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.

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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.

The Crap Aussie Curriculum Competition

The Evil Mathologer is out of town and the Evil Teacher is behind on sending us our summer homework. So, we have time for some thumping and we’ll begin with the Crap Australian Curriculum Competition. (Readers are free to decide whether it’s the curriculum or the competition that is crap.) The competition is simple:

Find the single worst line in the Australian Mathematics Curriculum.

You can choose from either the K-10 Curriculum or the Senior Curriculum, and your line can be from the elaborations or the “general capabilities” or the “cross-curriculum priorities” or the glossary, anywhere. You can also refer to other parts of the Curriculum to indicate the awfulness of your chosen line, as long as the awfulness is specific. (“Worst line” does not equate to “worst aspect”, and of course the many sins of omission cannot be easily addressed.)

The (obviously subjective) “winner” will receive a signed copy of the Dingo book, pictured above. Prizes of the Evil Mathologer’s QED will also be awarded as the judges see fit.

Happy crap-hunting.

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.