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:

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:

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:

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.

Depressing.

We do a bit of that “working as a mathematician” stuff here in Wollongong. It is at least 6/144-ths of the degree, students can choose to make it more, depending on what exactly their degree is. We don’t use the word “mathematising”. That’s called abstraction. Abstraction (and some other things) are the topic of about 2/13-ths of that 6/144-ths of the degree. The other 11/13-ths are not on abstraction. It is pretty sad (and just wrong) if the message told to our kids will be that mathematicians sit around all day “mathematising”.

Thanks, Glen. I am aware that some of this exploring/abstracting/generalising stuff is good and necessary. And even deep end “what do you think of this problem?” Can be good. Anthony Harradine’s MathsCraft stuff seems to me very good. But it is not the main game, and it is a matter of timing and degree. In primary school the only important game is arithmetic. In early secondary school the only important games are 2) algebra and 1) doing the arithmetic that wasn’t done in primary school.

I can confirm for MathsCraft being good. One of the very few professional developments I went to that was useful in my teaching. Probably cause they had real life mathematicians develop the program.

Hi, Potii. Undoubtedly, the strong participation of and support of mathematicians is critical to the success of MathsCraft, but I think you may be giving the mathematicians too much credit. I may be wrong, but I don’t think MathsCraft was primarily developed by mathematicians. Harradine is mostly definitely not a mathematician. However, and unlike the vast majority of edutwats, Harradine knows what he doesn’t know and he has the good sense to talk to mathematicians.

Harradine ran the workshop with a mathematician. He seemed to have the teaching side of things covered while the mathematician had the more technical aspects of workshop covered. Without a doubt Harradine brings things together and his approach supports MathsCrafts quality. MathsCraft has been the only professional development that actually had a mathematician involved – the rest had teachers or “educators”.

Yes, we’re agreeing. The involvement of mathematicians is essential for this kind of thing, and their involvement is almost verboten in standard PD bullshit. All I’m suggesting is that I think it was more Harradine who initiated the whole project, and he looked to bring in mathematicians. (And, critically, the right mathematicians.)

Harradine reads this blog, but he may be too busy prostituting himself to Casio to comment.

I remember being blown away when I learnt that AB = 0 implies that either A or B is 0.

During a placement, I gave a lesson on algebra – their first – to a Year 7 class on calculating the date of Easter for any year. (Attached). We all enjoyed it. I know because the class teacher surveyed the students later for feedback.

2009-Vinculum-Easter

Hi TM. Nice lesson. And therein lies the problem ….

As a pre-service teacher (with an extensive mathematics background) you can invest the time to prepare this lesson and make it great. Let’s say you spent T1 hours preparing it.

Now the average classroom teacher has 5 classes of 4 periods/week, say, and each period is 45 minutes, say.

To make every lesson great (and remember that you also have the advantage of an extensive mathematical background, which makes it a lot easier to make a lesson great) would require the following amount of time:

Total time each week = (T1)(5)(4)(0.75) = 15(T1).

There is not this much time available during school hours, so a lot of time must be spent doing this outside of school hours. Either way you slice it, this is an unsustainable amount of time in the long run and the conclusion is obvious …

Sure, there are some time savings in the long term as you gain experience, but the conclusion is still inexorable and obvious. Particularly for a recently graduate teachers (who also have the unreasonable burden of the Vampires process for full registration). Teachers either develop a good stock ball and the occasional ‘effort ball’ to bowl to their classes (ala Glen McGarth) or they perish.

If you want to improve teaching standards, the solution is obvious and simple: Give classroom teachers more time! Steps in this direction are:

1) remove most of the administrative bullshit that continues to get piled onto classroom teachers. It is death by a thousand cuts.

2) decrease maximum class sizes to 20.

3) place a greater focus on PD such as assessment preparation, lesson preparation, curriculum development, peer observation, subject meetings etc. rather than the gravy train PD run by opportunists.

4) decrease the number of classes taken by a teacher but increase the contact time for each class. Eg. 4 classes (instead of 5) with 6 periods/week (instead of 4) of contact time.

The AEU is currently negotiating the new EBA. I doubt it has the backbone or spine to negotiate this sort of stuff but time will tell. (It is ridiculous that a Union should even have to negotiate this, it should be mandated by the DET if it is serious about quality education).

There is another branch on this particular tree that, no matter how many branches are pruned, new ones keep sprouting whilst the fruit rots (and yes, I’m being cynical…) – spreading the workload within a school.

If a school were to hire (say) six well qualified, well intentioned mathematics teachers and resource them well, they, as a group, could deliver a genuinely good Year 7 Mathematics curriculum to 120 or even 150 students.

However, if a school hires only two such teachers and then gives four classes to other teachers who require their timetables to be loaded up a bit more, the workload on these two, whether it was intended this way or not and despite the protestations of the four “outsiders” grows to anywhere between double and 8 times that of the aforementioned six.

