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.

 

 

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.

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.

 

 

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.

Leading By Example

What a month. It’s raining mendacity.

Today, the ridiculous AMSI-AAMT-MERGA statement received further press coverage, this time in a report from education stenographer, Suzan Delibasic (paywalled, Murdoch):

“Leading experts are calling for a maths curriculum overhaul, with a major review set to focus on fixing declining academic results.”

Once the stage has been set with straight-faced paraphrasing of AMSI-AAMT-MERGA nonsense, Delbonis’s report consists of quotes from three of these “leading experts”, beginning with AAMT‘s CEO, Allan Dougan:

“The whole idea of a maths class where the teacher teaches the content and the students practise it 300 times, that’s what we’re moving away from.”

300 times? If a kid is assigned 30 exercises as practice, the school will call Child Services. 3 times is much closer to the current mark, particularly in primary school, where the real damage is being done.

We have no idea where Dougan dredged up his Dickensian dream, but of course it has nothing to do with reality. The reality is that decades of “leading experts” killing the teaching of technique, of denigrating proper practice is a huge part of why Australian mathematics education is currently a disaster. Dougan apparently imagines the cure is less practice than the trivial amounts that currently exist.

To illustrate the point, Dougan provides his own, striking example:

“[Dougan] said one problem-solving task could involve year 6 students taking part in an activity called It All Adds Up, where each letter of the alphabet is given a dollar value” 

“Letter A is $1 to Z being $26. You can start asking students open questions such as finding a four-letter word that costs $50 —the success of this task is how they approach it and how they think about problem solving.”

Looks like a fun game. How about VOID? Or CLOT? Do I win?

Seriously, Year 6? As an add-on activity for Year 2, maybe Year 3, sure. But if you imagine it reasonable to expect Year 6 students to gain anything from such an addition game, then your sense of appropriate skill level bears no relation to reality. And even for Year 2 or Year 3 students, it’s a game, which by definition cannot be the main game. You learn addition by practising addition – the carefully structured 30 times thing – not by the occasional random sum in the middle of a game.

Our second Leading Expert is AMSI‘s Director, Tim Marchant:

“Australian Mathematical Sciences Institute director Professor Tim Marchant said he was concerned by the shortage of qualified maths teachers.”

“The data shows about 50 per cent of schools have maths classes taught by teachers that aren’t qualified in maths,”

Well, it wouldn’t be AMSI if they weren’t punching down, whining about unqualified teachers. But Professor Marchant also considers classroom activities:

Prof Marchant said group activities in the classroom helped learning and made maths “fun” … He suggested hands-on learning experiences including using Rubik’s cubes to help with problem solving.

Rubik’s cubes. Not enough games, not enough “fun”, that’s the problem.

Once upon a time, we had hope that AMSI would be a genuine force for improving Australian mathematics education. Now, we’d be happy if AMSI would just shut up, stop signing ridiculous statements and go away.

Our final Leading Expert is Peter Sullivan, Emeritus Professor of Education at Monash University:

“The revised curriculum needs to be simply written so teachers can understand and comprehend it; we want the big ideas clearly articulated,”

That’s Peter the Great there, the guy who led the writing of the current Australian mathematics curriculum.

Leading Experts. The “experts” part is debatable, but the “leading” is absolutely clear. These people are leading Australia to an even deeper level of educational Hell.

Why Mathematics Education Must Change

The revisions to Australia’s mathematics curriculum will be out soon, and it appears that the fix may be in. This fix will, of course, fix nothing; our guess is that things are about to get much worse.

As reported in yesterday’s SMH, Australia’s major league Maths Ed groups have released a “Joint Statement on Proposed Maths Curriculum”. Cosigned by AMSI, AAMT and MERGA, as well as AAS and ATSIMA, the statement is titled Why Maths [sic] Must Change. The statement is a triumph of modern educational ignorance.

The statement begins by noting “the proposed revisions to the Australian maths curriculum” are forthcoming, and “the importance of getting it right”. We are then told what “getting it right” means. The statement is poorly written and vague, inappropriately and inaccurately colloquial, but the message is clear enough:

“More than ever, our society needs students who are adaptable, resilient, responsive to challenges and able to handle unfamiliar situations. It is not enough to have knowledge – they must have the skills to take that knowledge and apply it to solve unknown problems, and do it quickly.”

Yes, the cure for our maths ed ills is yet more problem-solving, yet more overhyped exploration. And, this is to be contrasted with the alternative, a focus on “knowledge”. The writers are so proud of this ridiculous straw man that they repeat it:

We need education systems and curricula that help deliver students to society who are up for such a challenge – just having knowledge is no longer enough. Instead, the abilities to problem-solve, mathematise, hypothesise, model are all skills that add worth to acquired knowledge. Mathematics learning cannot sit in silos that focus on content and procedures. Instead, it must be something that gives the knowledge purpose.

