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.

ACARA is Confronted With the Big Ideas

In this column, ACARA will be playing the role of the Good Guy.

Now that we have your attention, we’ll confess that we were exaggerating. ACARA is, of course, always the Bad Guy. But this column also contains a Worse Guy, a bunch of grifters called Center for Curriculum Redesign. ACARA appears to be fighting them, and fighting themselves.

Last week, The Australian‘s education reporter, Rebecca Urban, wrote a column on ACARA’s current attempts to revise the Australian Curriculum (paywalled, and don’t bother, and it’s Murdoch). The article, titled Big ideas for mathematics curriculum fails the test, begins as follows:

Plans for a world-class national school curriculum to arrest Australia’s declining academic results are in disarray after a proposal to base the teaching of mathematics around “big ideas” was rejected twice.

So, apparently Australia has plans for a world-class curriculum.1 Who knew? At this stage we’d be happy with plans for a second rate curriculum, and we’d take what we got. But a curriculum based upon “big ideas”? It’s a fair bet that that’s not aiming within cooee of first or second. We’ll get to these “big ideas”, and some much worse little ideas, but first, some background.

The sources of this nonsense are two intertwined and contradictory undertakings within ACARA. The first undertaking is a review of the Australian Curriculum, which ACARA began last year, with a particular emphasis on mathematics. On ACARA’s own terms, the Review makes some sense; if nothing else, the Australian Curriculum is unarguably a tangled mess, with “capabilities” and “priorities” and “learning areas” and “strands” and “elaborations” continually dragging teachers this way and that. The consequence, independent of the Curriculum being good or bad, is that is difficult to discern what the Curriculum is, what it really cares about. As such, the current Review is looking for simplification of the Curriculum, with emphasis on “refining” and “decluttering”, and the like.

This attempt to tidy the Australian Curriculum, to give it a trim and a manicure, is natural and will probably do some good. Not a lot of good: the current Review is fundamentally too limited, even on its own terms, and so appears doomed to timidity.2 But, some good. The point, however, is the current Review is definitively not seeking a major overhaul of the Curriculum, much less a revolution. Of course we would love nothing more than a revolution, but “revolution” does not appear in the Terms of Reference.

The hilarious problem for ACARA is the second, contradictory undertaking: ACARA have hired themselves a gang of revolutionaries. In 2018, ACARA threw a bunch of money at the Center for Curriculum Redesign, for CCR “to develop an exemplar world-class mathematics curriculum”. ACARA’s “oh, by the way” announcement suggests that they weren’t keen on trumpeting this partnership, but CCR went the full brass band. Their press release proudly declared the project a “world’s first”, and included puff quotes from then ACARA CEO, Bob the Blunder, and from PISA king, Andreas Schleicher. And the method to produce this exemplar world-class, ACARA-PISA-endorsed masterpiece? CCR would be

“applying learnings from recent innovations in curriculum design and professional practice …”

And the driving idea?

“… the school curriculum needs to allow more time for deeper learning of discipline-specific content and 21st century competencies.”

This grandiose, futuristic snake oil was an idiot step too far, even for the idiot world of Australian education, and as soon as the ACARA-CCR partnership became known there was significant pushback. In an appropriately snarky report (paywalled, Murdoch), Rebecca Urban quoted ex-ACARA big shots, condemning the ACARA-CCR plan as “the latest in a long line of educational fads” and “a rather stealthy shift in approach”. Following Urban’s report, there was significant walking back, both from Bob the Blunder, and from the then federal education minister, Dan “the Forger” Tehan. But revolutionaries will do their revolutionary thing, and CCR seemingly went along their merry revolutionising way. And, here we are.

Urban notes that the proposal that ACARA has just rejected – for a second time – placed a “strong focus on developing problem-solving skills”, and she quotes from the document presented to ACARA, on the document’s “big ideas”:3

Core concepts in mathematics centre around the three organising ideas of mathematics structures approaches and mathematising [emphasis added] …Knowledge and conceptual understanding of mathematical structures and approaches enables students to mathematise situations, making sense of the world.”

Mathematising? Urban notes that this uncommon term doesn’t appear in ACARA’s literature, but is prominent in CCR’s work. She quotes the current proposal as defining mathematising as

“the process of seeing the world using mathematics by recognising, interpreting situations mathematically.”

So, all this big ideas stuff appears to amount to the standard “work like a mathematician”, problem-centred idiocy, ignoring the fact that the learning of the fundamentals of mathematics has very, very little to do with being a mathematician.4 Really, not a fresh hell, just some variation of the current, familiar hell.

So, why write on this latest version of the familiar problem-solving nonsense? Because what has reportedly been presented to ACARA may be far, far worse.

Most sane people realise that before tackling some big idea it is somewhat useful to get comfortable with relevant small ideas. In this vein, before the grand adventure of mathematising one would reasonably want kids to engage in some decent numbering and algebra-ing. You want the kids to do some mathematising nonsense? Ok, it’s dumb, but at least make sure that the kids first know some arithmetic and can handle an equation or two.  And this is where the proposal just presented to ACARA seems to go from garden-variety nonsense to full-blown lunacy.

