## WitCH 61: Wheel of Misfortune

We decided ACARA’s psychedelic circle, which we discussed briefly here, was worthy of its own post. So, apart from the potential to trigger an epileptic fit, what is wrong with ACARA’s wheel?

ACARA labels their wheel as depicting

[the] relationship between the six strands and three core concept organisers

The six strands make up the inner wheel, and are explained here (pages 4-5). The three “core concept organisers” are the three colours on the wheel rim, with the categories and subcategories as pictured below, and which are explained here (pages 5-8).

## How Do You Solve a Problem Like ACARA?

When I’m with them I’m confused
Out of focus and bemused …

That’s pretty much it, except for the “bemused” bit. But our cheap-joke title is also asking a genuine question: what does ACARA think is the essence of “problem-solving”? How do you solve a problem like ACARA (does)?

The answer is a classic bait and switch; the bait is Singapore, and the switch is to “inquiry-based learning“. Here is ACARA CEO, David de Carvalho, in a recent report (Murdoch, paywalled):

However, Mr de Carvalho said problem solving was at the core of the curriculum in Singapore, whose students consistently topped the global education rankings, …

There is plenty more, similar bait in ACARA’s comparative study of Australia and Singapore (discussed here and here). So, let’s take a closer look at the bait, at the problem-solving “core” of Singapore’s mathematics education.

A “problem” in mathematics can mean many different things. In particular, a problem can be absolutely routine, what would normally be referred to as an “exercise”, and is there for the practice of basic skills. But not all exercises are routine. An exercise may require more care in setting up, or involve nastier numbers entailing trickier computation, or more subtle manipulations of the equation(s). It is still an “exercise”, in the sense that it is there primarily there to test and to practise specifically chosen skills, but it can be a hard exercise. It may stretch the student, but within clearly defined parameters, with the required facts and skills clearly understood.

At some point such hard exercises would more naturally be called “problems”. If they’re sufficiently difficult you might call them “hard problems”. But none of that changes the essential nature of these exercises/problems, that they’re there for the testing and practicing of clearly defined facts and skills. And, in that way, these problems presume some prior mastery of those facts and skills. The harder the problem, the greater the mastery presumed.

This is the way to understand “problem-solving” in Singapore’s mathematics education. We have more to learn, but everything we have found so far points to exactly what one would expect: in Singapore, “problem-solving” largely amounts to the serious practicing of hard, up to very hard, exercises, based upon a prior mastery of fundamental facts and skills.

It is easy to get a sense of this simply by searching for “Singapore test papers”. This is one such site, and this is a Primary 6 test paper from that site. Not all the questions are hard, but they get plenty hard. Some of that difficulty is in the material being more advanced — Primary 6 students do a decent amount on rate and ratio problems, including some algebra — but that’s not the only reason. There is plenty harder, and the reader is encouraged to hunt, but here is a quick, telling example from the Primary 6 paper:

Which of the following fractions is nearest to 2/3?

1) 3/4         2) 5/6         3) 7/9         4) 1/3

That’s a Singapore maths problem. Just a fraction comparison question, but a hard fraction comparison question. You can’t possibly do the question quickly without being light on your fraction toes.

That’s the bait, Singapore’s problem-solving. And now, the switch: what does ACARA mean by problem-solving?

It is abundantly clear that ACARA’s notion of a “problem” is not remotely like Singapore’s focussed and difficult exercises. ACARA’s “problem-solving” is of a much more open-ended and exploratory nature. It is inquiry-based learning, with the little kids being intrepid little Lewises and Clarks. This is immediately clear from De Carvalho’s conscious decision to highlight a ridiculous “why”-hunting exercise, with the kids supposedly discovering Pythagoras for themselves.

It is also abundantly clear from ACARA’s documentation. Front and centre in the draft mathematics curriculum is the diagram below. It is one of the silliest, over-egged pieces of nonsense we’ve ever seen:

This craps smells very much of CCR. Whatever its origin, notice that at the bottom of the pretty blue list of “Mathematical approaches” is “problem-solving and inquiry”. This is then explained:

Problem-solving and inquiry – skills and processes that require thinking and working mathematically to understand the situation, plan, choose an approach, formulate, apply the relevant mathematics, selecting appropriate and efficient computation strategies, consider results and communicate findings and reasoning; Problem-solving and inquiry approaches that involve thinking and working mathematically include experimenting, investigating, modelling and computational thinking.

Ugh! But let’s go on.

ACARA is explicitly linking “problem-solving” to inquiry based learning, but it is worse than that. This problem-solving is more than an approach to the curriculum, it is the curriculum. From ACARA’s What Has Changed and Why:

The content descriptions and the achievement standards in the consultation version now explicitly include the critical processes of mathematical reasoning and problem-solving from the proficiency strands. This results in a mathematics curriculum that supports deeper conceptual understanding to make mathematical learning more meaningful, applicable and transferable to students. [emphasis added]

That is, “problem-solving”, meaning inquiry-based learning, is now to be part of the content of the Australian Curriculum. De Carvalho can claim that “ACARA is not making any recommendations about pedagogical approaches”, but his claim is clearly, ridiculously false. And here is the falsehood in the flesh. Here is just one of a zillion such content descriptions, this one from Year 2 Number:

model situations (including money transactions) and solve problems involving multiplication and division, representing the situation as repeated addition, equal groups and arrays. Use a range of efficient strategies to find a solution. Explain the results in terms of the situation

This is garbage and, with absolute certainty, it is not Singapore.

What is Singapore doing while Australia is playing these idiot inquiry games? The students are learning their damn multiplication tables, so they can go on and do Singapore problems. Problems worth doing. Problems that the vast majority of Australian students haven’t a hope of being able to do.

