Last year, after the appearance of ACARA’s appalling draft curriculum, we ran a competition: find the best Aboriginal and Torres Strait Islander elaboration. No one took our competition seriously. This was perhaps unsurprising, since most readers of this blog would have been sceptical already, and then our introduction to the competition hammered the ATSI cross-curriculum priority as enacted in the draft mathematics curriculum. We were serious, but no matter. There is a new mathematics curriculum, with revised ATSI elaborations, and we move on.

We’re not here to praise the revised ATSI elaborations. They are, in sum, poor, and the purpose of this post is to reveal a somewhat hidden poor aspect. Nonetheless, there are some reasonable and arguably good ATSI elaborations. It seems interesting and natural and fun, for example, for Prep kids to look at indigenous methods of body-tallying (AC9MFN03). Similarly, taking at least a peek at indigenous number names seems worthwhile (AC9MFN04). Other elaborations, concerned with reconciliation and the like, are somewhat activist in tone, and are thus more fringe and more open to question. Still, Indigenous Australians have been dicked over since the beginning, they continue to be dicked over, and it is important that school education pay some attention to this dicking; so, one might cut the curriculum writers a little slack, particularly since elaborations are intended to be optional. But, mostly, the ATSI elaborations are poor, contrived to the nth degree and with little or no clear mathematical purpose. This post is on a group of such elaborations.

Of the eighty-nine ATSI elaborations, fourteen are based around indigenous games, with specific reference to twelve different games. The latter number is not unreasonable on the face of it, particularly given that most of these game elaborations are for the early primary years: children’s games can naturally contain a geometric or arithmetic element, and so could be used as (occasional) playful reinforcement of some mathematical concept. The question is, then, what is the game and what is the precise purpose of employing it in the classroom?

The first such elaboration in the Australian curriculum is in Foundation Number, for the very first content descriptor:

*name, represent and order numbers including zero to at least 20, using physical and virtual materials and numerals* (AC9MFN01)

*connecting quantities to number names and numerals when reading and reciting stories and playing counting games or determining and reasoning about the size of sets of objects within First Nation Australians’ instructive games; for example, Segur etug from Mer Island in the Torres Strait region *

The goal is the naming and ordering and (thus) counting up to 20, or more, for which there are then five elaborations. The game elaboration suggests “for example” playing the “instructive” game of *Segur etug*. The “for example” offers no guidance, so we’ll just consider *Segur etug*.

It is not so easy to find clear and detailed information on indigenous games. The most comprehensive and scholarly study appears to be by retired education academic, Dr. Ken Edwards, who has written a bibliography and a typography of ATSI games; these works are concerned with categorising and referencing games in general, rather than with the naming of specific games of specific Indigenous groups. Dr. Edwards, however, was also a key contributor to the Australian Sports Commission collection (existing also as a website), which lists by name and then describes many specific games. Notably, all but one of the games cited in the curriculum elaborations appear in the ASC list, and the few other references we could typically locate often appeared to be derivative; it is plausible that the ASC list was the main resource used by ACARA (and many others), to create their elaborations.

Now, what of the game *segur etug*? ASC summarises the game as follows:

*One player takes a quantity of small objects and places them in a closed hand or cup.*

*The other players attempt to guess the number. The player who is correct has the next turn. If no player guesses correctly the player has another turn.*

A garden-variety, bare bones guessing game. Sure, it fits with the curriculum content, since there are numbers and names. But, even for such early concepts, it is very small beer. It is difficult to see the purpose of the elaboration other than to affix a Torres Strait Islander (maybe creole) label to a globally practised, and quickly boring, activity.

The next game elaboration is also part of Foundation Number:

*represent practical situations involving addition, subtraction and quantification with physical and virtual materials and use counting or subitising strategies* (AC9MFN05)

*representing addition and subtraction situations found in leaf games involving sets of objects used to tell stories, such as games from the Warlpiri Peoples of Yuendumu in the Northern Territory*

As suggested, leaf games are concerned with storytelling, with the leaves representing the characters in the story. Here is the Australian Museum description of such a story (seemingly extracted from a Masters thesis on Aboriginal games):

*The longest leaf was a man, a shorter leaf the woman, and the smallest leaf the baby. In one story a broken leaf was used to represent the infirm grandmother. The patterns were continually being changed to relate daily occurrences in the camp. For example, when the man went hunting, the long leaves were removed from the sand, leaving the women and children behind. Talking and chanting accompanied this activity throughout.*

So, more of the same, and less. Recall, the content goal is to practise addition and subtraction, and counting and subitising (the instant recognition of the size of a collection). Yes, again, the game elaboration fits this goal, but in only a minor and tangential manner; the role of quantity is almost entirely irrelevant to the cultural purpose of the game.