Recall that the stated, non-revolutionary goal of the current Review is to clarify and refine and declutter the Australian Curriculum. Along these lines, the proposal presented to ACARA contained a number of line-item suggestions to accompany the big ideas. Urban quotes some small beer suggestions, such as the appropriate stage to be recognising coin denominations, the ordering of the months and the like. But, along with the small beer, Urban documents some big poison, such as the following:

\color{red}\mbox{\bf Year 4} \quad\boldsymbol{-}\quad  \left(\aligned&\mbox{\bf recognise represent and order numbers}\\ &\mbox{\bf to at least tens of thousands}\endaligned\right) \quad \mbox{\bf Not essential at year level}

Christ. If students don’t have a handle on ten-ing by the end of Year 4 then something is seriously screwed. At that stage the students should be happily be zooming into the zillions, but some idiots – the same idiots hell bent on real world problem-solving – imagine tens of thousands is some special burden.

The next poison:

\color{red}\mbox{\bf Year 5} \quad\boldsymbol{-}\quad \mbox{\bf Using fractions to represent probabilities} \quad  \left(\aligned&\mbox{\bf students are not ready,}\\ &\mbox{\bf promotes procedural knowledge} \\ & \mbox{\bf over conceptual understanding} \endaligned\right)

Here, the idiots are handed a gun on a platter, which they grab by the muzzle and then shoot themselves. There is absolutely zero need to cover probability, or statistics, in primary school. Its inclusion is exactly the kind of thoughtless and cumbersome numeracy bloat that makes the Australian Curriculum such a cow. But, if one is going to cover probability in primary school, the tangible benefit is that it provides novel and natural contexts to represent with fractions. Take away the fractions, and what is this grand “conceptual understanding” remaining? That some things happen less often often than other things? Wonderful.

One last swig of poison, strong enough to down an elephant:

\color{red}\mbox{\bf Years 7-10} \quad\boldsymbol{-}\quad \mbox{\bf Solving equations algebraically} \quad  \left(\aligned&\mbox{\bf Not essential for all students,}\\ &\mbox{\bf especially for more complex equations.} \\ & \mbox{\bf Technology can be used as a support} \endaligned\right)

On the scale of pure awfulness, this one scores an 11, maybe a 12. It is as bad as it can be, and then worse.

PISA types really have a thing about algebra. They hate it. And, this hatred of algebra demonstrates the emptiness of their grand revolutionary plans. Algebra is the fundamental mechanics of mathematical thought. Without a solid sense of and facility with algebra, all that mathematising and problem-solving is fantasy; it can amount to no more than trivial and pointless number games.

The teaching of algebra is already in an appalling, tokenistic state in Australia. It is woefully, shamefully underemphasised in lower secondary school, which is then the major source of students’ problems in middle school, and why so many students barely crawl across the finish line of senior mathematics, if they make it at all.

What is “more complex equations” supposed to mean for 7 – 10 algebra? The material gets no more complicated than quadratics, so presumably they mean quadratics, the hobgoblin of little saviours. True, this material tends to be taught pointlessly and poorly. But “complex”? Simply, no. It amounts to little more than AB = 0 implying that either A or B is 0, a simple and powerful idea that many students never solidly get. The rest is detail, not much detail, and the detail is just not that hard.

Of course, a significant reason why algebra is taught so, so badly is that it is almost universally taught and tested with “technology”, from calculators to nuclear CAS weapons, to online gaming of the kind that that asshole Tudge is promoting. And all of this is “used as a support”? That idea of “support”, just as stated, is bad enough, bringing forth images of kids limping through the material. But all this technology is much worse than a crutch; it is an opiate.

It is a minimal relief if ACARA has rejected the current proposal, but we have no real idea what is going on or what will happen next. We don’t how much much poison the proposal contained, or even who concocted it. We don’t know if the rejection of this proposal amounts to a war between CCR and a new, more enlightened ACARA, or a civil war within ACARA itself.5 We should find out soon enough, however. ACARA has promised to release a draft curriculum by the end of April, giving them a month or so to come to terms with the truly idiotic ideas that they are being presented. ACARA has a month or so to avoid becoming, yet again and still, Australia’s educational laughing stock.

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

1) We really wanted to slip “Urban myth” into the title of this post, but decided it would have been unfair. Yes, “world class” required quotation marks, or something. It seems, however, that Rebecca Urban was just carelessly, or perhaps snidely, repeating a piece of ACARA puffery, which is not the focus of her report. In general, Urban tends to be less stenographic than other education (all) reporters; she is opinionated and, from what we’ve seen, she seems critical of the right things. We haven’t seen evidence that Urban knows about mathematics education, or is aware of just how awful things now are, but we also haven’t seen her repeat any of the common idiocies.

2) We hope to write on the Curriculum Review in the next week or so, give or take a Mathologer task.

3) The proposal just presented to ACARA is not publicly available, and Urban appears to have only viewed snippets of it. It is not even clear, at least to us, who are the authors of the proposal. We’re accepting that Urban’s report is accurate as far as it goes, while trying to avoid speculating on the much missing information.

4) Urban’s report includes some good and critical, but not sufficiently critical, quotes from teacher and writer, Greg Ashman.

5) David de Carvalho, ACARA’s new CEO, appears to be an intelligent and cultured man. Maybe insufficiently intelligent or cultured, or insufficiently honest, to declare the awfulness of NAPLAN and the Australian Curriculum, but a notable improvement over the past.

Alan Tudge, Annotated

Alan Tudge, the Federal Minister for Education and Youth is, of course, an asshole. He is a nasty, down-punching, vindictive, glass-jawed, born to rule shithead. But, is Tudge an idiot?

Yesterday, Minister Tudge gave a major policy speech – Being our best: Returning Australia to the top group of education nations. The title indicates the subject, and a very smart teacher-friend of ours suggested Tudge’s speech was “quite good”. So, we read it. Our feelings are mixed.

What follows is Minister Tudge’s speech,* with our brief thoughts – critical and supportive – interlaced. At the end, we give a quick summary of our thoughts.

