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.

**BACKGROUND**

*On 12 June 2020, Education Council tasked ACARA to undertake a review of the Australian Curriculum for Foundation to Year 10 (F-10) … ACARA will work in close consultation with the profession and key stakeholder groups … *[emphasis added, here and throughout]

Absurdly, nothing in the ToR indicates the “profession” that was to be “closely consulted”. Certainly, mathematicians were not closely consulted, or consulted at all, either as members of a “profession” or as a “key stakeholder group”, a phrase repeated ad nauseam. For reviewing the mathematics curriculum at least, ACARA worked overtime to “consult” with education-aligned mates, and only with education-aligned mates.

**AIM**

*The review will aim to improve the Australian Curriculum F-10 by refining, realigning and decluttering the content of the curriculum*

Somehow, all this “refining” and “decluttering” has increased the current curriculum’s 73 pages to the draft’s 159 pages. Any more refining and decluttering and the thing will have to be published as a multi-volume set.

The draft is a bloated, ideologically driven mess, but the draft also violates the ToR in a much more important manner. The stated Aim is self-evidently modest, effectively an instruction to tidy things up. Which does not remotely resemble what ACARA has done to the mathematics curriculum. There is also absolutely nothing in the Aim, or anything in the Terms of Reference, that gave ACARA the license to undertake such a radical overhaul. ACARA simply ignored the clearly stated Aim of the curriculum review.

*Specifically, the review will:*

*a) refine and reduce the amount of content across all eight learning areas of the Australian Curriculum F-10, with a priority on the primary years, to focus on essential content or core concepts*

To the extent that this is true, it is absurd and a disaster. There has been no reduction in the pointless, endless pseudo-real-world nonsense; the very opposite has occurred. What has been reduced is attention to the proper development of fundamental knowledge and skills.

*b) improve the quality of content descriptions … by … ensuring consistency and clarity of language and cognitive demand*

This is false, amounting to farce.

*c) rationalise and improve content elaborations, ensuring … the most authentic ways to treat general capabilities and cross curriculum priorities …*

Whatever “rationalised” is intended to mean, it hasn’t happened. The current curriculum has 421 elaborations; this has been “rationalised” to the draft’s 1132 elaborations, many of which are pointless, or much worse.

**PRINCIPLES**

*the learning areas of Mathematics and Technologies will be prioritised in the review timeline*

This is unclear, but “prioritised” cannot mean “do whatever the hell we want, and ignore the rest of the Terms of Reference”.

*content changes will be made by subject matter experts and …*

Evidently, they were not. It is unclear how ACARA interprets “subject matter experts”, or the nature and the extent of the role of these supposed “experts”, but the resultant product exhibits anything but mathematical expertise.

**LEARNING AREAS: CONTENT**

*Content descriptions specify the knowledge, understandings [sic] and skills that young people are expected to learn*

The problem is, ACARA’s “understandings” are absurd, and they swamp the knowledge and skills.

*The review will look … to focus on the development of foundational literacy and numeracy skills and personal and social capability in the early years.*

A “focus” on “foundational numeracy” that removes counting backwards and telling time to the half-hour. All this “foundational numeracy” seems to amount to playing with blocks and coins for three years.

**LEARNING AREAS: ELABORATIONS**

*Content elaborations are optional elements … they provide teachers with suggestions …*

ACARA manipulates the “optional” aspect of the elaborations into an all-purpose and unassailable argument that ACARA can do whatever they damn well please with the elaborations and no one has grounds to object. The argument is offensive and absurd. It is absurd to include hundreds of elaborations to “model” and to “explore” and to “investigate” and then proclaim, with Snow White innocence, “Oh, they’re just suggestions”.

Moreover, the Terms of Reference explicitly deny ACARA a free hand to write whatever they please:

*The review will look to*

*a) reduce the number of content elaborations …*

As noted above, the the number of elaborations has been “reduced” from 421 to 1132. ACARA has blatantly violated the terms of reference.

*b) improve the quality of content elaborations ensuring they … they make the content descriptions … accessible and meaningful to teachers and provide illustrations and suggestions of how to program and teach the content*

Similarly, this guideline, has simply been ignored. Most of the elaborations are poor. Specifically and much worse, the vast majority of the elaborations provide no guidance on *teaching* the content or mastering the skills. Rather, the elaborations indicate how to *apply *the content and, much more often than not, by way of aimless and valueless real-world exploration. There is very little genuine elaboration of teaching unless, that is, one regards the exploration nonsense as a way to “teach the content”. Which of course ACARA does, again while affecting Snow White innocence. The changes to the elaborations blatantly violate the Terms of Reference, and they are a recipe for disaster.