On it goes. As best as we could determine, every game elaboration contains, at most, a trivial amount of mathematics, and provides, at best, a trivial and time-wasteful reinforcement of curriculum concepts.

Below are the fourteen game elaborations and their parent content descriptors. For each elaboration, we’ve given a very brief description of the nature of the game, and we’ve provided what seemed the most informative link – usually from ASC – for information on the associated game. Perhaps others can see some purpose to all this. We cannot. We cannot see that any of the chosen game elaborations warrant inclusion in the mathematics curriculum.

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**FOUNDATION**

*name, represent and order numbers including zero to at least 20, using physical and virtual materials and numerals* (AC9MFN01)

*connecting quantities to number names and numerals when reading and reciting stories and playing counting games or determining and reasoning about the size of sets of objects within First Nation Australians’ instructive games; for example, Segur etug from Mer Island in the Torres Strait region*

A number quantity guessing game: ASC.

*represent practical situations involving addition, subtraction and quantification with physical and virtual materials and use counting or subitising strategies* (AC9MFN05)

*representing addition and subtraction situations found in leaf games involving sets of objects used to tell stories, such as games from the Warlpiri Peoples of Yuendumu in the Northern Territory*

Storytelling: Australian Museum.

*represent practical situations involving equal sharing and grouping with physical and virtual materials and use counting or subitising strategies* (AC9MFN06)

*exploring instructive games of First Nations Australians that involve sharing; for example, playing Yangamini of the Tiwi Peoples of Bathurst Island to investigate and discuss equal sharing*

Throwing marbles or similar into a hole: ASC.

*describe the position and location of themselves and objects in relation to other people and objects within a familiar space* (AC9MFSP02)

exploring First Nations Australians’ instructive games; for example, **Thapumpan** from the Wik-Mungkan Peoples of Cape Bedford in north Queensland, describing position and movement of self in relation to other participants, objects or locations

Chasey: ASC.

**YEAR 1**

*make, compare and classify familiar shapes; recognise familiar shapes and objects in the environment, identifying the similarities and differences between them** *(AC9M1SP01)

*exploring string games used in story telling by First Nations Australians; for example, Karda from the Yandruwandha Peoples of north-east South Australia, recognising, comparing, describing and classifying the shapes made by the string and their relationship to shapes and objects on Country/Place*

“Karda” would appear to be a mislabelling (and misspelling) of a game ASC refers to as Kamai, which is a Cat’s Cradle-like game. In discussing such games, the Australian Museum describes the string representation of a “kardra”, indicating the word is Yandruwandha for “yam”.

*represent collected data for a categorical variable using one-to-one displays and digital tools where appropriate; compare the data using frequencies and discuss the findings* (AC9M1ST02)

*exploring First Nations Australian children’s instructive games; for example, Kolap from Mer Island in the Torres Strait region, recording the outcomes, representing and discussing the results*

Throwing small objects into a circular region: ASC.

**YEAR 2**

*use mathematical modelling to solve practical problems involving additive and multiplicative situations, including money transactions; represent situations and choose calculation strategies; interpret and communicate solutions in terms of the situation* (AC9M2N06)

*modelling problems involving equal grouping and sharing in First Nations Australian children’s instructive games; for example, Yangamini from the Tiwi Island Peoples, representing relationships with a number sentence and interpret and communicate solutions in terms of the context*

See above.

**YEAR 3**

*identify angles as measures of turn and compare angles with right angles in everyday situations *(AC9M3M05)

exploring First Nations Australian children’s instructive games to investigate angles as measures of turn; for example, the game **Waayin** from the Datiwuy People in the northern part of the Northern Territory

Creating and guessing animal tracks: ASC.