It is a blatant and insidious lie to claim that ACARA’s problem-solving push in mathematics is even remotely like Singapore. And it is a hugely damaging lie. Inquiry-based learning is a disaster; it is already here in Australia and it is already disastrous. As we have written elsewhere, the poor kids aren’t Lewis and Clark; they’re Burke and Wills. They don’t have a chance in hell of getting anything solid, of retaining anything from these aimless treks.

Does one need a proof that inquiry-based learning is a disaster? No. It is obvious on its face, to anyone with any decent understanding of what mathematics is and how children learn. But, for anyone who needs a proof that dumb is dumb, Greg Ashman has written an excellent post on ACARA’s Singapore nonsense and the evidence for the failure of inquiry-based learning.

ACARA are bait-and-switch swindlers and swill merchants, and they should be disbanded. That’s how to solve a problem like ACARA.

## De Carvalho, AMSI and that Other Singapore

Sigh. So much crap …

This one is even more brazen than Chico. It’s more like

Who are you gonna believe, me, or your own eyes and me from two minutes ago?

Rebecca Urban, The Australian‘s education reporter, is notable for her poor stenography skills. Urban has this peculiar habit of not simply buying and then repeating unchallenged a formal authority’s propaganda. Urban’s strange style was on display yesterday, with a report on the Daft Australian Curriculum: Curriculum changes to maths and science are not adding up to success (Murdoch, paywalled).

Urban reports and pushes back hard on ACARA’s problem-solving crusade, this crusade of course in no conceivable manner contradicting David de Carvalho‘s statement that “ACARA is not making any recommendations about pedagogical approaches“. Urban quotes a number of people to query De Carvalho’s nonsense, including Greg Ashman, who is always worth reading and is always too polite. Ashman has a very good and, for him, very snarky post on the Daft Curriculum, and there is probably more to come.

Pretty much everything De Carvalho is quoted as saying in Urban’s report is nonsense, But there is one particular line that rises above and beyond the Chico level of gaslighting:

However, Mr de Carvalho said problem solving was at the core of the curriculum in Singapore, whose students consistently topped the global education rankings, …

Singapore, huh? Well, David, we’ve looked at Singapore, and we’ve also looked at your looking at Singapore. So, we’re sorry, but we’ll choose to believe our own eyes, and that other you from two minutes ago.

Here is what you, ACARA, wrote about Year 6 mathematics in your Australia-Singapore comparative study (p 77):

The [Singapore syllabus] builds on the depth and fluency of Mathematics established in previous years. For example, operations with decimals are considered complete and time is given to completing mastery of the four operations with fractions without the use of calculators. … The comprehensiveness of the problem sets offers Primary 6 students a sense of mastery and confidence in applying Mathematics in useful ways. [emphasis added]

There is plenty more: the comparison of the earlier years is hilarious, as long as you appreciate black humour. Does Singapore do problem-solving? Sure, lots, at least of certain, specific types. But it is absolutely clear to anyone with eyes — or anyone who reads ACARA’s literature with sufficient thoroughness and thought — that Singapore’s problem-solving is built upon a really solid grounding in arithmetic and algebraic facts and skills, a grounding that Australia simply does not offer and is looking now to undermine further.

Urban quotes Fiona Mueller, former Director of Curriculum at ACARA, to counter De Carvalho’s Singapore nonsense. There is also, however, one person Urban quotes supporting ACARA’s Daft Curriculum, and this is well worth noting:

Australian Mathematical Sciences Institute director Tim Marchant backed the changes.

“Adjusting the curriculum to focus on problem-solving is crucial to improve their skill sets and deliver students that are able to take knowledge and apply it to solve challenges,” Professor Marchant said.

That is Professor Tim Marchant, Director of the Australian Mathematical Sciences Institute there, claiming problem-solving is the “the way to improve [students’] skill sets”.

What can one say in the face of such ignorance? Just, as usual, the Evil Mathologre is correct.

## Being Carvalho With the Truth

There are bigger, stupider fish to fry, but this also needs to be done, and it’s now or never.

Earlier this week, David de Carvalho, the CEO of ACARA, gave a speech at The Age Schools Summit. flagging the Daft Australian Mathematics Curriculum (the spelling is correct). Our most recent WitCH is based on an excerpt of de Carvalho’s speech, but the entire speech — also condensed to an op-ed — is worthy of scrutiny. And so, here we are.

Below are parts of de Carvalho’s speech that relate in some manner to the mathematics review, followed by our, mostly redundant, comments. What de Carvalho says is clear, and clearly ridiculous.

The data that we get from NAPLAN is important, but it is not a measure of overall school quality, and we need to remember that education is a complex multi-dimensional process where improvement does not rely on the rationalistic analysis of data and the application of associated managerial techniques.

“Rationalistic” is now a boogie-man word? That’s where we are? And once again, we have this idiotic selection: NAPLAN or touchy-feely. A pox on them both.

For the thousandth time, NAPLAN is garbage. Numeracy is garbage. And, while we’re at it, PISA is garbage. If there were decent national tests of arithmetic and mathematics, these would be a godsend; the subsequent “rationalistic analysis” would do more than anything else imaginable to lift Australian mathematics education. But, of course, courtesy of two very poxy houses, there’s not a snowflake’s chance in Hell of this occurring.

This is because the essential nature of education is that it involves a sense of historic continuity and conversation between generations, between teachers and their students, where a learner is engaged in the process of becoming a well-rounded human being …

This conversation between the generations is the basis of the curriculum.

An A+ for irony. If there is one central theme to the now decades of destruction to Australian education, it is an utter contempt for the past, the active denigration and wilful forgetting of Australia’s one-time educational excellence.