**APPROACH**

*ACARA curriculum officers will lead the review process in each learning area, engaging a small team of subject matter experts and practitioners to assist in the content refinement.*

As we have noted above, whatever team ACARA engaged and however it engaged them, it did not in effect include “subject matter experts”.

*Meaningful consultation with jurisdictions and teachers will be key to the review process.*

But not with mathematicians.

*ACARA will establish two new reference groups for each of the eight learning areas as the formal mechanism for consultation and feedback throughout the review process:*

*a) A teacher reference group, made up of practising primary and secondary teachers nominated by state/ territory education authorities and the non-government sectors, to provide practitioner feedback on content changes*

*b) A curriculum reference group, made up of learning area curriculum officers/specialists from state/ territory education authorities and the non-government sectors, to provide jurisdictional advice and feedback throughout the review process.*

Neither of which contains a single mathematician.

ACARA’s F-12 Curriculum Reference Group will be the key advisory group …

But of course. Apparatchiks are the keystone to a strong mathematics curriculum.

*Subject matter teacher professional associations, teacher unions, academics, principal and parent groups and other key stakeholder groups will be extensively engaged and consulted throughout the review process in a range of ways appropriate to each learning area.*

It is not clear whether “academics” refers to mathematicians or mathematics education academics. In any case, mathematicians as a “key stakeholder group”, or otherwise, were not “extensively engaged and consulted”. They were consciously and systematically ignored.

The Terms of Reference written by ACARA gave themselves the license to wholesale ignore proper academic input. The grotesque progeny of such incestuousness was entirely predictable.

**TIMELINE**

*The review will commence in 2020 following Education Council’s agreement to the terms of reference, and the review of all learning areas will be completed by the end of 2021 …*

So, like the Doomsday Machine in *Dr. Strangelove*, the draft curriculum will be released on schedule, no matter how appalling it is and no matter the havoc it will wreak.

ACARA, while ignoring its own systemic violation of the Terms of Reference, has claimed powerlessness in the face of the timeline, as an excuse to completely ignore mathematicians and ministers, and to plow ahead. It is hypocritical and it is obscene.

Part of this seems like typical public service stuff – documents get longer with each “revision” and perhaps as a consequence, less people read them in their entirety, save a few quality journalists who will then get accused of being “too left-leaning” or “too right-leaning” by some other media organisation or publication… and the cycle continues.

But as an aside to all of that, what (and I pose this question to all readers who are willing to offer an opinion) is ACARA’s REAL agenda?

ACARA’s real agenda is to implement a numeracy curriculum, which is then to be taught by enquiry.

What the hell is numeracy?

(Maybe that is a redundant question)

Numeracy is applied mathematics.

In the draft curriculum for “Foundation pathways certificate: Numeracy” the definition used by VCAA is similar-but not as succinct.

BTW, I did not know about “systematics” before I read this draft for Foundation pathways … but I am new to the area.

Define “is”.

“Numeracy is applied mathematics”. Interesting, but I’m not convinced.

The examples of “numeracy” I see in things like PISA tests are contrived examples at best, and so if they are “applied skills” they are:

1) Applying a redundant skill

or 2) Testing the application of said skill in an often meaningless way.

Fundamentally, I cannot accept that numeracy is applied Mathematics because, to me:

1) Applied mathematics IS mathematics

And 2) Numeracy is not.

Let me explain what I mean by saying that numeracy is applied mathematics.

I have looked at many attempts at defining numeracy, and the one thing they have in common is that numeracy deals with applying mathematics. So I decided that numeracy is applied mathematics.

This will not be to everyone’s taste. For example, some will see applied mathematics as dealing with using differential equations to model certain phenomena; it does not deal with figuring out the new price of a t-shirt when a 10% discount is applied. To be sure, some applications require more sophisticated mathematics than others, but they are all applications of mathematics.

Arithmetic is part of mathematics. Preparing a meal for 3 people from a recipe for 4 people that uses imperial units requires the application of mathematics.

I suspect – but this is just my theory – that the word “numeracy” has taken off to avoid using the word “mathematics”. Mathematics is hard; we don’t want to put people off; numeracy is for everyone and should be easy.

I hope that this clarifies my point of view.