What is worse, in many schools the proportions are even more dire because some schools (for many, many reasons, some beyond their control) cannot attract nor retain mathematics teachers.

I’m lucky in some regards that I work as part of a group of 12 mathematics teachers of which I would say 8 meet the definition of “suitably qualified”, but I know of schools that have it even better. Mathematics teachers at these schools tend to appear much happier and satisfied in their work and hence the trend (migration of good mathematics teachers to schools that least need them) continues!

RF, do you think that I would regard your 8/12 teachers as “suitably qualified”?

The suitably bit is a difficult qualifier… You have met 5 or 6 of them at various events (back in your MAV speaking days, for example – ah memories!).

So would you consider them qualified? According to the VIT definition, yes.

The events “qualified” and “able to tell gold from kangaroo turds” are not mutually exclusive.

So I will simply say their suitable qualifications are equal to or greater than what I have found in all minus one of the schools I have worked in (the one exception being an IB-only school which is an outlier by almost all measurable scales).

Hmm. I think you may have answered my question.

The Easter lesson to Year 7 was memorable – for me at least. This was a Christian school, so the introductory discussion went like this.

TM: What is the most important day in the Christian year?

Student1: Christmas

TM: Christmas is important but it’s not the most important day in the year.

Students 2 and 3 (independently): Tuesday (I didn’t get this.)

Student4 (a bright girl) : Easter

TM: And when is Easter?

Student4 (again): It varies from year to year.

TM: Why does it vary?

Student4 (yet again): Because it is a lunar feast.

This comment went way over my head. If I was in your class, I’d have cheekily said “My birthday” in response to your question, and then later felt slightly annoyed. But I wouldn’t understand why I was annoyed until I became much older, and had long since forgotten about it.

Thank you for keeping us updated. I just started teaching this year, so I’ve been really exhausted. To be honest, a lot of curriculum stuff is really confusing for me.

One big surprise for me is that Year 7 kids didn’t know or recognise square numbers, even after we’d spent a lesson on what they were. I guess that is a side effect of not knowing times tables? Is this new? Did children know squares at the end of primary school before?

One lesson, I had them add the first odd number, the first two odd numbers, etc., because I thought it might be kind of a fun way of reviewing the lesson on squares. They calculated 1, 4, 9, 16, 25, 36, … but only a few out of 50 students recognised them. So now that’s kind of my focus right now – getting them to know square numbers. It’s kind of an important subset of the times table, right? How will they do difference of squares tricks without squares?

Hi wst, and congrats for getting through the MB.

I’ll write more carefully tomorrow, and I’m sure others here will have some words of wisdom. But briefly on coping with the confusion of the AC: just ignore the damn thing. Your mathematical sense is a much, much better guide than anything you’ll find there. In the lower years, none of what ACARA or VCAA or VIT says matters one iota. It is either irrelevant or critically confusing or wrong, or all three.

Follow Dr. Spock: trust your own common sense.

Kids in primary school “do” square numbers in that they have seen them before and have been told about them on occasion. But they aren’t drilled, so they don’t really truly intrinsically know them as we would like.

It is a constant struggle for me, with my son who is currently in year 3. I just want him to know his times tables. Apparently that’s an insane suggestion. He can work them out easily, but I want him to have it memorised. That will make so many things so much easier for him later on. It is also true for the rest of the students.

In your situation, post-primary, I would do as much as your freedom allows. If they don’t know the first twelve squares (is it too much to ask them to know squares up to 15?) by sight, then I think you should definitely address that. The times tables in general, if you can get that across, I think you’d be doing so many students a big favour. It really is SO IMPORTANT that students know these by heart. Once they do, it takes away a lot of the angst and barriers to other important concepts.

Hah! Kids in primary school typically “do” nothing. To claim that they “do” squares but then cannot immediately recognising 49, implies “do” has lost its meaning.

Glen, of course you are absolutely correct, that the multiplication tables, up to 12, by heart, are non-negotiable. As for squares, I’d suggest up to 16 should be non-negotiable.

Beyond that, what the Year 7 kids really need is very quick and perfectly accurate mental arithmetic. For example, they should be able to mentally compute 48 x 7 quickly and correctly and without whining. Pretty much whenever I’m handballed a ≤ 8 kid, and also plenty of older ones, I point them to Harradine’s Numerical Acumen.

Hi, wst. Just a little more on coping with the workload.

To begin, I don’t think there’s any way a first year of teaching will not be exhausting, and even later years will be long and tiring, unless you’re a don’t-give-a-shit sloth (which I happen to know you very much aren’t). My childhood memories are full of images of my (single) mother, working away for hours in the evening, grading students’ work and the like, while I did whatever (watching TV).

However, the fact that a dedicated teacher will have tons to do doesn’t mean that they cannot dramatically reduce their workload. And the fundamental way to do that – for teaching or anything – is to ask: What really matters? And, in a nutshell that is a very easy one to answer for a teacher: your students matter; nothing else matters.