 

My argument today is that we are not yet living up to this aspiration of a world class education system set out in [the Alice Springs Mparntwe] Declaration where every child is reaching their potential. In fact, based on international benchmarks, we have moved further away from it over the last twenty years.

I want to take you through the evidence of this and outline where I believe we need to focus to lift school standards and realise the aspiration of that Declaration. There are many great reforms already in place, but more will need to be done.

We should set ourselves a new goal of being back amongst the world’s best within a decade.

We will only achieve this if we work together. The Australian Government does not run schools, and no state or sector can achieve this goal alone. My approach will always be to work collaboratively with those who share the ambition of a world-class education system that provides opportunities for every student.

I have spent two decades involved in schools policy in some form – from working with Dr Brendan Nelson when he was Education Minister, to assisting with some of the toughest schooling challenges in remote communities as Noel Pearson’s Deputy Director, to being a founder of Teach for Australia, and then in parliament, as a member of the Parliamentary Education Committee and as the Prime Minister’s Parliamentary Secretary looking after indigenous affairs.

We know very little about it, but our understanding is that Teach for Australia is a very good thing. (EDIT 13/03/21: And maybe not. See the comments below.)

Noel Pearson’s work on education seems worth evaluating and difficult to evaluate, and we won’t attempt it here. We have not much liked anything we have read by Pearson, and he may be a fool. But, at least Pearson doesn’t suffer other fools, and he’s put his heart and soul into trying something different. We’re open-minded.

I have learnt that there is no silver bullet in education. However, I have also learnt that there is good evidence of what works, and that if we are focused, amazing things can be achieved. This is about our children and our nation’s future so what can be more important!

Where I want to start the discussion today, however, is on school funding. I have watched or been involved in the funding debate for many years and I am pleased that the school funding wars are now over.

Yes. We lost.

Funding for schools has increased by 38% in real per capita terms over the last decade. The School Resourcing Standard model for funding schools has been agreed by the Commonwealth with all State and Territory governments.

Since 2013, the Australian Government’s school funding has increased in nominal terms by 80% to a record $23.4 billion, and we have committed a further 40% increase to reach $32.8 billion by 2029. From 2013 to 2029, government schools funding will increase the most by 193%, catholic schools by 109% and independent schools by 161%.

Scotch College gets an eighth polo field

The federal funding is locked in and agreed through to the end of the decade. The states and territories will need to live up to their side of the bargain also, but with record funding to all schools, our focus is now on how to use the money not how much schools should get or the distribution between the sectors.

Tudge really is an asshole. The federal funding of private schools is obscene.

I mentioned at the outset that over the last two decades, international benchmarks suggest we are moving away from the ministerial aspiration of a world class education system. Our standards have dropped in both absolute terms and relative to other countries.

Consider the evidence, as provided by the most authoritative international assessments: the OECD’s PISA tests of 15 year olds.

Since 2000, Australia’s performance in reading has declined by 26 points, or the equivalent of nine months of schooling.

In maths, we have fallen 33 points since 2003, or by 14 months of schooling.

Tudge is, of course, unaware that PISA’s testing of mathematics is garbage. No one should pay any attention whatsoever to PISA.

In science, we have fallen 24 points since 2006, or by 11 months of schooling.

This decline has been consistent across different groups of students. Our top students are less likely to score in the highest achievement bands and our lower performing students are more likely to have fallen below the proficient standard. The problem is not a growing divide in student results; it is a decline in performance across the board.

As our student results have fallen, we have dropped behind more and more countries.

In the early 2000s, we ranked 4th internationally in reading, 8th in science, and 11th in maths. By 2018, we had fallen to 16th in reading, 17th in science and 29th in maths.

We are being significantly outcompeted in our neighbourhood. For example, Australian students are now, on average, about one and a half years behind Singaporean students when it comes to reading and science, and three years behind on maths.

But it is not just the Asian tigers that have leapt ahead of us. The UK, Canada and New Zealand – all countries we used to outperform in education – are now ahead of us on all three assessment domains.

If this was our economy, this decline would be a national topic of conversation. Perhaps the lack of attention is because the decline has been gradual rather than sudden. But when viewed over a twenty-year period, it is profound – and it will have consequences for our long-term productivity and competitiveness if we cannot lift our education performance.

Two other international tests do not show quite the decline as PISA. TIMMS (which covers mathematics and science) and PIRLS (which covers reading literacy) have shown slight upticks recently. Our performance in TIMSS in 2019, especially in Year 8, was promising and perhaps an early indicator of a turnaround. I hope this is the case.

A false hope. TIMSS is an excellent international test of Year 4 and Year 8 mathematics (and science), and our education overlords should really, really really be paying attention to what it tests and Australia’s (woeful) performance. But “Australia” did not improve in 2019: all of the improvement indicated by the Year 8 TIMSS results was in New South Wales.

There is no consensus as to why our performance has declined over the last twenty years.

It is certainly not because of a decline in funding. As outlined, our funding has gone up considerably in real per capita terms while at the same time our standards have declined.

Nor is it class sizes which have steadily declined over the past few decades and are now considerably smaller than other countries that significantly outperform us. Moreover, many of our schools are now brand new, with facilities that older generations look at with envy.

But these things don’t have as much of an impact as what happens inside the classroom. The quality of the teaching, the rigour of the curriculum and the discipline in the classroom matter most.

Tudge is correct, and this is hugely important. The blowing of money on polo fields and technological snake oil hasn’t helped, and Tudge ignores the massive and insane administrative-accountability burden that has been placed upon teachers. Nonetheless, he is correct. KKK.