Up to now, we have been working with 18 teacher and curriculum reference groups established to support the review, made up of 360 teachers and curriculum authority representatives from across Australia, as well as consulting with our peak national subject bodies and key academics. I’ve also had discussions with the staff from 24 primary schools across the country.

That’s a lot of people. What could go wrong?

But on Thursday, we begin public consultations on the proposed revisions to the Foundation to Year 10 Australian Curriculum.

No, you aren’t. You are permitting people to fill in a survey, which, presumably, will never see the light of day. In no manner does this sham hold ACARA publicly accountable to publicly available opinion.

I’ve heard some stakeholders say that we should be “taking a chainsaw to the curriculum”, but chainsaws are not particularly subtle, and can leave an awful mess behind.

What is currently wrong with the Australian Curriculum is also not subtle. We’d go for dynamite, but a chainsaw would do in a pinch.

We need to avoid perpetuating a false dichotomy between factual knowledge and capabilities such as collaboration and critical thinking.

Yes, …

You can’t engage critically and creatively on a topic if you lack the relevant background knowledge …

Go on, …

So the ability to recall facts from memory is not necessarily evidence of having genuine understanding.

A very cute straw man, but please continue.

A student might, for example, memorise the formula for calculating the length of the hypotenuse if given the length of the other two sides of a right-angle triangle, but do they understand why that formula, known as Pythagoras’ theorem, works every time? The process of discovering that for themselves, with the assistance of the teacher, is what makes learning exciting. And it’s what make teaching exciting. Seeing the look of excitement on the face of the student when they experience that “aha!” moment.

Ah, so that’s what you’re getting at. You nitwit.

This example is so monumentally, multidimensionally stupid, it has its own post.

Some learning areas have only required some tidying – but others have required more focus. Maths for example has required greater improvement and updating.

If we look at our PISA and our TIMSS results, Australian students are not bad at knowing the “what”, but we are not as strong at “why” of mathematics, …

This is, to use the technical term, a fucking lie. It is an absurd, almost meaningless dichotomy. And you forgot the “how”, you idiot. But in any case Australian students absolutely suck at the “what”, and the “how”, and ACARA damn well knows it.

This is THE lie. This pretence, that Australian maths students are doing just fine on the basic knowledge and skills, is why it is absolutely impossible for ACARA to revise the mathematics curriculum in a meaningful manner. This is why, without even needing to read it, you know the Draft Curriculum is a farce.

… this joint statement from five of the leading maths and science organisations in the country is an indication of the level of interest out there about the curriculum.

Yep, “five of the leading maths and science organisations” can endorse this poisonous twaddle. That’s where we are.

Again – knowledge and capabilities being acquired together.

Mate, it doesn’t work that way. More often than not, and particularly in primary school, your precious “capabilities” are just getting in the damn way. You can wish it all you want, but learning mathematics just doesn’t work that way.

It should be noted that the current Australian Curriculum in Mathematics already includes four Proficiency Strands: understanding, fluency, problem-solving and reasoning. The issue has been that these proficiencies have not been incorporated into the Content Descriptions, which is what teachers focus on.

So the major change we have made in the proposed revisions to Maths is to make these proficiencies more visible by incorporating them into the Content Descriptions.

In other words, you are changing the Curriculum content, and you are pretending that these changes are simply an innocent act of tidying up. Do you imagine anyone believes you?

It is also important to note that in proposing these revisions, ACARA is not making any recommendations about pedagogical approaches.

So that Pythagoras nonsense back there was just for the Hell of it? There’s a technical term for this. What was it again?

I expect we will see a stirring of the passions.

So you’re ok with passions. How do you feel about white-hot fury?

No doubt some will argue the proposed revisions don’t go far enough, while others will say they go too far, …

Of course it never crossed your mind that people might say, accurately, that you’re going in entirely the wrong fucking direction.

This discussion and civil debate is a good thing.

It is not a discussion, it is a fait accompli, and there is no benefit here in being civil. What is called for is complete and utter contempt.

## The ACARA Mathematics Draft is Out

ACARA’s draft Mathematics Curriculum is out. Feedback can be given, in the form of survey only, until July 8.

We have had no time to look at the draft, although of course we will. Our posts on the review literature leading up to this draft are here, here, here, here and here.

We’ll be interested in what people note in the comments below. Please try to keep the comments focussed on substantive criticism (or praise), rather than unanchored abuse (even if deserved). For now, what matters is the detail.

Here are the relevant documents and links, as far as we can see:

Again, we very much look forward to reading people’s comments. And, again, please keep it focussed. Comments may be about the curriculum generally, and of course may be critical, but should be dealing with the substantive issues.

## UPDATE (30/04/21)

Thank you to everyone who has commented so far, and please keep the comments coming. We’ll be reading with keen interest, and we’re definitely intending to go through the Daft Curriculum with a fine-tooth comb. However, won’t look to be posting further on the curriculum for at least a few days.

In brief, the ACARA literature marathon has exhausted us. Plus, the Evil Mathologre is breathing down our neck: a deadline for Son of Dingo is looming, and 200 mini-Mathologer essays are about to come crashing down, demanding to be graded.

We’ll end here with a genuine and very interesting question:

Will Alan Tudge take on ACARA?

The Minister for Education is clearly serious, if largely misguided, about raising Australia’s educational standards. And, in particular, Tudge is presenting himself as Mr. Back To Basics. True, Tudge has given no indication that he understands what “the basics” are, but it is in his sights. So, what’s he gonna do with the Daft Curriculum and the people responsible for it? Whatever the hell this curriculum is, it is decidedly not going back to the basics.

## WitCH 60: Pythagorean Construction

Yesterday, David de Carvalho, the CEO of ACARA, gave a speech at The Age Schools Summit. de Carvalho used his speech to set the stage for ACARA’s imminent launch of the draft of the revised Australian Curriculum. (See here.)