Marty, the answer you give is very easily given and is correct. And in practice, you will find that’s always the answer given and marketed by the powers that be – until pragmatism and convenience gets in the way. (The latter does not get marketed).

Thank you. I read and enjoyed your mother’s story in 2019 and find it inspiring and relatable. I’m sorry that she passed away last year – my belated condolences to you.

I was stupid and agreed to teach a Yr 11 subject that I am unqualified to teach (computing) to a smallish class of teenagers, which takes 90% of my planning time (including all my spare time), so that I have just a little remaining time to plan teaching maths; which is a bit like her story, only I don’t have classes of 40-50 to contend with! And at least computers don’t smell bad.

I think I will try to work part time next year, and insist I only teach maths; and in this way dramatically reduce my workload. I won’t make this mistake again – I think I’d rather be under-employed than over-committed for the whole year, because it’s really pretty awful. And I’m sure if my school doesn’t want me just for maths, another one will. It’s clarified some things I guess. 🙂

Ah, I see. Yes, agreeing to computing, particularly in your first year, was a mistake.

But there is something weird here. You have a very strong mathematics background: why would you be needing to agree to teach computing or whatnot? You definitely shouldn’t be agreeing to any such nonsense for next year. Email me if you want to discuss this offline.

wst, let’s get one thing straight. You weren’t stupid, you were naive and a victim of inexperience. Most graduate teachers are babes in the woods.

All schools will try to exploit you at some stage. And graduate teachers are particularly vulnerable. You will be told it’s a small class, it will be easy, just follow the curriculum, you’ll be doing us a big favour etc. And of course you’re eager to please, you want to make a good impression, you don’t want to be seen as ‘difficult’ etc. It’s even harder when you’re on a fixed-term contract because you want your contract renewed (or ideally to be made permanent).

Learning to say no is a hard thing to learn, and some people never learn how to do it. But the more you say it, the easier it gets 🙂

Rather than working part-time next year, I would encourage you to work full-time as a Maths Teacher and refuse out-of-field classes, extra-curricular etc. Just say No and don’t get duped. Your experience is one of the many reasons that many graduate teachers quit teaching after a couple of years.

And you’re right, “if [your] school doesn’t want [you] just for maths, another one will.” One question: Were you originally appointed as a Maths Teacher or was it implied there could be other ‘related’ classes you might be asked to teach?

In case you’re still feeling gormless, here are three stories from my life as a teacher:

1) My first teaching job (at a small private school) was a replacement position at the start of Term 4. The teacher I was replacing – experienced and very senior – handed me a box and said “I’ve left you some marking to do, it will be good experience for you, it will help you get to know the students”. Inside the box was this teachers marking for all of his subjects since the start of Semester 2. It included a Methods Unit 1/2 Investigation Task (and we all know what fun these are to mark).

This taught me a valuable lesson.

(Sidenote: I still occasionally see teachers hand their mentees marking to do, saying it will be good experience for them. Those teachers get unhappy when I go to the student teacher, retrieve the marking, hand it back to the teacher and tell that teacher not to be such a prick).

2) At my second school (a rich private school with delusions of grandeur), I was asked to coordinate the Maths Enrichment Program (https://www.amt.edu.au/maths-enrichment) for Year 10. The person who usually did it was on long service leave. I said OK. After the projects were finished and I’d collected them all (there were about fifty or so), I was told I also had to mark them and submit the results. All of this without any remuneration or time-allowance. Fortunately I was a bit wiser and had done my homework – I knew that the work could be sent to the AMT for marking. So that’s what I did. There was a charge of course, which the school had to pay.

This reinforced some lessons I’d previously learned. Schools will always try and get something for nothing from you.

(Side-note: The person who usually did this was the Maths HoD. A HoD gets a time allowance for doing administrative work, and for this HoD it included coordinating the Maths Enrichment program. But I was not a HoD and the school should have offered me something- a time allowance would have been satisfactory).

3) At the same school, a teacher asked for my help with some things because she was busy. So I helped her out. I later discovered she was asking other teachers to help her, and that she was actually getting paid a Responsibility Allowance for doing the things she had conned us into doing.

That’s when I learnt – or perhaps was reminded of – a really valuable lesson: Every school has a prick who will con you if they can. This really taught me to always be alert for the con-artist – which is a very sad and cynical lesson to have to learn: Schools are a microcosm of the world we live in.

Schools are political environments and teachers are as ruthless and ambitious as any politician – they will snipe from the shadows and exploit anyone who they think can further their ambitions. I know of teachers who have had their class notes (refined from 30 years of teaching experience) stolen, photocopied and returned. Most teachers are kind and generous – schools and a particular subset of teachers will always try to exploit this.

JF offers good advice here.

“You will be told it’s a small class, it will be easy, just follow the curriculum, you’ll be doing us a big favour etc” Oh, it seems almost like you were there!