So how do we get Australia back to being amongst the best in the world?

The first step has been done; state and territory ministers, along with the former federal minister, have agreed the ambition to be world class.

Whoa. Big first step. Let’s all be sure to catch our breath.

But we should go further.

Really? That first step was just so helpful, maybe that’s enough.

We should set ourselves a 2030 target to be again amongst the top group of nations across the three major domains of reading, maths and science. We used to consistently be in the top group, which means we can get there again.

Fine. By what measure of success? PISA results? TIMSS results? 

I will be taking this to the next Education Ministers Meeting in April.

Such a target would then become a guiding principle and place urgency to the task.

Ten years is a reasonable, while ambitious, timeframe to again be amongst the top nations. By achieving the goal, we would be living up to the aspiration of giving Australian students the opportunity to achieve their best.

We have many building blocks already in place to achieve the target.

For example, there are already great initiatives in place across a variety of areas and I commend the state education ministers and Minister Tehan and Birmingham for these. This includes accreditation of initial teacher education courses, the Year 1 phonics check, the national unique student identifier, a new education evidence institute, and many more reforms.

Great to see phonics noted. The teaching of reading in primary schools is arguably worse and more damaging than the teaching of arithmetic.

I will continue to work with the state and territory ministers to implement these initiatives. They will make a considerable impact.

I will also prioritise new reform areas in the months ahead to accelerate our progress.

Building on our progress to date, my focus and the Government’s focus will be on three areas: quality teaching, particularly initial teacher education, curriculum and assessment. In addition, I will be leading a continued focus on indigenous students, particularly those in remote communities, whose level of educational attainment remains catastrophically poor.

Let me start with quality teaching.

We have tens of thousands of passionate teachers who transform our children’s lives, giving them skills that they seem to magically acquire. After parents, they are frequently the most important person in a child’s life, and in some cases, the most important person.

Quality teaching is by far the most important in-school factor in determining student performance. If we get this right, we will achieve our goal.

Tudge is correct.

Consider: a student with a teacher in the top 10% of effectiveness achieves in a half a year what a student with a teacher in the bottom 10 percent achieves in a year. That is, a good teacher has twice the impact of a poorer teacher on student learning.

What does this even mean? How does one begin to quantify “effectiveness” and “achievement” and “impact”? This numerology suggests that Tudge has no clue how to evaluate the quality of a teacher or their teaching.

Most of the challenge of quality teaching lies with the states and the non-government education authorities who employ the teachers and run the schools. They manage the issues associated with salaries, conditions, hiring, and firing. There is still much work to do on this front to better reward the brilliant teachers and to more easily let go the ones who are better suited in alternative careers.

The federal government’s main leverage over quality teaching is its funding of universities to deliver Initial Teacher Education courses, and through the provision of high-quality teacher professional development.

All teacher professional development is pointless and a waste of everybody’s time, as a matter of fact and, pretty much, of necessity. Teachers learn by teaching, then reflecting, then teaching again, and that’s pretty much it. KKK.

Our Initial Teacher Education courses play two central roles – selecting the future teacher workforce and then training that workforce.

Top-performing education systems set high standards for who becomes a teacher. They know and apply Michael Barber’s maxim that, ‘the quality of an education system cannot exceed the quality of its teachers’.

Finland, for example, rigorously assesses potential teachers through standard school leaver exams, additional tests of critical thinking, and mock teaching activities. Only one in 10 applicants make the grade. Singapore has a similar level of selectiveness.

Once selected, top-performing systems ensure that teachers are rigorously trained, equipped with the skills, confidence and knowledge to be highly effective from day one in the classroom. The best ITE courses are focused on practical capabilities, essential content knowledge, and proven pedagogical strategies rather than fads. For example, primary teachers in Singapore are rigorously trained in systematic and explicit teaching of grammar – a key to great literacy teaching.

This is sounding better. We’re not convinced that Finland is the great role model it is sometimes presented as, but at least Tudge is saying the right words. The noting of teaching grammar, which is currently non-existent in primary schools, is particularly good to see.

In Australia, we have made real inroads into the task of raising standards in the selection and training of our teachers in the last few years.

No we haven’t.

Guided by the Teacher Education Ministerial Advisory Group (TEMAG) recommendations, every initial teacher education course must now be assessed and accredited. This is a big breakthrough that over time will be fundamental to improving student outcomes.

We very much doubt it. Before reading Tudge’s speech we had not heard of the TEMAG report or the Government response. To us, it appears to be very much the standard swill.

Further, every teaching student now sits a test before graduation to ensure they have personal literacy and numeracy skills that are in the top 30 per cent of the adult population. If they do not pass the test, they cannot enter the classroom to teach.

ACER’s literacy and numeracy test is pointless and evil. We haven’t yet written on this obscenity, but it is on the list.

In addition, we have invested in Teach for Australia, a proven model that I helped found, that supports an accelerated pathway into the classroom for top graduates from non-teaching faculties.

We have made good progress, but there is still room for improvement.

We are still not consistently attracting the best students into teaching.

So you’re gonna offer teachers more money and make the job less shithouse? Or, is that suggestion too weirdly free market for you?

Moreover, some teachers are still graduating from their courses insufficiently prepared to teach in a classroom either because there has been too much focus on theory at the expense of practice, or because evidence-based teaching methods are not taught. I hear this consistently from school principals and graduates alike.

The OECD data backs this up: teachers in Australia feel less well prepared than the OECD average across curriculum content, pedagogy, managing student behaviour and monitoring student development.