We shall take a more careful look at de Carvalho’s speech in the near future. For now, we’ll settle with a WitCH, an excerpt from de Carvalho’s speech:

“So the ability to recall facts from memory is not necessarily evidence of having genuine understanding.

A student might, for example, memorise the formula for calculating the length of the hypotenuse if given the length of the other two sides of a right-angle triangle, but do they understand why that formula, known as Pythagoras’ theorem, works every time? The process of discovering that for themselves, with the assistance of the teacher, is what makes learning exciting. And it’s what make teaching exciting. Seeing the look of excitement on the face of the student when they experience that ‘aha!’ moment.”

And when we understand a topic, it is easier to recall the facts because they are no longer just random bits of information but are organised into intelligible ideas. Not only do we know where the dots are, but we know why they are there and how to join them.”

### UPDATE (29/04/21)

Just a reminder, this is a WitCH. So, what specifically is crap about de Carvalho’s Pythagoras suggestion?

To guide the discussion, below is (arguably) the simplest, algebra-free proof of Pythagoras, which, undeniably, all students should see. Where does/should this proof fit in with the teaching of Pythagoras, and where does de Carvalho’s suggestion fit in with either of these?

### UPDATE (03/05/21)

It is extremely helpful of De Carvalho to have selected such a fundamentally flawed example. If he had chosen more judiciously it would be more work to counter, to make the case here against inquiry-based learning. De Carvalho having chosen almost an anti-example, however, makes clear that ACARA’s inquiry push is nothing like a reasoned best-choice approach in given situations, and much more a religious fundamentalism: inquiry is, simply by being inquiry, the preferred method.

De Carvalho contrasts the WHAT of Pythagoras — the equation — with the WHY, the proof (or proof-like evidence for) that equation. Putting aside for the moment De Carvalho’s atrocious suggestion for getting to the WHY, we’ll first note that De Carvalho has failed to ask two fundamental questions:

• HOW does Pythagoras’s theorem work?
• WHY2 do we teach Pythagoras’s theorem?

The first question is about the HOW of the mechanics of dealing with the equation : manipulating for the unknown, taking roots and so on. This HOW is not glamorous, and not intrinsically difficult, but it is fundamental. Of course the application of Pythagoras’s theorem, including the mechanics, is in the draft curriculum (beginning in Year 8), but De Carvalho’s casual airbrushing of the HOW is a tell.

(As  a side note, we’re pleased to see that the single stupidest line in the Australian Curriculum is still there, in the Pythagoras elaborations.)

And now, the second question: WHY2 teach Pythagoras’s theorem? There are two strong answers to this question, both of which, in different ways, demonstrate that De Carvalho has no understanding of his example.

The first reason, the WHAT to teach Pythagoras is because it is so important: it is the fundamental formula for distance in Cartesian (and Euclidean) geometry.

The second reason, to teach the WHY of Pythagoras’s theorem is because it is a historical icon and because it is so beautiful. The proof illustrated above is gorgeous, it can easily be learned by a primary school student, and it should be learned, by all students, as one learns a poem. (One can of course extend this to be a third reason, to teach other proofs and the nature of geometric proof.)

Here is why these reasons show De Carvalho’s example to be so empty:

• The two reasons for teaching Pythagoras are almost totally disconnected.
• Hunting for a proof is the absolute worst way to appreciate the beauty of Pythagoras.

Arguing for the WHY, De Carvalho notes,

And when we understand a topic, it is easier to recall the facts …

And of course, as a general point, De Carvalho is correct. In regards to Pythagoras, however, De Carvalho is simply wrong. Pythagoras is one of the easiest equations to learn, and students simply don’t need the WHY to know WHAT it is and HOW it works. Secondly, the WHY doesn’t help with the recall whatsoever. Pythagoras is a theorem about areas, and its application in school is always to distances. The idea that a longer proof about areas will help students recall and understand the use of a simple formula about distances is utterly ridiculous.

As for appreciating the beauty of Pythagoras: if you are given a beautiful poem then you simply teach the poem. It is absurd to think that De Carvalho’s “discovering that for themselves” — which, anyway, will almost certainly be faked — will give students any proper appreciation of Pythagoras. All it can do, and inevitably what it will do, is obscure the simple beauty.

There are zillions of examples of the WHY being critical to understanding the WHAT, and there are even examples where the WHY should replace the WHAT altogether. There are examples where a limited form of inquiry is worthwhile in discovering the WHY and the WHAT. Pythagoras, however, is none of none of these. Pythagoras is only an example of ACARA’s constructivist dogmatism, and of De Carvalho’s ignorance.

## Australia v Singapore

This post is on ACARA’s comparative study of the Australian and Singaporean curricula. It will be, thank God, our last post on the literature supporting ACARA’s curriculum review; previous posts are here, here, here and here.

As we noted, ACARA’s Key Findings document somehow concluded that the Australian Curriculum was broadly similar, in style and difficulty, to the four other curricula considered, including Singapore’s:

Evidence from these comparative studies identifies how high performing education systems are incorporating 21st century capabilities/competencies into their curricula. …

Recent developments in these curricula also include increasing emphasis on essential/core concepts at the expense of detailed statements of mandatory content …

Across the four curricula compared, there was general consistency in the levels of breadth, depth and rigour within and between learning areas/subjects.

Could this be true? The answer is, of course, “No”. Singapore’s educational outcomes are not remotely similar to Australia’s and, whatever is going on in Singapore’s schools, it is not remotely similar to what happens in Australia. So, how could ACARA arrive at such a patently false conclusion?

One of the Singaporean documents that ACARA points to again and again is 21st Century Competencies. That’s the whole-student stuff that ACARA loves to go on about: inventive thinking, responsibility and so on. We don’t know how this works in Singapore in practice, but the fact these competencies overlay the Singapore curriculum seems to distract ACARA from the curriculum itself, perhaps deliberately so.

