This is our final post on the Australian Curriculum.* We’ll try to keep it short. We shall make the simple point that it does not matter what the curriculum purports to cover since there is not also included a clear indication of the extent and depth of what the teacher is expected to teach and, thus, what the student is expected to learn.

To make the point, we shall consider just one very specific topic: the addition of natural numbers. What is to be mastered for this? One can haggle, but the 1-2-3 backbone of natural number addition is something like:

**1) automatic recall of single-digit sums;**

**2) speedy mental computation of double-digit sums;**

**3) efficient written computation via the standard algorithm of triple-digit sums, and effectively of sums of numbers of any size.**

In Singapore this work is all clearly laid out, to be completed by the end of Primary 3 (roughly corresponding to Australia’s Year 3). Moreover, with government approved textbooks close to universal, it is absolutely clear what is to be mastered. Moreover moreover, with Singapore’s solid culture of testing it is absolutely clear that mastery is not simply a goal; it is also a solid expectation.

Australia is different.

In Australia, primary school textbooks are as rare as hen’s teeth. Instead, teachers are expected to fish for a range of “resources”. These resources have no necessary government approval and, even if so approved, they come with no guarantee or likelihood of coherence or quality or usefulness. Then, the testing of what students have or have not learned is more hen’s teeth.

These are not primarily curriculum issues. They are general issues of Australia’s educational mediocrity. The point we wish to make here is that the mathematics curriculum will undermine even the current feeble attempts to teach and to test. The curriculum utterly fails to make clear, for example, the centrality of 1-2-3 above or of anything remotely similar and adequate.

Ignoring the adding and subtracting of (virtual) blocks in Foundation, the first reference in the mathematics curriculum to addition is in the Year 1 Achievement Standard:

*[Students] solve problems involving addition and subtraction of numbers to 20 and **use mathematical modelling to solve practical problems involving addition, subtraction, equal sharing and grouping, using calculation strategies.*

The meaning of which, God only knows. The meaning is then clarified not at all by the associated Year 1 content descriptor:

*add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies *(AC9M1N04)

The elaborations for this content descriptor contain nothing more concrete than noting computations of the type 7 + 5 = 7 + 3 + 2, along with “creating and performing addition and subtraction stories told through First Nations Australians’ dances”.

On to the Year 2 Achievement Standard, which, once again, is as clear as mud:

*[Students] use mathematical modelling to solve practical additive and multiplicative problems, including money transactions, representing the situation and choosing calculation strategies.*

There are then two associated content descriptors, the first of which is just more mud:

*add and subtract one- and two-digit numbers, representing problems using number sentences and solve using part-part-whole reasoning and a variety of calculation strategies* (AC9M2N04)

Predictably, the elaborations for this descriptor contain nothing beyond a couple tricks and, seriously, thinking further about First Nations’ dances.

The second Year 2 descriptor is, finally, almost solid:

*recall and demonstrate proficiency with addition facts to 20 …* (AC9M2A02)

The phrase “addition facts to 20” is vague and nauseating. The command to (be able to) recall these facts is confused by the presumably redundant requirement to “demonstrate proficiency”: the point is that a student either knows the sums or they don’t. The content is then further undermined by an aimless elaboration. Still, after a year of interpreting Aboriginal dancing, at least the requirement to know the single digit sums is semi-sort-of declared. It then gets worse again, however.

In Year 3, the Achievement Standard addresses multi-digit addition:

*Students extend and use single-digit addition … facts and apply additive strategies to model and solve problems involving two- and three-digit numbers. *

The two related content descriptors clarify nothing about these “additive strategies”:

*add … two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist in calculations without a calculator *(AC9M3N03)

*extend and apply knowledge of addition … facts to 20 to develop efficient mental strategies for computation with larger numbers without a calculator* (AC9M3A02)

There is not a single clear mention of the standard algorithm and much less the suggestion to master it, and nothing points to an ability to perform general mental addition. All the elaborations suggest the opposite, that the ability to perform addition amounts to nothing more than the accumulation of a bag of ad hoc tricks.

That’s about it. The Year 4 achievement standard and related content simply reiterates the meaningless “proficiency” and “stategies”:

*Students use their proficiency with addition … facts to add … numbers efficiently.*

*develop efficient strategies and use appropriate digital tools for solving problems involving addition … *(AC9M4N06)

To be fair, the *optional *elaboration to this content descriptor does finally mention “algorithms”, although one requires a magnifying glass to locate it:

*using and choosing efficient calculation strategies for addition and subtraction problems involving larger numbers; for example, place value partitioning, inverse relationship, compatible numbers, jump strategies, bridging tens, splitting one or more numbers, extensions to basic facts, algorithms and digital tools where appropriate *

This is all pointless and it is appalling. It is guidance for the acquisition of absolutely nothing with any solidity. And, every topic in the mathematics curriculum is treated in this manner. Every topic is a meaningless mish-mosh of “do some stuff” nonsense.