La Trobe University has recently offered a short course in teaching phonics to existing teachers. A thousand teachers have signed up already. It is great that they offer this course and teachers are keen to learn, but it is an indictment on some education faculties that they were not taught this in the first place given how clear the evidence is.

The next evolution of reforms is needed, to build from the TEMAG reforms. I will soon be launching a review to help shape such reforms. This review will investigate where there is still further work to do to ensure that all ITE courses are high-quality and adequately prepare our teachers to be effective from day one.

This has been talked about for almost two decades now, going back to the National Inquiry into the Teaching of Literacy in 2005, so l will be impatient with education faculties that are not implementing evidence-based practices. It is the kids that miss out!

This is very good to read, but the weak point is the term “evidence-based”. What counts as evidence, and who will evaluate the evidence? Think of the craziest education idea, and you’ll be able find “evidence” to back it, and an education “authority” claiming to be convinced by that evidence.

Further, for many of the changes that a sane person would make, is any evidence required or helpful? Does anyone need evidence, for example, that if kids aren’t sitting still and paying attention to a teacher then they’ll learn bugger all? Sure, Tudge needs “evidence” for political reasons, but to appreciate the major educational and cultural changes required, all one needs is a sense of history, a pair of eyes and a brain. 

 

I will also be looking for mechanisms to enable school principals and expert teachers to have a greater input over the content and delivery of teacher education courses in a similar way that practitioners and employers are in medicine and law.

We need to find additional pathways to attract outstanding students to teaching, including talented mid-career professionals.

This is very good. Intended or otherwise, it is more viewing teaching as vocational rather than professional.

Twenty years ago, when our standards were higher, a person could be trained to become a teacher through a one-year Diploma. Now it takes a minimum of a two year Masters. It would be a rare mid-career person who could afford to take two years off work. Shorter pathways are required.

For everyone. The push from a 1-Year Graduate Diploma to a 2-year Masters was monumentally stupid: needless, costly torture to trainee teachers, and almost certainly lowering teaching standards.

We need a system that recognises that many professionals have deep expertise and relevant experience that would make them highly impactful teachers. I would love to see more engineers and accountants, for example, using their mathematical expertise to help us address our critical shortage of maths teachers.

In the end, the quality of teaching is the most important factor in student outcomes. It is my most important priority when it comes to schooling.

That Tudge listed this as his first and most important priority is very good.

My second area of focus will be on the Australian Curriculum, which is currently under review by ACARA.

Tudge is presumably unaware that ACARA is run by clowns.

This is an opportunity for us to take a step change improvement and put us on the pathway to again being amongst the top nations.

The Alice Springs Declaration sets the objective of ‘promoting [a] world-class curriculum’. It is the right objective: without a world-class curriculum, we will not achieve world-class learning outcomes.

The curriculum sets the standard for the student outcomes we expect – and so our curriculum must reflect our aspiration to be among the best in the world again.

This can be done by benchmarking our curriculum standards against top performing countries like Singapore and using this analysis to set our expectations for student learning.

As with “evidence-based”, benchmarking is easily gamed and is effectively pointless, except for political purposes.

Education Ministers have given ACARA the job of refining, updating and decluttering the content across the current curriculum. By the start of next year, we will have a more streamlined, coherent, focused Australian Curriculum available to be implemented in our schools.

Signs are that this updating of the Curriculum will make things even worse. We hope to write on this in the next day or so.

We will not bridge the three-year gap between us and Singapore overnight, but my hope would be that our revised national curriculum will put us on a pathway over the next decade that will see Australia rise to the top tier of global reading, maths and science standards.

Within the national curriculum content, I would like to see greater focus put towards the fundamentals of reading, mathematics and civics and citizenship. These are the building blocks which underpin other content areas and set individuals up for a greater contribution in our society and democracy.

Yes! Finally, the three Rs! Reading, mathematics and … civics.

Jesus H. Christ. A proper classroom culture (not ScoMoFo’s fucking “Australian values” bullshit) is critical, coming before the three Rs.  But it’s not a goddam area of learning, it’s the way you create a medium for learning. 

Tudge’s push for “fundamentals” is very welcome, but he really screwed up the dismount.

I will have more to say on these content areas in the months ahead including how we can use technology better (particularly in maths teaching) to make up for teacher shortages in particular areas.

He means Mathletics, or some other brand of dog shit. Inevitably, this will be monumentally stupid and monumentally damaging.

We will need a renewed push in reading where too many are transitioning to secondary school without the fundamental reading skills.

Good.

We need to improve the knowledge that young people have of our society and our democracy.

Start with Peter Dutton and your other goon mates, you turd.

My third priority area will be assessment.

John Hattie’s research tells us that effective assessment and feedback influences student achievement as much as prior cognitive ability – that’s a significant effect that should make us sit up and pay attention. It’s clear that assessment empowers teachers – putting student data at their fingertips to personalise learning plans and address areas of weakness.

Our uninformed understanding is that Hattie is a bit of an idiot. But, good assessment is good.

This is why our national annual assessment of student progress – NAPLAN – is so important.

And bad assessment is bad. NAPLAN is garbage.

We must protect NAPLAN, and not give in to those who call for less accountability and less information for teachers and parents.

At the same time, we will continue to refine the NAPLAN tests to ensure they are optimised to provide the information that schools, teachers, parents and policymakers need to lift school standards. The shift to online assessment will be completed in 2022, which will help deliver results faster. This year, we will assess other opportunities to adjust the tests or their implementation.