The real question is, what is in the Singaporean Curriculum and how does it compare? To this end, ACARA’s comparative study considers various subjects at various year levels. For each subject and level, there is a reasonably extensive discussion together with a summary of the “breadth”, “depth” and “rigour” as high (“comprehensive” or “challenging”), medium or low; these concepts are defined in Chapter 1 of the comparative study. In the case of mathematics, ACARA compares the Singaporean and Australian curricula at three different levels. We shall consider each of these comparisons in turn.

Year 2 Australia and Primary 3 Singapore

The first comparison is of the third year of schooling — Singapore has no Prep/Foundation year — which may not be the most apt comparison. It won’t affect the conclusions, but Singapore P3 students are typically a year older than Australian Year 2 students. Furthermore ACARA indicates that there is a reasonably clear sense of “numeracy” instruction in Singaporean kindergartens, which, then, should perhaps be regarded as more of a Prep year. But, again, it won’t matter.

ACARA summarises the breadth/depth/rigour of Australian (and Singaporean) Year 2 mathematics as high, which will come as a surprise to many an attentive parent. How did ACARA get there? Well, for breadth, there’s a lot of stuff listed in the Australian Curriculum, so there you have it. As for depth:

The year-level descriptions for Year 2 reveal significant cognitive demand by referring to the Mathematics proficiencies contained in the content descriptions. Understanding includes building robust knowledge of adaptable and transferrable concepts, and in Year 2 this is evident in students making connections, partitioning and combining numbers and identifying and describing the relationships between the four number operations. …

And so on. And, there’s rigour:

The level of rigour in the [Year 2 Australian Curriculum: mathematics] is regarded as challenging as it places a considerable demand on students to engage in reasoning and problem-solving. Problem-solving requires students to make choices, investigate problem situations and communicate their thoughts. Reasoning develops the capacity for logical thought and actions such as explaining answers and the processes of solving problems. …

Anyone with any familiarity with Australian primary schools knows that these grandiose claims are utter nonsense. Whatever the teacher might be attempting, the kids aren’t reasoning and problem-solving: they’re simply screwing around, if only because they have insufficient knowledge or skills to reason or problem-solve with. They are learning nothing through these games.

To properly appreciate how this plays out, one needs to ignore the (supposed) deeper meaning and look at the actual content. Two extracts from ACARA’s summary will suffice. First, Australia:

By the end of Year 2, [Australian] students count to and from 1000 and recognise increasing and decreasing number sequences. They perform simple addition and subtraction calculations using a range of strategies and represent multiplication and division by grouping into sets. Year 2 students learn to divide collections and shapes into halves, quarters and eighths and associate collections of Australian coins with their value.

And, Singapore:

By the end of Primary 3, [Singaporean] students can work with numbers to 10 000, including increasing and decreasing number sequences. They add and subtract four-digit numbers and know their multiplication and division facts [sic] for 6, 7, 8 and 9 (having learnt 2, 5 and 10 [and 3 and 4] in Primary 2). They are introduced to the concepts of quotient and remainder via sharing and apply their skills to problem-solving. They can compare and add and subtract related fractions with denominators up to 12. Students add and subtract money in decimal notation and apply their skills to problem-solving. [emphasis added]

Yep, two peas in a pod.

Year 6 Australia and Primary 6 Singapore

Singapore has two version of Primary 5-6: Standard, and Foundation, “which revisits some of the important concepts and skills learnt in the previous years”. That is, if a Singaporean kid doesn’t sufficiently grasp the earlier material, the basic arithmetic, then there are consequences. That pretty much tells you everything you need to know.

ACARA’s study compares Year 6 Australian mathematics with Singapore’s Standard Primary 6. Predictably, Australia scores full marks again on breadth/depth/rigour, using the same absurd method of evaluation.

Formally, the Singaporean and Australian curricula are more similar in content at this year level. The obvious and important difference is Singapore’s incorporation of rate and ratio problems, and the beginnings of algebra. In Australia,

By the end of Year 6, [Australian] students recognise the properties of prime, composite, square and triangular numbers. … They are introduced to negative numbers through practical applications in areas such as temperature. Students connect fractions, decimals and percentages as different representations of the same number and solve problems involving the addition and subtraction of related fractions. Students make connections between the powers of 10 and the multiplication and division of decimals. They add, subtract and multiply decimals and divide decimals where the result is rational and locate fractions and integers on a number line. They calculate a simple fraction of a quantity.

Singapore is similar, in the sense of being totally different:

The [Singapore syllabus] builds on the depth and fluency of Mathematics established in previous years. For example, operations with decimals are considered complete and time is given to completing mastery of the four operations with fractions without the use of calculators. Mechanical fluency in number operations is focused on applications to a minimum of clearly specified problem types in the areas of percentages, ratio and speed. The comprehensiveness of the problem sets offers Primary 6 students a sense of mastery and confidence in applying Mathematics in useful ways.

In Australia, this is, of course, unthinkable. You can “cover” primes and decimals and fractions and so on, but if your kids don’t have the needed facility with arithmetic then the coverage will necessarily be wafer-thin and meaningless. But of course, ACARA provides the excuse reason:

Although their ages are comparable at Year 6/Primary 6, the fact that Singaporean students have received many of their introductory mathematical experiences via a well-defined, national pre-school program means they are able to spend additional time on mastery of basic processes (e.g. tables and algorithms) and move more rapidly through their respective curricula during the early primary years.

So, Singaporean kids are able to do significant arithmetic problems in Primary 6 because of all that “pre-school” work? The difference has nothing to do with Australia’s fetish for exploration and problem-solving? Sure, keep telling yourself that; it’ll make it true.