First of all, it is much more accurate to say numeracy is trivial applied mathematics, and probably even more accurate to describe it as trivial applied arithmetic.

Secondly, you, just now, pinpoint why the term “numeracy” is so insidious, and why blithely writing “numeracy is applied mathematics” is obtuse, and asking to be whacked.

“Numeracy” is supplanting mathematics. Primary schools don’t have mathematics lessons or arithmetic lessons anymore, they have numeracy lessons. Some of this is because “mathematics” and “arithmetic” are dirty words, but it is not simply a matter of changing the name. They are changing what is taught, and how it is taught.

Numeracy is poison and “numeracy” is poison.

That’s where 12 years of childminding will get you. It’s still trivial.

That’s also what happens when VCE financial maths = put everything into the TVM solver on CAS and push Enter. The only thing for which this is “preparing” students is how to use “home-loan calculators” (ie. TVM solvers) on bank websites.

Prospective teachers should know the meaning of numeracy. Almost every teaching position, in any area, in Victorian government schools requires that the applicant has “the ability to incorporate the teaching of literacy and numeracy skills”. Applicants are expected to address this criterion.

Some senior positions that involve numeracy – which are often based on substantive permanent positions – have as a KPI “improvement in NAPLAN data for numeracy” or something similar.

The state government’s concern with numeracy is the driving force behind “Foundation pathways certificate: Numeracy”.

I don’t defend any of these things – far from it – but they are part of the current climate.

Terry, what tends to concern you is pretty eccentric.

Does “the review of all learning areas will be completed by the end of 2021” really mean that a new curriculum must be in place for the start of 2022? ACARA is drawing a very long bow by claiming that this is the case. Completion of review Implementation of new curriculum.

All the people responsible for the current farce should be told by the Minister to sod off and never go near a curriculum document ever again. ACARA have clearly failed to deliver a product that is fit for purpose. But the people responsible should be told to sod off for the simple and demonstrative reason that they failed to work within the Frames of Reference. Significantly INcreasing clutter Decluttering.

It’s hard to imagine ACARA being responsible for doing a worse job, but I’m sure it will give it the old college try if and when the time comes.

There are two possibilities here:

1. The new curriculum has already been decided, textbook publishers have been told all the fine details and new books will conveniently be ready for the 2022 school year.

2. The review will be completed but not made public until goodness knows when.

Both are worrying.

1) Any “new curriculum [that] has already been decided” and “new books [that] will conveniently be ready for the 2022 school year” will be useless if schools unite and refuse to follow it or to use them.

That will make the publishers smile.

Publishers can always show some moral courage and refuse to commission the writing of any textbook based on such a dodgy curriculum. And schools can grow a pair and refuse to teach from a dodgy curriculum. Where then would that leave ACARA? Back to the drawing board …?

There’s nothing more stupid than stubborn and unyielding stupid.

2) Nothing to worry about here if “goodness knows when” is NEVER.

As much as I would love to see schools taking some sort of unified action… can’t see it happening.

I recall when the heads of private schools maths group sent a joint letter to VCAA (2014ish) someone who will remain nameless sent a polite reply saying that we were not representative and pretty much ignored what we had to say.

Publishers have morals…?

Maybe the group should have demonstrated to Mr Nameless exactly how representative it really was. Make it too hard to be ignored … A lot of the trouble is that teachers are too often too nice instead of being bastards and going for the throat. Toerags like Mr Nameless count on it.

There is a saying in the Freemasons: There are circles within circles.

I suspect (but cannot prove) that within the group of heads of mathematics there is a smaller and better connected group that wishes to stay well connected to key VCAA figures and as such tries very hard to not piss them off.

Of course, if this is done without the knowledge of the larger, encompassing circle…

And Mr (or Ms) nameless is only such because I wasn’t told exactly who “they” were who had authored the reply.

Meh.

RF, I think your suspicions are entirely plausible. And it’s those gutless inner circle sycophants that prevent VCAA being held to account for its mistakes and deceptions. And its frustrating lack of leadership in recent times. And its total lack of understanding or empathy with what all VCE teachers continue to grapple with.

Those clowns are probably still wringing their hands over their precious GAT … An on-going debacle created when some idiot blinked a few months ago and re-scheduled it (the first of several re-schedulings). It is very unfortunate that there are some very incompetent individuals responsible for very important things. We all suffer the consequences of their incompetence (but I doubt there are any consequences for them).