In a typically contrived defense of the curriculum, ACARA’s CEO attempted to claim the absurd vagueness of the curriculum was a positive:

*“What [two critics] perceive as a lamentable degree of potential variability in what content is taught is, arguably, really a reflection of one of the strengths of the Australian Curriculum …”*

Of all the monumentally stupid utterances of David de Carvalho, that is probably the stupidest.

The title of this post is an obvious play on a familiar saying, but our title understates the problem. The problem is not simply that the curriculum demonstrates no expectation that students will learn anything; the curriculum reflects no *desire* that students will learn anything. Nothing is desired beyond kids playing around with mathsy stuff, year after year and year.

This is insane and it is abhorrent. The curriculum is a disaster, and ACARA is a disaster. There will be no meaningful improvement until ACARA is gone.

*) The Curriculum contains rich veins of nonsense on every page, and one could mine it forever. If thirty posts hasn’t gotten the point across, however, another hundred is unlikely to help. So, unless someone flags some special horror, we figure we’ve done enough. (While, for instance, AMSI and AustMS and AAS and AMT have done nothing.)

I know I shouldn’t, but I’ve given up trying to read the Australian Curriculum – it makes my brain hurt. I simply go for the Singapore one which even I can understand.

I am not a math teacher. The best terms that can describe me are: ‘a mathematically inclined concerned parent’. The only students I observe are my children who learn their math from me and don’t really depend on school. After reading posts on this website I can see why schools are practically destined to fail. While there are good teachers here and there the system is just rotten to the core. Sad, very sad.

I think the highly-paid goons who craft all this will tell themselves, and perhaps others, “here goes Marty editorializing again. How can anyone take this guy seriously?” Which of course misses many important points you are making (and with the editorializing I would have an issue too) and allows to nourish their own self-complacency that lets Australian maths ed go down the gutter a further few inches or kilometres.

Thanks, Christian, although your terminology is not quite correct: VCAA has goons, but ACARA has loons.

And, yes, of course ACARA has nothing but contempt for me, as I do for them. But I’m not writing for them. I’m writing for myself, and for all the victims of ACARA’s incompetence.

I watched some students doing a long-multiplication the other day; 2 digit number x 2 digit number; calculators not allowed. I don’t doubt that their method led to the right answer, but I could not follow it. Isaac Todhunter (c. 1870) did it differently.

Was it the stupid box shit?

Yes

The stupid box shit is stupid and shit. And has boxes. I discussed it in this post:

Hi Marty, there is a reason why Singapore has been doing well and is currently no 1 in the latest PISA results. The difference in standards are significantly alarming.

I also agree that ACARA is lacking in clarity and the descriptors do not have sufficient elaboration especially at most levels. For instance, there are no worked examples with mark scheme to instruct teachers on the standards required. There is no differentiated level of difficulty examples in problem solving but just vague descriptions. A new or beginning teacher will not read ACARA or even understand half of what is written. Only experienced teacher will be able to navigate the treacherous document with a migraine at the end of the day and many are already retiring. There is also the issue of non-Maths teachers being forced to teach Maths due to timetabling which compounds the problem.

One example from Official ACARA V9 : Year 7 STRAND – Number: Content Descriptor

Use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies. (AC9M7N06)

Content Elaboration: Developing efficient strategies with appropriate use of the commutative and associative properties, place value, patterning, and multiplication facts to solve multiplication and DIVISION problems involving fractions and decimals;

for example, using the commutative property to calculate (2/3) of (1/2) and (1/2) of (2/3) is =(1/3)

From my understanding DIVISION is not commutative or associative. Is this an error or am I reading ACARA wrongly?

Thanks, Matt. On the specific elaboration I think you’re reading ACARA incorrectly, but it’s such a woefully misguided and badly worded piece of twaddle, I know who I blame.

Here, they’re suggesting a cheap trick, using commutativity of multiplication:

2/3 x 1/2 = 1/2 x 2/3 = one half of 2/3 = 1/3.

The trick is fine in itself, but of course as part of a proper understanding and facility with fraction arithmetic it’s a nothing and a distraction. And the AC is bloated with such nothings, to the exclusion of almost all else.

I’m not quite sure of the proper presentation of graded exercises and such in curriculum materials. To be functional, a curriculum should be pretty bare, with the standards reliant upon good secondary materials and/or an understood and accepted culture. The Singapore curriculum also does not have the kind of material you’re suggesting. But the SC does have very clear statements of the facts and skills to be learned, and it is backed up by government approved texts and regular testing.