Whatever. ACARA continues:

This difference is still evident in Year 6/Primary 6, where successful Singapore students have acquired greater breadth and depth on their mathematical journey because of their earlier exposure to the development of basic and necessary skills[emphasis added]

Basic and necessary skills? Of course they are basic and necessary. So why the Hell doesn’t ACARA emphasise their teaching? This is the obvious, critical message of ACARA’s comparative study with Singapore. But ACARA happily, deliberately, leaves this message buried on page 73, where the only person who will read it is an idiot blogger with too much time on his hands.

And, worse than burying the message, ACARA immediately denies the message:

Students in both countries are well prepared to commence Mathematics in secondary school.

This statement is way beyond false; it is an obscene denial of reality.

Year 9/10/10A Australia and O-Level/AM 3-4 Singapore

Once again, Australia scores full marks for breadth/depth/rigour and, once again, this is fantasy.

We won’t attempt to summarise ACARA’s comparison at this level. The preparation in primary school tells you pretty much everything you need to know, and the conclusions are obvious and inevitable. The detailed analysis is complicated by the significant streaming in Singapore, with different course content for different students. For a quick summary, the reader can compare the table of Australian content (pages 80-81) with Singapore’s (pages 82-83). ACARA concludes:

At the end of Year 10, successful Australian students should have a broad range of numerical, algebraic, geometrical and statistical concepts and skills enabling them to investigate and solve a wide variety of problems including those from real-world situations. They should have the necessary knowledge and familiarity with mathematical processes to be well prepared to continue their study of Mathematics in Years 11 and 12.

At the end of Secondary 4, successful Singaporean students will be similarly equipped with an even broader range of concepts and skills. They are likely to have a more sophisticated knowledge and facility with mathematical processes enabling them to continue their mathematical education at a higher level.

Just the same, and totally different.

What to make of this? What does ACARA make of this? As we have noted, the Key Findings tries its hardest to pretend the Singapore-Australia differences simply don’t exist. Such pretence is much harder, however, when the contrary facts are crowding the room. So, ACARA concludes their discussion of the mathematics curricula with the excuses reasons:

Singapore has a centralised system of education. The national Mathematics Curriculum is closely monitored and implemented in well-resourced schools by highly trained teachers, most of whom are subject specialists and use mandated or recommended textbooks. Teachers are supported with instructional or pedagogical guides and they undergo regular school inspections and audits. Pedagogy is highly influenced by various forms of testing and high stakes examinations. Singapore’s small size allows for greater control over the whole education system, meaning that national directives and policies and feedback from schools can be quickly communicated. [emphasis added]

And somehow, as ACARA then explains, all of that is impossible in Australia.

SIngapore really is a foreign country; they do things really differently there. ACARA can pretend this is not true, or that there is some unavoidable, Everest reason why it is true, why Australia can’t do much of the same. ACARA have tried both on. But it doesn’t matter. Either way, they are lying through their teeth.

## The Key to ACARA’s Universe

We’re still attempting to make our way through the literature supporting ACARA’s curriculum review. We have written, and again, on ACARA’s absurd and insidious Literature Review. Next was supposed to be ACARA’s Key Findings document, and that is the subject of this post. It turns out, however, that capturing this document is close to impossible, like trying to grab fairy floss. This post will be brief.

The purpose of the Key Findings is to summarise ACARA’s four comparisons of the Australian Curriculum (AC), with those of Singapore, Finland, New Zealand and British Columbia:

[The Key Findings] summarises key insights and considerations across the four comparative studies that can help inform future advice on refinements and improvements to the AC.

ACARA puts its thumb on the scales early on:

Evidence from these comparative studies identifies how high performing education systems are incorporating 21st century capabilities/competencies into their curricula.

Yep, somehow all these countries just happen to be singing from ACARA’s songsheet. And then, another song:

Recent developments in these curricula also include increasing emphasis on essential/core concepts at the expense of detailed statements of mandatory content, catering for student diversity, and emphasising the importance of equal access for all students including First Peoples and those with additional needs. [emphasis added]

Perhaps this is referring more to the humanities — where it still sounds like a very bad idea. Of course, the idea of decreasing mandatory content in mathematics is ridiculous. As is any suggestion that Singapore, for example, might be doing this.

After this five-part harmony introduction, the Key Findings goes onto to consider differences in the curricula. The comparison is made in terms of three characteristics: breadth, depth and rigour:

Breadth refers to the number or range of content or topics covered in the curriculum, often referred to as ‘coverage’.

Depth refers to the detail or amount of knowledge that leads to the development of deep understandings of key concepts, principles and knowledge, and the ability to apply these understandings to real-world contexts.

Rigour refers to the cognitive demand in the curriculum required for students to engage in higher order thinking.

None of these definitions is remotely close to being sufficiently tight. This permits ACARA to fish for whatever it wants and, whatever it finds, to declare it to be a fish. Thus, ACARA’s subsequent conclusion is predictable, and predictably silly:

Across the four curricula compared, there was general consistency in the levels of breadth, depth and rigour within and between learning areas/subjects.

Fascinating. We’re used to people arguing, or simply assuming, that Singapore is different but that Australia should not compete. It’s new to hear that we’re all doing great together.

Is there more? Yes, of course: there’s a total of nineteen pages of vague or trivial distinctions, and fluffy God-knows-what. All pretty much impossible to read, and pretty pointless. Except for the occasional ACARA nudge, which, after all, is really the point:

In comparison to the other curricula, the AC was found to be a more prescriptive curriculum, characterised by disciplinary knowledge, skills and understandings … .

The international curricula all give a more prominent role and function to the development and implementation of core competences/capabilities/skills than could be argued does the AC.