We expect no better from AAMT or MERGA, but what about AMSI? Aren’t they like mathematicians, or something? Do AMSI’s glorious leaders really believe this nonsense? Do they really believe that school mathematics is, or was ever, a purposeless “silo” of knowledge-acquisition? Do they honestly think that the problem with Australia’s mathematics education, the reason, for example, why the majority of secondary students have no proper concept of or facility with fractions, is because there has been too much focus on content and procedure? Do they really imagine that these fraction-deficient students can nonetheless boldly venture forth to “solve unknown problems”?

The idea is, of course, absurd. The whole statement is absurd, a mission statement from the very same constructivist, discipline-hating, technique-hating ignorants who have been selling this snake oil for decades, and who are one of the major reasons why Australian mathematics education is now such a disaster. And, of course, their suggested cure for the problem they very much helped create is more of the same snake oil.

There is more in the statement. There is the predictable pointing to Australia’s woeful but irrelevant PISA scores, and the predictable silence on Australia’s woeful and highly relevant TIMSS scores. The writers express the hope, indeed the promise, that PISA results will improve. Which may well be true; it is the mathematics education, and the education generally, that will suffer.

We will remark upon one more, very troubling line from the statement:

As such, the suggested revisions in the curriculum are not just welcomed …

What, exactly, are these “suggested revisions”, and how do the cosigners of this statement know the revisions are “welcomed”? There are strong indications of what ACARA intends, and that what they intend will be awful. As far as we are aware, however, ACARA has yet to make any proposed revisions available for public comment.

What this implies, assuming that the above line is not simply more poor wording, is that the drafters, and perhaps the cosigners of the statement, are privy to ACARA’s inner workings, and that they are pleased with them. As we wrote, it appears that the fix is in.

Anything that will please the cosigners of the statement Why Maths Must Change will be a disaster for Australian mathematics education, and it seems as if the cosigners have reason to be pleased. God help the rest of us.

ACARA’s Illiterature Review

A few weeks ago we wrote about ACARA‘s review of the Australian Curriculum. The mathematics component of ACARA’s review appears to be at least partially in the hands of some loose cannons – the Center for Curriculum Redesign – which ACARA seems now to regret having hired. CCR is still on our to-whack list, but ACARA’s general documentation for their review is also worth scrutiny, particularly the document we consider in this post. In all, it makes a fine example of how hundreds of pages on best practising and evidence-basing and world benchmarking can amount to little more than manipulative blather.

The main webpage for ACARA’s curriculum review consists of overview: welcoming videos, motherhood declarations, the terms of reference, a timeline and the like. The substantive basis for the review then appears on a separate page, Program of Research. It is the documents on this PoR page that we’ll be analysing.

The PoR provides links to six documents. Four of these documents are long “comparative studies” of the current Australian Curriculum with other curricula: in turn, British Columbia, Finland, Singapore and New Zealand. A fifth document then attempts to summarise these four comparative studies, indicating the “key findings”. We intend to write about the Key Findings and the Australia-Singapore Comparative Review in future posts.

The subject of this post is the sixth and final PoR document, a “Literature Review“. Listed first and subtitled “contemporary approaches to comparative education research”, the Literature Review purports to give the theoretical grounding for the application of the substantive curriculum comparisons that follow. The Literature Review begins

“This paper explores developments in the field of comparative education research, including references to methodological approaches that may inform the design and focus of ACARA’s program of research and international comparison (2017-2020)”

And, the Literature Review closes with a final, one-sentence paragraph:

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

Ignoring the questionable grammar, how did the Literature Review get from A to Z, and what does it mean? The Review is dense with jargon and name-dropping, as literature reviews tend to be, and we’ll attempt to give some sense of the Review below. But already ACARA’s main, double-barrelled message is pretty clear:

Regardless of what other countries are doing, ACARA has license to do what they want and, whatever subsequently happens, it is not their fault.

That is bad enough, but things are much, much worse.

The Literature Review begins by noting that international comparisons are all the rage, in education and everything. In particular there are major international tests – the ridiculous PISA, and the not-ridiculous TIMSS, and PIRLS – which invite such comparisons, and which tend to be the focus of media reports, and of subsequent social and political reaction.

The Literature Review continues by discussing this trend, meandering from authority to authority. There are few endorsed conclusions but there is plenty of gaming, with the Review hovering around two implied concerns. Firstly, and presumably the central purpose of the Review, it is suggested that more general national differences make educational comparisons fundamentally difficult:

This area of research has become increasingly contested, however, insofar as there are perceptions of a focus on systemic improvement without a concomitant appreciation of socio-cultural (and other) context, philosophy of education and capacity to effect change. The risks posed by inadequate consideration of local issues are raised in discussions of the ‘rationality and irrationality of international comparative studies’ (Keitel & Kilpatrick, 1999).