**YEAR 5**

*conduct repeated chance experiments including those with and without equally likely outcomes, observe and record the results ; use frequency to compare outcomes and estimate their likelihoods* (AC9M5P02)

*investigating First Nations Australian children’s instructive games; for example, Diyari koolchee from the Diyari Peoples near Lake Eyre in South Australia, to conduct repeated trials and explore predictable patterns, using digital tools where appropriate*

Skittles: ASC.

**YEAR 6**

*recognise that probabilities lie on numerical scales of 0 – 1 or 0% – 100% and use estimation to assign probabilities that events occur in a given context, using common fractions, percentages and decimals* (AC9M6P01)

exploring First Nations Australian children’s instructive games, such as **Weme** from the Warlpiri Peoples of Central Australia, to investigate and assign probabilities that events will occur, indicating their estimated likelihood

Marbles: ASC.

**YEAR 7**

*conduct repeated chance experiments and run simulations with a large number of trials using digital tools; compare predictions about outcomes with observed results, explaining the differences* (AC9M7P02)

exploring and observing First Nations Australian children’s instructive games; for example, **Koara** from the Jawi and Bardi Peoples of Sunday Island in Western Australia, to investigate probability, predicting outcomes for an event and comparing with increasingly larger numbers of trials, and between observed and expected results

Propeller toys: ASC.

**YEAR 8**

*determine all possible combinations for 2 events, using two-way tables, tree diagrams and Venn diagrams, and use these to determine probabilities of specific outcomes in practical situations* (AC9M8P02)

*exploring First Nations Australian children’s instructive games; for example, Battendi from the Ngarrindjeri Peoples of Lake Murray and Lake Albert in southern Australia, applying possible combinations and relationships and calculating probabilities using two-way tables and Venn diagrams*

Throwing balls with a woomera: ASC.

**YEAR 9**

*design and conduct repeated chance experiments and simulations, using digital tools to compare probabilities of simple events to related compound events, and describe results* (AC9M9P03)

*using repeated trials of First Nations Australian children’s instructive games; for example, Gorri from all parts of Australia, to calculate the probabilities of winning and not winning*

Bowling: ASC.

**YEAR 10**

solve linear inequalities and simultaneous linear equations in 2 variables; interpret solutions graphically and communicate solutions in terms of the situation (AC9M10A02)

*investigating the strategies inherent in First Nations Australian children’s instructive games; for example, Weme from the Warlpiri Peoples of central Australia, and their connection to strategies to solve simultaneous linear equations in 2 variables*

See above.

Firstly, thanks Marty for chasing all of these down; quite an effort.

Now, on one specific game (and the ACARA elaborations): Gorri.

I cannot imagine very many Year 9 students being able to calculate theoretical probabilities for this game even with some serious instruction. Likewise, depending on the skill and experience of students, theoretical probabilities I would expect to differ wildly.

I am all for games in probability (yes, even Greedy Pig) IF there is a discussion of the theoretical vs experimental probability involved.

Have I missed something or is this more akin to finding a game that has some numbers involved and trying to force it to fit into an already crowded curriculum?

Most of the ATSI elaborations, throughout the entire Australian curriculum, are tokenism.

The answer to your question is yes.

So… yes I have missed something or yes this is ACARA trying to force an example into the curriculum?

“Both” is an acceptable response and probably what I am expecting.

You haven’t missed anything. Not in my opinion, at any rate.

A bit off topic, (and note I am not a teacher) but surely the Vic teachers pay deal of 2022 has proved to be an absolute disaster for teachers? Not even three percent a year, with inflation at 7.8%.

Apparently now there is an incredible shortfall of teachers for this year in Vic-notably of course with maths teachers. Its crazy.

A

bitoff topic?Frank, happy for you to send me an email if you think it’s something I should write on. (Which is no promise I’ll agree or get to it.)

Fair enough, its very off-topic. But still, it must be affecting maths teaching etc very much…

Anything involving the Warlpiri has to be great!

Not that I have anything against (or know anything about) the Warlpiri, but why?

This analysis is spot on and without further “examples in practice” of how many of these are carried out and then linked to the curriculum its basically just adding wordcount.

I can easily see Battendi being useful and easily applied for precision and accuracy in the Science curriculum, but the probability and simultaneous equations – i’d be keen to see someone explain or demonstrate.

Thanks, Steve.