So let’s have less of that what-do-you-teach-when stuff, and more of that let-the-kids-be-creative-and-ethical-with-their-techno-toy. You know, like Singapore.

This document really is a key to ACARA’s universe. And it really is an alternate universe.

## Alan Tudge, Annotated Again

A bit over a month ago, Alan Tudge, gave a major policy speech, Being our best: Returning Australia to the top group of education nations. Tudge’s speech, which we annotated here, was not all bad, a weird mix of goods and stupids and non sequiturs; we graded the speech a C+

The most encouraging part of Tudge’s speech was the promised scrutiny of teacher training and, in particular, of the pointless, ridiculous and actively destructive 2-year Masters that is currently required. Now, about a week ago, Tudge’s office issued a media release, announcing a review into initial teacher education. The media release was accompanied by a Tudge-fed puff piece in the Australian Financial Review (paywalled). What follows is our annotation of Tudge’s media release, followed by a quick discussion of the AFR report.

## Initial teacher education review launched

Federal Education Minister Alan Tudge has today launched a review of initial teacher education, a key element of the government’s ambition to lift Australian school standards.

A key element? Well, that is depressing.

Last month, the Minister outlined a new target to return Australia to the top group of education nations globally by 2030, noting that our school standards have steadily slipped over the last two decades.

The review of initial teacher education courses is the most critical element towards lifting standards,

No, it is not.

noting that the quality of teaching is the most important in-school factor influencing student achievement.

Yes, it is. Initial teacher training, however, has, and can have, almost no bearing on the quality of teaching. Pretty much all ITE can do is get in the way and screw people up and piss people off.

The review will address two key questions: how to attract and select high-quality candidates into the teaching profession,

You need a review to tell you to have the job pay more and not be so burdened with government-imposed garbage?

and how to prepare them to become effective teachers.

You can’t. Give it up. Teachers learn by teaching and reflecting and teaching, and that’s pretty much it. KKK.

Since 2006, the number of top students choosing to study education has declined by a third, and many teachers are still graduating from their courses insufficiently prepared to teach in a classroom.

What does this mean? No one is prepared for their first class.

The review will be conducted by a panel chaired by former Department of Education and Training Secretary Lisa Paul AO PSM, supported by:

• Malcolm Elliott – President of the Australian Primary Principals Association
• Derek Scott – 2019 Australian School Principal of the Year
• Bill Louden AM – Emeritus Professor of Education at the University of Western Australia

We do not know these people, but some form of reverse Groucho applies. Anybody who has risen to prominence in the current educational system is almost certainly unqualified to review the current educational system.

The first public discussion paper will be released by June, followed by a period of public consultation. The review will be completed in six months.

This is Sirens of Titan. Is there any evidence that at any time, in any place, “public consultation” has had any effect whatsoever?

Minister Tudge said Australia’s teachers are some of the most dedicated and hard-working in the world and the review would help grow and support the workforce.

One of the main aspects of being an adult is learning to judge people on what they do, rather than on what they say. If only we had more adults.

“Particularly over the last year, we have seen how important our teachers are to Australian kids and we want to provide them with the best platform to produce better student outcomes,” Minister Tudge said.

“We used to consistently be in the top group of education nations and I am confident we can get there again.

If you are, you’re a fool.

“The recommendations of this review will help ensure we attract high-quality, motivated candidates into teaching and develop them into teachers with the skills our students need.

No it won’t, and no it won’t.

“We want the finest students choosing to be teachers and we also want to make it easier for accomplished mid- and late-career individuals to transition into the profession, bringing their extensive skills and knowledge into our school classrooms.

This seems to be hinting at having at least some prospective teachers avoid the idiot Masters. Of course, all prospective teachers should be permitted to avoid the idiot Masters.

The review builds on the reforms the government has already made to improve ITE, including assessing and accrediting ITE courses and testing graduates’ literacy and numeracy before they can enter a classroom to teach.

Meaning ACER’s grotesque and pointless literacy and numeracy test? That’s an example of the brilliance to be expected from this review? Lord spare us.

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

The media release is not great, although it is standard to oversell the importance of such a review, and to avoid declaring the pre-determined conclusions. More forthright is the accompanying puff by AFR education editor, Julie Hare (paywalled). Hare’s Tuff-fed piece, titled Alan Tudge’s 10-year plan to get schools back to basics, is both encouraging and deeply discouraging.

The encouraging aspect of Hare’s piece is Tudge’s explicit questioning of value the 2-years Masters:

“People just used to have to do a nine-month diploma of education. And that was when our education standards were much higher. In the UK, it’s a nine-month diploma and their education standards are going up, not down. So if others can do it, and we have done it in the past, I can’t see why we can’t do it in the future.”

One discouraging aspect is Tudge’s genuflecting to “technology”, pretending that Khan Academy or some such nonsense is going to help. That “quality of teaching” thing sure lasted a long time. And, much more discouraging, it is pretty clear that Tudge, and Hare, have absolutely no clue what “basics” means.

Hare’s report goes on and on and on and on about Australia’s PISA scores. It is a theorem, if someone rabbits on about “basics” and PISA (and/or NAPLAN) then they have no clue about the meaning of either “basics” or PISA, or both.

Overall, we’ll give Tudge another C+ for this one. Tudge tries, but he is just a C kind of student.

### UPDATE (27/04/21)

Tudge is about to give a speech at The Age Schools Summit, whatever the Hell that is, and has given early access to his speech, at least to The Age. It seems clear that Tudge thinks it’s all about “the quality of teachers”, nothing about funding and, incredibly, nothing about Australia’s education system being intrinsically and fundamentally fucked. If Tudge clearly doesn’t realise the idiocy is entrenched in ACARA and State authorities, administered by the high-profile clowns that he’s about to pal around with, then fuck him. He’s useless.