Secondly, the focus upon international tests may result in an excessive focus on “literacy and numeracy”, narrowing the comparison of curricula:

… some researchers [claim] that ‘international comparison bolsters an evaluation mandate that promotes a superficial global awareness while stifling originality by displacing the core objectives of education’ (Hebert, 2012, p. 18). This reflects a view that comparative research must move beyond mere comparison of scores (e.g. PISA), and that more studies are needed in areas such as creativity, talent, ethical sensibilities and also in relation to values and attitudes more relevant to the needs of 21st century students (Hebert, 2012).

This leads to a consequent concern, that a “league table” focus on international comparison can result in pressure to “teach to the test”, thus narrowing the curriculum itself:

“In rejecting evaluation mandates, Hebert (2012) observes that literacy and numeracy often overshadow other education objectives (e.g. creativity, ethics, knowledge of history, etc.) central to educational systems as a consequence of ‘unbalanced policy-making’.”

Although containing a kernel of truth, there is plenty to criticise in ACARA’s statements, not least the disingenuous “some people say” framing. What, indeed, is the purpose here of a “literature review”? The only value for such preliminary documents is to determine the basis of the curricula comparisons to come, and a sequence of unsubstantiated claims from unendorsed authorities cannot possibly provide a proper basis. If ACARA has determined the basis of their curriculum review, which of course they must, then they are obligated to take their stand and to state it clearly. The implausible deniability inherent in ACARA’s literature review is ridiculous and cowardly.

As for ACARA’s concerns, well, yes, and no. Sure, there are good reasons for rural Peru to not compare themselves too critically to South Korea; it is much less clear, however, why Australia, with about the same GDP as South Korea and with half the population, should flinch from such a comparison. And true, the league tables don’t necessarily make even a superficial comparison easy; if South Korea is ranked third on some test with a score of 607 and Australia is tenth with a 517, that of itself tells us nothing. If, however, only 61% of Year 8 Australian students can figure out the fourth, very easy angle of a quadrilateral, while 86% of Korean students can do the same (p 181), that suggests something. And, if the same relative failure occurs question after question, that suggests a lot.

On ACARA’s concerns about the narrowing of the curriculum and of curriculum comparisons, one can only wish it were so. ACARA’s “values and attitudes more relevant to the needs of 21st century students” is undefined and undefinable; it is meaningless twaddle. And, whatever the place of “creativity” and “ethical values” and so forth in a curriculum, it can only be meaningful coming on top a solid foundation of reading and writing and mathematical sense. The deep and proper teaching of the three Rs, and establishing the necessary classroom culture in which to do it, is the critical basis of any coherent curriculum, as it has always been.

Ironically, while ACARA’s conscious undermining of international comparisons is strained and weak, ACARA also fails to raise other, much more substantial concerns. To begin, ACARA doesn’t even consider the possibility that international tests can intrinsically, on their merits, be awful; this is regrettable, since the only rational response to the question of how to use PISA scores for international comparison, or anything, is “Don’t”. Further, even if the test is not awful, it is not automatic that using the test results for comparison is necessary or particularly enlightening. What, for example, if less than half of Year 8 Australian students can give the prime factorisation of 36 in answer to a multiple choice question (p 6)? What if less than half of the same cohort can rewrite \boldsymbol{\frac{4}{14}} as \boldsymbol{\frac{\Box}{21}}, again in a multiple choice question (p 14)? Does one really need to look to how Korean kids are doing to recognise that something is seriously screwed up in Australia?

It is arguably worse than that. International comparisons, even those based upon intrinsically good tests, may not be just unnecessary but also misleadingly optimistic. What if, as there is reason to believe, the tests are getting dumber? What if, as there is reason to believe, the entire World is getting dumber?  Australia coming a constant tenth in a dumbing world is not a constant; it is a decline, and possibly a steep decline.

ACARA’s simultaneous failure to grasp the clear benefits and the genuine flaws of international comparison education is entirely predictable. It stems from ACARA’s inability to contemplate, let alone declare, a simple, objective basis for a coherent and productive school curriculum. If ACARA had any such ability then they would realise that, rather than current Australia being compared to other places, it should be compared to other times, to other centuries. If one wallows in a nonsense-swamp of 21st century idolatry, it is impossible to contemplate that anything might have been done better, and much better, in an earlier time. Such is ACARA’s blinkered thinking and such is Australia’s fate, and the fate of the World.

We could go on. ACARA’s Literature Review contains much more, and almost nothing. We could point out further, monumental flaws in the Review, but there is probably no need. We’ll simply note that nothing in the Review could assist in making useful international comparisons of education. And, much more importantly, there is nothing in the Review that could assist in the creation of a simple, coherent and productive school curriculum.

ACARA’s review of the Australian Curriculum is destined to be a disaster. The review will undoubtedly leave Australia with the same bloated, baseless, aimless idiocy that it has now. ACARA, and the educational authorities with which they consort and upon which they rely, are congenitally incapable of anything else.