Send me a postcard, drop me a line Stating point of view Indicate precisely what you mean to say Yours sincerely, wasting away

Give me your answer, fill in a form Mine for evermore Will you still need me, will you still heed me I’m nineteen sixty-four

Below is a document from a foreign country, one of yesterday’s finds. We have our thoughts, and we shall update the post pretty soon. First, however, we’ll give people a chance to ponder. Think of it as a WinCH.

UPDATE (09/05/21)

Courtesy of the Evil Mathologre, the PDF below now has (somewhat clunky) OCR. That means you can search for words, such as “mathematising”.

We went to a strange jungle-bookshop yesterday, hunting for copies of the mythical Fitzpatrick and Galbraith. No such luck, but we did find plenty of fascinating and forgotten items. And, below is the lovely shop assistant Jill, totalling our many purchases.

Of course we rebuked Jill for not doing the sum in her head.

We’ll write about some of these very interesting finds in the near future.

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).

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)?

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.

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.

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”.

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.

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.

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.

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.

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.

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?

WHY^{2} 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: WHY^{2} 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.

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.