### UPDATE (27/04/21)

Below is Tudge’s press conference from April 15, announcing the ITE review. The discussion is more wide-ranging than the media release, and is more encouraging. Tudge says some of the same dumb things, but he also says some smart things, starting around 6:00. (Lisa Paul, who will head the review, says some really dumb things, starting around 10:30).

## Massing Evidence

A week ago we wrote on ACARA’s “Literature Review“. We tried to make clear why the document is fundamentally useless, while nonetheless giving clear sign that ACARA is hell-bent upon making the Australian Curriculum worse. We indicated our plan to get on with critiquing ACARA’s other curriculum review documents,  a Comparative Review of the Australian and Singaporean curricula, and the Key Findings from four such comparative reviews. That is still the plan but, first, there remains an irritant from the Literature Review which simply has to be addressed. We have to consider the full significance of the Review’s final sentence:

“A critical consideration is the fact that curriculum is only one part of the educational equation.”

Our previous post indicated why ACARA’s Literature Review was useless as a basis for comparative education, while also demonstrating that ACARA had no sense of the limited benefits and genuine drawbacks of such comparisons. Apart from this pointlessness and cluelessness, the Literature Review suffers from two major problems. The first problem is that the Literature Review repeatedly conflates the difficulties of comparative education analysis with the difficulties of creating a coherent and useful curriculum. This conflation makes the document confusing to read, and makes any intended conclusion of the document difficult to discern. The second, and much more important problem is the manner in which the Literature Review treats those difficulties in creating a curriculum.

Of course, a national curriculum will be embedded in and will reflect the culture of that nation. This obvious truth, however, can quickly slide into a warped view of the proper role of a curriculum:

A curriculum necessarily originates in a specific society. Conceptualising the curriculum using a systemic and holistic view ‘opens up’ the curriculum, rather than constricting it to a rigid model (Jonnaert & Therriault, 2013). Coming from a constructivist and Piagetian perspective, that is, including curricular achievements that are being implemented in relation to trends in society and training needs, the curriculum may be construed as a ‘tool for regulating and adapting education systems to social trends’ (p. 400) [emphasis added].

And, again:

A curriculum is generally constructed on a set of compromises that are foisted upon it by societal needs, and through which it serves its education system (Jonnaert & Therriault, 2013, p, 413). Adopting a more holistic perspective engenders a view of curriculum that is grounded in societal realities and detached from a ‘technocratic vision, embedded in a rational curricular system and focused exclusively on the delivery of knowledge’ (Jonnaert & Therriault, 2013, p. 413; Keitel & Kilpatrick, 1999). Essentially, a holistic perspective of curriculum seeks to optimize students’ integration into their environment and the contemporary world. [emphasis added]

ACARA loves “holistic”; it’s their second favourite word. God forbid that one deal instead with the parts, with the details. And, what could possibly be the use of a “technocratic vision”, of a “rational curricular system”? What could we be thinking?

This “holistic perspective” places schooling as just one part of students’ socialisation, with the curriculum being the link between the two. In effect, ACARA is declaring that school education is powerless, that it is at the mercy of “societal realities”. Society is what it is, and ACARA will “regulate” and “adapt” the curriculum accordingly.

ACARA fails to consider that not all societal forces are forces for good, and that forces are not a given. ACARA does not appear to even contemplate that a national curriculum may act as a necessary and powerful countervailing force. Indeed, ACARA seems to fundamentally oppose the notion that they might have the power, and the responsibility, to tell people what to do:

“To understand a curriculum, researchers place it in its social and cultural environment, with the implications that emerge in any given society. In the current standards-driven climate, in which alignment of classroom teaching and learning to the national curriculum may be viewed by teachers as a compliance activity …” [emphasis added]

“Compliance activity”. As if that is a bad thing.

The next logical step is for ACARA  to give up on the very notion of a curriculum. Which they do:

“As Nieto et al (2008, p. 179) assert,

We view curriculum as including not only texts, but also other instructional materials, programs, projects, physical environments for learning, interactions among teachers and students, and all the intended and unintended messages about expectations, hopes and dreams that students, their communities, and schools have about student learning and the very purpose of schools.’ ” [emphasis added]

And, again:

Henchey (2007, pp. 446-447) explains:

Curriculum is more than a body of legislation, a régime pédagogique, a set of documents with exhortations, tables, diagrams and lists, a compilation of approved textbooks and learning materials, or a series of official examinations. It is the script for a dialogue between a society and its young people, a narrative about what we think is important, an idealization of what is significant in our past, a selection of what we know and believe in the present, and a vision of what we would wish for the future.’ ” [emphasis added]

Some of us would love nothing more than a régime pédagogique. We would really love a curriculum to declare simply and dirctly that students must learn their multiplication tables by heart, and we would really love teachers to be instructed, as an unambiguous, on-pain-of-death compliance activity, when to teach this. We are doomed to disappointment.

Notice in the last two quotes the use of ACARA’s favourite word, “curriculum”. We no longer have a curriculum, a document prescribing what is to be learned and when; instead, we have the mass noun “curriculum”, as the meaningless medium in which one learns. The notion of a curriculum has been vaporised from a solid to a gas.

The Literature Review uses or quotes the use of “curriculum” as a mass term over a dozen times, including in the concluding sentence:

“A critical consideration is the fact that curriculum is only one part of the educational equation.”

And that is the import. ACARA is either uncaring or actively dismissive of a curriculum, of a prescriptive document as specific guidance for a discipline. Which is unfortunate, since it’s their damn job to deliver one.

ACARA doesn’t want a curriculum, it wants “curriculum”, of which it has way too much already. If ACARA really gets its way – and who is there to stop them – we’re all screwed.