A national, lower-year testing scheme for arithmetic and spelling-grammar and comprehension would be valuable and worth the effort. We cannot see how the idiocy of NAPLAN could ever morph into that. 

NAPLAN assessments must be supported by a range of other assessments. Great teachers use formative assessment on a daily or weekly basis to assess student learning and identify where more instruction and support is required.

We will do more to embed formative assessment in every classroom in the country. The Online Formative Assessment trial, initiated under the National Schools Reform Agreement, is being developed now.

This trial has great potential to increase the effectiveness of classroom teaching by making robust assessment quick and easy for teachers to regularly complete. It is critical that this trial delivers on its great promise, and I will be monitoring its progress closely and supporting its implementation.

I will also be looking into how we can develop a repository of proven assessment tools that teachers and parents can use, in classrooms and at home, to see how children are performing.

It’s not clear what this all means, but it sounds bad. Good teachers will always have their own methods, of varying degrees of formality, of assessing their students, suitable to the topic and the students. Perhaps Tudge is proposing to offer assistance for this, but it sounds more declarative and needlessly micromanaging.

Finally, I will continue the Government’s priority on indigenous students, particularly those in remote areas. This has been a long term commitment of mine, as it has been for many Australians. There are no simple solutions, but I do think we can do more. I particularly want to see a greater focus on the early years so that kids don’t start school from behind.

And you know, whatever the intention it’ll change almost nothing.

School education is a topic that every person has experience with, a view on, and every Australian should have an interest in. We have all been through the schooling system and many of us have children, nieces, nephews or grandchildren still in the system.

Overall, our school system works well. But as a whole we can do better to ensure that we deliver on our ultimate goal of ensuring that every child reaches their potential.

I am optimistic that we can lift Australian school standards to put us among the world’s best education systems again. And, more importantly, I am confident that we know what it will take to achieve this goal.

We will see.

*) We cut out a statement Tudge gave on sexual assault in schools, as well as the opening, boilerplaterish part of his speech.

 

SUMMARY

OK, does anybody else have whiplash?

After reading Tudge’s speech, we wrote to our teacher-friend and graded it a D+, maybe a C. After reflecting and writing and reflecting, we’re probably willing to raise that to a C+ or B. Although containing a number of genuine idiocies, the speech is focused upon flagging genuine problems with Australian education, and suggests some plausible approaches to at least alleviate those problems. As such, we cannot see that Tudge’s proposals will end up causing much harm, and they may even do some good.

But not much good. At best, Tudge will be relying upon the evidence and the experts to implement changes. But, as we have queried above, which evidence and which experts?

The reality is, Tudge will be relying upon half-wits at ACER and ACARA and the like, along with God knows which academic nitwits. And what is the alternative? Who can you think of in Australia, who has both the educational clout and proper sense-knowledge-intelligence to make a decent go of Tudge’s proposals? Is there a single person?

Tudge’s speech is good in sum, but Tudge doesn’t understand the depth or the fundamental sources of the problem. To go properly into that is another, long, post. We’ll just make one note: any proposal for education reform that doesn’t begin with a blanket ban of computers in the primary classroom is not a serious proposal.

Yep, C+ is probably about right.

MAV’s Sense and Censor Ability

We’ve written about MAV’s censorship previously. It seems, unfortunately, that we may have another such incident to write about in the near future. We’ll see.

There is also a third incident that we’ve long planned to write about, but have never gotten around to. It is rather involved, and we won’t give the full story here, but one specific aspect is perhaps worth telling now.

In 2016, we accepted an invitation from the MAV to give a keynote address at their Annual Conference. We chose as our keynote title Same Sermon, New Jokes. We also submitted a “bio pic” – the graphic above – and an abstract. The abstract indicated our contempt for twenty or so organisations and facets of Australian mathematics education.

A couple months later, the Conference organisers emailed to indicate their objection to our abstract. One can argue the merits of and the propriety of this objection, and we will write generally on this at a later date, but one aspect of the objection was particularly notable. The email included the following:

“While we welcome all points of view, we do need to be respectful of the organisations we work with, and with whom we need to maintain good relations … We would like you to re visit the text … without the criticism of formal organisations.”

We pushed back against the criticism, and ended our reply with what we intended as a rhetorical question:

“You wrote that you (plural) welcome all points of view, which I was very reassured to read. Given that, which formal organisations do you consider to be above criticism?”

The email reply from the organisers included a response:

“In regards to the formal organisations with which the MAV has relations, you have stated some of them, e.g. ACARA, VCAA.”

No one at the MAV, including the then President, indicated to us any problem with this request or its clarification.

For now, we’ll leave it there.

NAPLAN’s Latest Last Legs

The news is that NAPLAN is on its way out. An article from SMH Education Editor Jordan Baker quotes Boston College’s Andy Hargreaves claiming tests such as NAPLAN are on their “last legs”. This has the ring of truth, since Professor Hargreaves is … who knows? We’re not told anything about who Hargreaves is, or why we should bother listening to him.

Perhaps Professor Hargreaves is correct, but we have reason to doubt it. And, Jordan Baker has been administering NAPLAN’s last rites for a while now. Last year, Baker wrote another article, on NAPLAN’s “death knell”.

Regular readers of this blog would be aware that this writer would love nothing more than to see ACARA sink into the sea, taking its idiotic tests and clueless curriculum with it. But it’s important to understand why, and why the argument for getting rid of NAPLAN is no gimme. It is here that we disagree with Hargreaves and (we suspect) Baker.

Baker quotes Hargreaves on national testing such as NAPLAN and its “unintended impact of students’ well-being and learning”:

[They include] students’ anxiety, teaching for the test, narrowing of the curriculum and teachers avoiding innovation in the years when the tests were conducted.

