ATSI Elaboration?”

  1. (I don’t want to enter the competition, but will try to contribute to the discussion)

    Two elaborations that *might* be worthy of some level of consideration:

    P42
    exploring progress in reconciliation between Aboriginal and Torres Strait Islander Peoples and non Indigenous Australians, investigating and evaluating sampling techniques and methods to gather relevant data to measure progress (AC9M8ST04_E3)

    OK, this is pretty basic statistics at Year 8 level but the concept of sampling is relevant now that there is so much of it in VCE Mathematics.

    P63
    exploring navigation, design of technologies or surveying by Aboriginal and Torres Strait Islander Peoples, investigating geometric and spatial reasoning and how these connect to trigonometry (AC9M10M05_E6)

    This one (although it really could have been spelled out a bit better…) has some merit, although navigation by astronomy is not unique to ATSI culture; does that mean it is ineligible?

    1. RF, I don’t know what either elaboration means, nor what purposes they are supposed to serve. if you want to try to clarify/solidify the elaborations, to something that can be properly critiqued, go ahead. (We also have alternative prizes for proud Dingo owners.)

      1. Thanks, but upon reflection I think these are more tokenistic than I first realised.

        If, for example, Chinese astronomers developed a navigation system and Greek astronomers did something similar but both connected back to the same fundamental idea of the tangent function, would I start a lesson with the astronomical context? I’m not sure.

        I’ll ponder further.

  2. I’m going to elaborate on what I tried to say earlier.

    Take the elaboration on p42 and shorten it a bit and it becomes “…investigating and evaluating sampling techniques and methods to gather relevant data to measure…”

    I don’t mind this at all in a statistics topic as if done properly it does require a bit of thought.

    Does the context have to be “…progress in reconciliation between Aboriginal and Torres Strait Islander Peoples and non Indigenous Australians.”? I would argue firmly NO. It is not a bad context, and there is enough data if you have the time to look for it (spoiler alert: “progress” is not the word I would choose). Hence my reference to ATSI as potentially “tokenistic”. Not the right word either, but I can’t find an appropriate alternative at present.

    1. Amusingly, I think I disagree with both parts. To begin, I don’t think your more general version of the elaboration has much worth as a Year 8 thing. However, given there is some worth, I think strongly considering to make the context Aboriginal is exactly how the priorities are supposed to work.

    2. Nice try, RF. But framing poll questions to measure “progress in reconciliation between Aboriginal and Torres Strait Islander Peoples and non Indigenous Australians.”

      is absurd. I can just imagine the lessons – no mathematics but plenty of discussion on what questions the poll should ask.

      Pretty much all of the ATSI elaborations in the Daft curriculum are crude examples of coercing concepts into a pre-determined context. They are cringeful, gratuitous and insulting. As has been pointed out, there are many cultures that SHOULD be elaborated on in any DECENT mathematics curriculum. Like it or not, ATSI is at the bottom of this list. Forcing everything to link to ATSI shows an enormous lack of cultural awareness and understanding. It is reverse discrimination. Quality of ATSI elaborations, NOT quantity, should have been the guiding principal. If there are only a few meaningful ones, so be it. At least they would have greater value, both morally and mathematically.

      Good luck with this challenge, people. I think a better/easier challenge might be to come up with an appropriate ATSI elaboration that’s NOT in the Daft curriculum. Simply to demonstrate to ACARA and others the proper way of doing it. It might also be easier on the old blood pressure.

      1. Thanks, John. As I wrote, I think there are a few decent ATSI elaborations in the maths draft. But the writers’ manic desire to include ATSI elaborations, no matter the misfit, make it very difficult to see. As I also wrote, I’m very supportive of having an ATSI priority. But, don’t be dumb and don’t make stuff up. As it is, it is simply embarrassing, and actively counterproductive.

        1. Thanks JF – “crude” was the word I think I was looking for to describe the situation.

          Another consideration (which may become simply a non-event in practice) is will these elaborations take time away from Mathematics?

          I guess that depends on how school curriculum audits are done.

          And your suggestion that the competition be changed to find a decent elaboration that the writers have missed is deserving of the prize by default!

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