ACARA’s Terms of Reference

Does anybody ever properly read Terms of Reference? Probably not, and in the case of ACARA’s Terms of Reference for their curriculum review, this was a fatal error. The Education Minsters who approved ACARA’s ToR screwed up. Royally.

Below, we work through the ACARA’s Terms of Reference, section by section, highlighting critical aspects to the review of the mathematics curriculum. We’ll indicate how the ToR gave, and continues to give, ACARA license to consciously and to thoroughly ignore mathematicians, as well as education ministers. We shall also indicate how, nonetheless, ACARA have violated their own Terms of Reference whenever and however it suited ACARA’s real agenda.

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The Singapore Primary Mathematics Syllabus

We’re working on a long ACARA post, which, hopefully, will be up in a day or so. In the meantime and as a bit of background for the coming post, readers may wish to have a wander through the Singaporean Primary Mathematics Syllabus.* (The syllabus begins with explanatory chapters, and the content description begins on page 34.) Continue reading “The Singapore Primary Mathematics Syllabus”

The Update Post

How should we improve this blog? Yeah, yeah, by deleting it. We know. But, other than that and similar ACARAesque thoughts, what would make the blog more interesting, and more functional? We have some ideas, and a few implementations are on the shortlist (so, don’t hold your breath). And, we’re always open to suggestions.

One thought/request we received was to notify followers when a post is updated, particularly since updates sometimes come months (or years) later. We looked, and it seems possible but not so easy (at least for a Luddite) to implement. So, instead we’ve decided to create this Update Post.

The idea is, whenever we make a significant update, to a WitCH or whatnot, we’ll record it here, with an indication of the update and a link to the original post. Then, at least there is just the one spot to check. The first such update is below.

Please tell us in the comments why this is a stupid idea, and let us know your superior ideas.

(22/09/21) The posts on the 2021 NHT exams, here and here, have been updated, with minor comments on the examination reports. There are also brief updates to the associated WitCHes, here and here.

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A Quick Word to Networking Mathematicians

Dear mathematicians, if you don’t really know about the draft mathematics curriculum, and if you are somehow unaware that the inclusion of new content that you happen to like necessitates the dilution or elimination of other content – content that is more important for everyoneand for a coherent curriculum, and which is already woefully underrepresented – then perhaps you should look beyond your own self interest, shut the hell up and listen to people who have been paying attention. Thank you.

ACARA Crash 18: Errors in the Draft Mathematics Curriculum

The following is a list of errors – and possible/arguable errors – in the draft mathematics curriculum. Commenters are invited and encouraged to suggest additions, and deletions.

By “error” we mean a statement or instruction that is factually wrong or that makes no logical/mathematical/everyday sense. Some of the listed “errors” are clear-cut, while others are less so. Of course the fact that a statement/instruction made no sense to us does not prove that it makes no sense; we’ve attempted to be fair, being tough on the improper use of technical terms while giving weird phrasings a good-faith pondering in context. Nonetheless, there may well be reasonable interpretations that we have missed. (Of course phrasing that is difficult to interpret has no place in a curriculum document, but that is a separate category of sin.) As well, it is not always clear whether to characterise a statement as an error or simply a really dumb idea, but we’ve tried to stick pretty closely to “error”, leaving the noting of really dumb ideas to our other ninety-eight posts.

The list follows. The majority are elaborations. There are a few content descriptors, for which associated elaborations are indicated by a further indentation. Again, commenters are encouraged both to suggest additions to the list, and to argue for deletions from the list.

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Maths Experts Do Not Reaffirm Support For Curriculum Changes

A few weeks ago, the Sydney Morning Herald published a report by Lisa Visentin and Anna Prytz, with the pithy title,

Maths experts reaffirm support for curriculum changes as leading group sounds alarm

The “leading group” refers to AMSI, which indeed sounded the alarm, calling for a halt of ACARA’s review of the mathematics curriculum. The claim, however, that “maths experts” reaffirmed support for the curriculum changes is, in a word, bullshit. Obviously AMSI did not do so, but also, to a reasonable approximation, no one did.

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ACARA CRASH 17: Algebraic Fractures

The following are Year 10 Number-Algebra content-elaborations in the current curriculum:


Apply the four operations to simple algebraic fractions with numerical denominators


expressing the sum and difference of algebraic fractions with a common denominator

using the index laws to simplify products and quotients of algebraic fractions


Solve linear equations involving simple algebraic fractions


solving a wide range of linear equations, including those involving one or two simple algebraic fractions, and checking solutions by substitution

representing word problems, including those involving fractions, as equations and solving them to answer the question

And what does the draft curriculum do with these?


And, why?

Not essential for all students to learn in Year 10.

God only knows how one develops fluency with expressions that cease to exist.

ACARA CRASH 16: Unlevel Playing Field

Each Year’s content in the draft curriculum begins with a Level description, and each of the thirteen Level description begins with the exact same sentences:

The Australian Curriculum: Mathematics focuses on the development of a deep knowledge and conceptual understanding of mathematical structures and fluency with procedures. Students learn through the approaches for working mathematically, including modelling, investigation, experimentation and problem solving, all underpinned by the different forms of mathematical reasoning. [emphasis added]

Yep, “an equal focus on building fluency“, no doubt about it.


ACARA CRASH 15: Digital Insertion

Continuing to try to rid ourselves of ACARA irritants, the following are the “calculator” elaborations from Year 1 – Year 6 Number and Algebra (sic):


using the constant function on a calculator to add ten to single digit numbers, recording the numbers to make, show and explore the patterns in a 0 – 100 chart

with the use of a calculator, exploring skip-counting sequences that start from different numbers, discussing patterns

modeling skip counting sequences using the constant function on a calculator, while saying, reading and recording the numbers as they go

Continue reading “ACARA CRASH 15: Digital Insertion”

One Week to Email Submissions on the Draft Curriculum

Submissions on ACARA’s draft mathematics curriculum close next week, on July 8, And, note, you do not have to use ACARA’s sheep-herding submission form. You can email your comments to ACARA, via the yellow “Email submissions and comments” button, near the bottom of ACARA’s consultation page. (We could include the email link here, but somehow that feels incorrect.)

Should you submit something? Yes, you should, for the same reason that you should vote against ScoMoFo in the next election. The point isn’t that your action is likely to change anything; the point is that it feels good. So, if it feels good to simply submit the open letter, then do that. But you should submit something.

Not convinced? Then maybe the following will help convince you. ACARA’s consultation page encourages feedback with the following line:

The online survey includes open fields to allow you to provide general comments about what you think we have improved and what you think needs further improvement.

So, either 1) what they’ve improved, or 2) what needs further improvement. On the off chance you believe something might fall into a third category, perhaps you might want to let ACARA know about it.