Let’s consider Hargreaves’ points in reverse order.

  • Innovation. Yes, a focus on NAPLAN would discourage innovation. Which would be a bad thing if the innovation wasn’t poisonous, techno-fetishistic nonsense. Hargreaves, someone, has to give a convincing argument that current educational innovation is generally positive. We’ll wait. We won’t hold our breath.    
  • Narrowing of the curriculum? We can only wish. The Australian Curriculum is a blivit, a bloated mass of pointlessness.
  • Teaching to the test is of course a bad thing. Except if it isn’t. If you have a good test then teaching to the test is a great thing.
  • Finally, we have to deal with students’ anxiety, a concern for which has turned into an academic industry. All those poor little petals having their egos bruised. Heaven forbid that we require students to struggle with the hard business of learning.

There is plenty to worry about with any national testing scheme: the age of the students, the frequency of the tests, the reporting and use of test results, and the ability to have an informed public discussion of all of this. But all of this is secondary.

The problem with the NAPLAN tests isn’t their “unintended consequences”. The problem with the NAPLAN tests is the tests. They’re shithouse.

 

NAPLAN’s Numeracy Test

NAPLAN has been much in the news of late, with moves for the tests to go online while simultaneously there have been loud calls to scrap the tests entirely. And, the 2018 NAPLAN tests have just come and gone. We plan to write about all this in the near future, and in particular we’re curious to see if the 2018 tests can top 2017’s clanger. For now, we offer a little, telling tidbit about ACARA.

In 2014, we submitted FOI applications to ACARA for the 2012-2014 NAPLAN Numeracy tests. This followed a long and bizarre but ultimately successful battle to formally obtain the 2008-2011 tests, now available here: some, though far from all, of the ludicrous details of that battle are documented here. Our requests for the 2012-2014 papers were denied by ACARA, then denied again after ACARA’s internal “review”. They were denied once more by the Office of the Australian Information Commissioner. We won’t go into OAIC’s decision here, except to state that we regard it as industry-capture idiocy. We lacked the energy and the lawyers, however, to pursue the matter further.

Here, we shall highlight one hilarious component of ACARA’s reasoning. As part of their review of our FOI applications, ACARA was obliged under the FOI Act to consider the public interest arguments for or against disclosure. In summary, ACARA’s FOI officer evaluated the arguments for disclosure as follows:

  • Promoting the objects of the FOI Act — 1/10
  • Informing a debate on a matter of public importance — 1/10
  • Promoting effective oversight of public expenditure — 0/10

Yes, the scoring is farcical and self-serving, but let’s ignore that.

ACARA’s FOI officer went on to “total” the public interest arguments in favour of disclosure. They obtained a “total” of 2/10.

Seriously.

We then requested an internal review, pointing out, along with much other nonsense, ACARA’s FOI officer’s dodgy scoring and dodgier arithmetic. The internal “review” was undertaken by ACARA’s CEO. His “revised” scoring was as follows:

  • Promoting the objects of the FOI Act — 1/10
  • Informing a debate on a matter of public importance — 1/10
  • Promoting effective oversight of public expenditure — 0/10

And his revised total? Once again, 2/10.

Seriously.

These are the clowns in charge of testing Australian students’ numeracy.

NAPLAN’s Numerological Numeracy

This year Australia celebrates ten years of NAPLAN testing, and Australians can ponder the results. Numerous media outlets have reported “a 2.55% increase in numeracy” over the ten years. This is accompanied by a 400% increase in the unintended irony of Australian education journalism.

What is the origin of that 2.55% and precisely what does it mean to have “an increase in numeracy” by that amount? Yes, yes, it clearly means “bugger all”, but bugger all of what? It is a safe bet that no one reporting the percentage has a clue, and it is not easy to determine.

The media appear to have taken the percentage from a media release from Simon Birmingham, the Federal Education and Training Minister. (Birmingham, it should be noted, is one of the better ministers in the loathsome Liberal government; he is merely hopeless rather than malevolent.) Attempting to decipher that 2.55%, it seems to refer to the “% average change in NAPLAN mean scale score [from 2008 to 2017], average for domains across year levels”. Whatever that means.

ACARA, the administrators of NAPLAN, issued their own media release on the 2017 NAPLAN results. This release does not quote any percentages but indicates that the “2107 summary information” can be found at the the NAPLAN reports page. Two weeks after ACARA’s media release, no such information is contained on or linked on that page, nor on the page titled NAPLAN 2017 summary results. Both pages link to a glossary, to explain “mean scale score”, which in turn explains nothing. The 2016 NAPLAN National Report contains the expression 207 times, without once even pretending to explain what it means. The 609-page Technical Report from 2015 (the latest available on ACARA’s website) appears to contain the explanation, though the precise expression is never used and nothing remotely resembling a user-friendly summary is included.

To put it very briefly, each student’s submitted test is given a “scaled score”. One purpose of this is to be able to compare tests and test scores from different years. The statistical process is massively complicated and in particular it includes a weighting for the “difficulty” of each test question. There is plenty that could be queried here, particularly given ACARA’s peculiar habit of including test questions that are so difficult they can’t be answered. But, for now, we’ll accept those scaled scores as a thing. Then, for example, the national average for 2008 Year 3 numeracy scaled scores was 396.9. This increased to 402.0 in 2016, amounting to a percentage increase of 1.29%. The average percentage increases from 2008 to 2017 can then be further averaged over the four year levels, and (we think) this results in that magical 2.55%.