Just suppose Marty is correct in his theory about what ACARA is trying to achieve (I’m not for a moment saying I disagree, but again, proving it will be a WOFTAM) in creating some “inquiry based learning” curriculum, is this because:

A) Mathematics Education “experts” (possibly self-declared) say this is a good idea.

B) Because some other country has proven the success of such an approach.

C) It creates a second gravy-train of PD opportunity (the current PD gravy train I would suggest has reached standing-room only status)

D) Some combination of the above.

A and C. And of course I am correct. It is entirely obvious, and ACARA have all but admitted it. They’re proud of it.

Indeed. And it will be a disaster. Again. And when this is realised, history will repeat itself. Again. I don’t understand why the imbeciles who create these messes continually get called in to ‘fix’ things. Since the current review is meant to ‘fix’ the mess of the previous review, the first thing that should have happened is that all the idiots responsible for the last review should have been sacked.

However, this would probably only result in new idiots being brought in, freshly picked from the idiot-tree (it bears fruit loops all year round and grows on special government plantations). For all we know, this is exactly what has already happened.

I have never had an issue with my failure to succeed at competitive sport or recreational card games, mostly because I could understand the rules required to play the game (even if I lacked the skills or motivation) and there were plenty of people available to give clear and consistent answers any time I queried a rule.

Teaching, and specifically teaching Mathematics in VCE, seems to have become more and more of a game. Except, in this case, I don’t understand the rules and any attempt to clarify them is met with contradictory “advice”. SACs are a good example, the inclusion of “normals” in Methods 3&4 is another.

Now, I’m willing to admit there are multiple possibilities here:

1. I don’t have enough experience or knowledge to properly understand the “rules”. OK, would be fair if I hadn’t completed a teaching degree or two that the “umpires” seem to regard as sufficient preparation to play the VCE teaching game and have been a teacher for half my life.

2. I haven’t asked the right people. OK, so when you “meet the examiners” and ask questions, these are not the right people?

3. The “rules” are not meant to be taken as strict rules, but more as guidelines. OK, so why do SAC audits penalise teachers and schools so heavily?

If ACARA starts to audit the 7 to 10 curriculum in any way similar to how VCAA audits SACs I dread to think what might happen.

RF, unfortunately teaching VCE mathematics a game. It’s a game where some of the rules are

1) vague, and/or

2) only revealed to a select few (the assessors, sworn to secrecy)

1) I’m sure this is intentional – in a given year VCAA doesn’t want to be bound by explicit rules. It wants the flexibility to change it’s mind and argue ‘interpretation’. It wants wriggle room to justify incompetency.

Some examples among legion:

a) The inclusion of the binomial distribution on the 2021 Specialist Maths NHT Exam 1.

b) Whether or not to substitute g = 9.8 into an answer involving g when the question does not say one way or the other.

2) Some examples among legion:

a) For quite a while, only assessors knew that answers such as 3/27 or 0.3/2.7 were unacceptable even though they are numerically equal to the ‘required’ answer of 1/9. None of the questions specified this form of answer, despite VCAA’s proclivity to do so in other questions. No advice was given in the VCE Bulletin. None of the Examination Reports mentioned this until quite recently. Up until then it was a deliberate secret.

b) When the equation of a line is required but the form is not specified, VCAA requires the y = mx + c form. The common slope-point form y – y1 = m(x – x1) is not acceptable. AFAIK this is still kept a secret – there is no official explicit statement anywhere.

c) If an exact answer is required but the form is not specified, an exact answer is required. Mixing a surd with a trigonometric value (eg. Sqrt[3] Sin[150 degrees]) is not acceptable. AFAIK this is still kept a secret – there is no official explicit statement anywhere. In fact, the Examination Report deliberately misleads one into thinking that such an answer acceptable. See VCAA 2008 Specialist Maths Exam 1 Question 7. To this day, only the assessors officially know that a answer found using Lami’s Theorem was not acceptable.

I can only speculate that VCAA is deliberately deceptive and evasive about things like this because it wants to encourage teachers to be assessors and getting told stuff like this in confidence is the bait.

Maybe there could be a blog that ‘outs’ this stuff so that every teacher has a chance to compete on a level playing field.

It’s a great shame that VCE is, practically, the only game in town. Because no-one would play if there was a cheap viable alternative.

Lami’s theorem is in textbooks and in a not insignificant number of cases it is an efficient approach. Much more-so than triangulating the forces (although F&G I’ve noticed do use the triangulation method); almost every physics teacher I know thinks this is a crazy method and would much prefer we all stuck to resolution into parallel and perpendicular components.

As for the answers… the sine of 10 degrees is exact. We all know this.

Surds in denominators (AFAIK) are permitted in SM but not MM exams. So we cannot even say that VCAA is internally consistent!

There no internal consistency. And explanation for this.

Another example to add to yours: There are less strict requirements in Specialist than in Methods for simplifying answers – so I’ve heard. This is consistent with your surd example, but seems contradictory in light of the ‘to substitute or not to substitute g = 9.8 and simplify arithmetically’ ambiguity.

I don’t understand why things like “Surds in denominators … are permitted in SM but not MM exams” is kept a secret. I can only speculate. Keeping the ‘rules of the game’ a secret is a total disgrace by VCAA – one day VCAA will be lined up against the wall because of it.

It’s a total disgrace that – unlike NESA – VCAA keeps its marking schemes secret. The logical conclusion is that its marking schemes cannot withstand close scrutiny and therefore VCAA has something to hide.

I’m not a huge fan of the NSW HSC exams (but will openly admit the timely release of papers and marking guides is a huge argument in their favour). They are good enough in and of themselves, but they seem to over-emphasise certain skills (yes, VCAA is guilty of this in a major way as well).

I do miss the IB days; particularly the way the syllabus actually declared the weighting of different topics – calculus at SL was (in 2000ish) meant to be given 36 hours of teaching time compared to 10 hours for matrices and the exams reflected this weighting (although vectors were often the “tough” marks).

ACARA though is not about making a product that people want to buy; which explains many things but not everything.

What, for example, is the big appeal of “inquiry-based-learning”???

The move to include 2 week investigations in VCE units 1&2 seems to be related to this and not in a small way.

Unless I’m seeing a pattern which is not there (it has been known to happen…)

Inquiry-based learning. Investigations. Etc. This is the latest snake-oil being sold. There are many eager buyers. In a couple of years, when things need fixing (yet again!!!), there will be more snake oil on sale. And no shortage of buyers. Reputations are made selling snake-oil. Not to mention buckets of money.

A short story by Phil K. Dick comes to mind – A Game of Unchance ( https://theworlddickmade.com/a-game-of-unchance/ )

At the end of the day, most teachers don’t give a shit (for a variety of reasons including apathy, more pressing priorities, FOMO and just plain stupidity). That’s why the snake-oil sellers are still in business. And that’s why they’ll remain in business. As a population, teachers are simply a mob of sheep. Easy fodder for the con artists.

“Mob of sheep” is a tad harsh.

In Years 11 and 12, schools, parents, and students expect that teachers will prepare students for the examinations.

At lower levels of high school, teachers strive to ensure that their students will be well-prepared for Years 11 and 12.

It appears to me that VCE examinations are the major force for what happens in the classroom – although that force diminishes as you move further away from year 12.

Furthermore, there are often many mathematics classes at the same level (e.g. Year 9 or Year 11 General Mathematics) and, not unreasonably, teachers stay in step according to an agreed plan of work.

Sounds like sheep to me.

@JF above: I have had the experience of students at university complaining to me about the form of a linear equation as y = a+bx. “We were told at school by our teacher, that the formula is y=mx+c. Why don’t mathematicians make up their minds?”

I am pleased to report that, at one of the schools where I am teaching, this matter is clarified at Year 8.

Thanks, Terry. Your experience is unsurprising and not singular. I won’t ask in what course this occurred (I’m guessing related to the biological sciences, which in my eyes mitigates the experience). But I would suggest that it’s indicative of entry standards universities have set themselves (in the quest for money. Students are cash cows. Some more so than others. Although the more so is less so these days). And I would suggest that the last few years will exacerbate such experiences. University Faculties (Science, Engineering, …) mewl about how they have to run various 1st Yr remedial subjects, and yet take no responsibility for the standards they’ve set that have led to the necessity of such subjects.

RF, I would say A is most likely. (And to a certain extent I think they are unduly influenced by all those people – who often do not work in mathematics or education – who blame difficulties in mathematics on (i) a lack of “real-world applications” and (ii) being expected to do so much practice of basic knowledge / skills.)

But just on B, Greg Ashman has some posts worth reading about Finland (which is really the main example used here, the SE Asian success stories being completely ignored), on the old version of his blog:

The comments also include some links worth following up on.