It is anybody’s guess whether that “2.55% increase in numeracy” corresponds to anything real, but the reporting of the figure is simply hilarious. Numeracy, to the very little extent it means anything, refers to the ability to apply mathematics effectively in the real world. To then report on numeracy in such a manner, with a who-the hell-cares free-floating percentage is beyond ironic; it’s perfect.

But of course the stenographic reportage is just a side issue. The main point is that there is no evidence that ten years of NAPLAN testing, and ten years of shoving numeracy down teachers’ and students’ throats, has made one iota of difference.

Obtuse Triangles

Whatever the merits of undertaking a line by line critique of the Australian Curriculum, it would take a long time, it would be boring and it would probably overshadow the large, systemic problems. (Also, no one in power would take any notice, though that has never really slowed us down.) Still, the details should not be ignored, and we’ll consider here one of the gems of Homer Simpson cluelessness.

In 2010, Burkard Polster and I wrote an Age newspaper column about a draft of the Australian Curriculum. We focused on one line of the draft, an “elaboration” of Pythagoras’s Theorem:

recognising that right-angled triangle calculations may generate results that can be integral, fractional or irrational numbers known as surds

Though much can be said about this line, the most important thing to say is that it is wrong. Seven years later, the line is still in the Australian Curriculum, essentially unaltered, and it is still wrong.

OK, perhaps the line isn’t wrong. Depending upon one’s reading, it could instead be meaningless. Or trivial. But that’s it: wrong and meaningless and trivial are the only options.

The weird grammar and punctuation is standard for the Australian Curriculum. It takes a special lack of effort, however, to produce phrases such as “right-angled triangle calculations” and “generate results”. Any student who offered up such vague nonsense in an essay would know to expect big red strokes and a lousy grade. Still, we can take a guess at the intended meaning.

Pythagoras’s Theorem can naturally be introduced with 3-4-5 triangles and the like, with integer sidelengths. How does one then obtain irrational numbers? Well, “triangle calculations” on the triangle below can definitely “generate” irrational “results”:

Yeah, yeah, \pi is not a “surd”.  But of course we can replace each \pi by √7 or 1/7 or whatever, and get sidelengths of any type we want. These are hardly “triangle calculations”, however, and it makes the elaboration utterly trivial: fractions “generate” fractions, and irrationals “generate” irrationals. Well, um, wow.

We assume that the point of the elaboration is that if two sides of a right-angled triangle are integral then the third side “generated” need not be. So, the Curriculum writers presumably had in mind 1-1-√2 triangles and the like, where integers unavoidably lead us into the world of irrationals. Fair enough. But how, then, can we similarly obtain the promised (non-integral) fractional sidelengths? The answer is that we cannot.

It is of course notable that two sides of a right-angled triangle can be integral with the third side irrational. It is also notable, however, that two integral sides cannot result in the third side being a non-integral fraction. This is not difficult to prove, and makes a nice little exercise; the reader is invited to give a proof in the comments. The reader may also wish to forward their proof to ACARA, the producers of the Australian Curriculum.

How does such nonsense make it into a national curriculum? How does it then remain there, effectively unaltered, for seven years? True, our 2010 column wasn’t on the front of the New York Times. But still, in seven years did no one at ACARA ever get word of our criticism? Did no one else ever question the elaboration to anyone at ACARA?

But perhaps ACARA did become aware of our or others’ criticism, reread the elaboration, and decided “Yep, it’s just what we want”. It’s a depressing thought, but this seems as likely an explanation as any.

Accentuate the Negative

Each year about a million Australian school students are required to sit the Government’s NAPLAN tests. Produced by ACARA, the same outfit responsible for the stunning Australian Curriculum, these tests are expensive, annoying and pointless. In particular it is ridiculous for students to sit a numeracy test, rather than a test on arithmetic or more broadly on mathematics. It guarantees that the general focus will be wrong and that specific weirdnesses will abound. The 2017 NAPLAN tests, conducted last week, have not disappointed. Today, however, we have other concerns.

Wading into NAPLAN’s numeracy quagmire, one can often find a nugget or two of glowing wrongness. Here is a question from the 2017 Year 9 test:

In this inequality is a whole number.

\color{blue} \dfrac7{n} \boldsymbol{<} \dfrac57

What is the smallest possible value for n to make this inequality true?

The wording is appalling, classic NAPLAN. They could have simply asked:

What is the smallest whole number n for which \color{red} \dfrac7{n} \boldsymbol{<} \dfrac57\, ?

But of course the convoluted wording is the least of our concerns. The fundamental problem is that the use of the expression “whole number” is disastrous.

Mathematicians would avoid the expression “whole number”, but if pressed would most likely consider it a synonym for “integer”, as is done in the Australian Curriculum (scroll down) and some dictionaries. With this interpretation, where the negative integers are included, the above NAPLAN question obviously has no solution. Sometimes, including in, um, the Australian Curriculum (scroll down), “whole number” is used to refer to only the nonnegative integers or, rarely, to only the positive integers. With either of these interpretations the NAPLAN question is pretty nice, with a solution n = 10. But it remains the case that, at best, the expression “whole number” is irretrievably ambiguous and the NAPLAN question is fatally flawed.

Pointing out an error in a NAPLAN test is like pointing out one of Donald Trump’s lies: you feel you must, but doing so inevitably distracts from the overall climate of nonsense and nastiness. Still, one can hope that ACARA will be called on this, will publicly admit that they stuffed up, and will consider employing a competent mathematician to vet future questions. Unfortunately, ACARA is just about as inviting of criticism and as open to admitting error as Donald Trump.