ACARA CRASH 15: Digital Insertion

Continuing to try to rid ourselves of ACARA irritants, the following are the “calculator” elaborations from Year 1 – Year 6 Number and Algebra (sic):


using the constant function on a calculator to add ten to single digit numbers, recording the numbers to make, show and explore the patterns in a 0 – 100 chart

with the use of a calculator, exploring skip-counting sequences that start from different numbers, discussing patterns

modeling skip counting sequences using the constant function on a calculator, while saying, reading and recording the numbers as they go

Continue reading “ACARA CRASH 15: Digital Insertion”

Does There Exist a Sensible Australian Maths Ed Academic?

Yes, the question is rhetorical, but it is not just rhetorical.

A couple months ago, Greg Ashman asked Twitter a more specific version of this question:

[W]ho are the education academics in Australia who specialise in mathematics teaching and who advocate for explicit teaching, times tables etc.?

Ashman has a decently large following, but the replies to his question were tellingly non-existent. The only specific people suggested were the very non-Australian Jim Milgram, a hard core Stanford mathematician who took time off to wallop Jo Boaler, and Stephen Norton, a Griffith University education academic who appears solid and thoughtful, and barely visible. Anyone else?

Continue reading “Does There Exist a Sensible Australian Maths Ed Academic?”

Robbing Peter to Play Appallingly

The time for submissions to ACARA’s review has ended. Which means it’s now time for machinations and clandestine transactions. One hopes that our Glorious Mathematical Leaders know who they are dealing with and how to deal with them.* In the main, we’ll get back to posting on other topics.** Still, there are ACARA irritants remaining, things left unwritten, and when we’re sufficiently irritated we’ll post on it.

One constant irritant has the been the “it’s all there” defenses of ACARA’s draft. Yes, so it goes, there is an increased emphasis on inquiry/modelling/whatever, but not at the expense of basic skills.

“We absolutely have to focus on problem solving [but there should also be] an equal focus on building fluency”.

So, it’s not “strategies/efficiency/skills/content” versus “problem solving/reasoning/exploring/thinking”:

“Great Maths teachers do both!”

See? The problem isn’t with the ACARA draft curriculum. The problem is that you’re not a great maths teacher.

Continue reading “Robbing Peter to Play Appallingly”

Last Day For Submissions to the ITE Review

We haven’t paid much attention to this, since there have been much smellier fish to fry. Still, it is worth some attention.

In April, Alan Tudge launched a Review into Initial Teacher Education, and in June a Discussion Paper was released, with an invitation for submissions. Today (midnight?) is the cut-off for submissions.*

We wrote on Tudge’s launching of the Review and, prior to that, on Tudge’s speech on general educational issues. We gave both a “meh” review. In particular in regard to ITE, we couldn’t get that excited, since reforming ITE can have no great effect while teachers are released into the current moribund, admin-bloated, directionless, culture-free educational system. Training a Jack Brabham and then throwing him into a Morris Minor is not gonna win you a lot of races.

Still, there are things worth saying, and so it is probably worth saying them for the Review. We’ll submit something.

The Discussion Paper for the Review seems well-written, although it is largely concerned with formal detail of little interest to us (and perhaps of questionable importance). Responses to the discussion paper are then intended to be guided by questions appearing at the end of each section. Again, most of these questions do not concern us, but a few seem suitable for the anchoring of criticisms. The following are the questions to which we intend to reply, followed by an indication of how we might reply:

What can be done to attract more high-achievers and career changers to the profession?

(Um, make the job not suck? Have a coherent curriculum, which assumes and encourages a culture of learning, and get rid of the endemic Little Hitlerism.)

What features of the current ITE system may prevent high-quality mid- to late-career professionals transitioning to teaching? 

(Everything. It is all pointless. For everyone. One learns to teach by teaching, and the rest is trivial.)

What are the main reasons ITE students leave an ITE course before completion?

(Perhaps a distaste for insanity.)

Are the Australian Professional Standards for Teachers fit for purpose in identifying the key skills and knowledge pre-service teachers need to be ready for the classroom?

(The Professional Standards are not fit for wrapping yesterday’s garbage.)

How can ITE providers best support teachers in their ongoing professional learning?

(By staying as far away as possible.)

Do the current HALT (Highly Accomplished and Lead Teachers) arrangements support the education ecosystem, particularly in relation to ensuring quality mentoring and supervision of ITE students?

(Of course not. “Highly accomplished” doesn’t mean highly accomplished, it means playing the game and playing it safe. Genuinely highly accomplished teachers take risks and make errors and put noses out of joint; these teachers, who are the true leaders, will seldom if ever be recognised by any such system.)

Does ACER’s Literacy and Numeracy Test Suck Balls?**



*) Notably there is no ACARAesque sheep-herding survey, and submissions can simply be written as text, or uploaded as a Word/PDF file.

**) The Discussion paper mentions ACER’s test, but somehow failed to question its worth. We’ve corrected their oversight.




Tony Guttmann’s Statement on the Draft Mathematics Curriculum

Tony Guttmann, AKA Mr. Very Big, is a member of or is associated with just about every mathematician organisation in Australia, excepting the Geelong Primary School Mathletics Squad.* Tony has signed the open letter and, much more importantly, has been working hard within the various organisations, arguing against the draft mathematics curriculum. He has been quoted in the recent, excellent reports of Rebecca Urban (Murdoch, paywalled).

As part of his efforts, Tony prepared a statement on the draft mathematics curriculum. With his kind permission, we have reprinted Tony’s statement here.

*) Membership pending.



Tony Guttmann, AM, FAA, FTSE, FSIAM, FAustMS

As Australia is falling behind its international peers in basic mathematical skills, it is important to remedy this. A major problem is the lack of an adequate supply of trained mathematics teachers at the secondary level, and  the too-frequent occurrence of math-phobia among primary school teachers, which risks alienating their students from an appreciation of, and facility with, basic numeracy. This problem has been recognized for at least 40 years, and piece-meal attempts to address it have been made, but little has changed in four decades.

Australia has frequently sought inspiration from successful countries, such as Finland and Singapore. Unfortunately, their success is founded on a highly skilled and well-trained cohort of teachers, along with an appropriate curriculum. Australia lacks both.

One aspect of the Singapore curriculum is the application of mathematics to so-called “real world problems”. But this application only takes place after the mastery of basic skills. These are not learnt by trying to solve problems, and picking up the basic skills by some sort of osmosis.

So while the present Australian Mathematics Curriculum definitely requires review, ACARA’s current draft is systemically flawed, being based on this flawed premise of teaching through investigation, problem solving etc. While these have their place, the basic skills need to be there first, so that the focus can properly be on applying those skills to the problem at hand.

The power of mathematics, and our ability to learn and to apply mathematics, comes from its simplicity and its precision. Mathematics simplifies and abstracts the real world: from “three apples” to 3, from “three apples and five oranges” to 3a + 5b, and so on. With particular abstractions sufficiently understood, then, and only then, mathematics can feed back, to be applied to and to help us better understand the real world. This two-step process is long and sometimes difficult, but it is natural. A beautifully clear description of such an approach to mathematics education is given in the just-released UK Government’s Ofsted mathematics review.

The current ACARA approach is much more difficult and convoluted. The draft proposes that students learn fundamental mathematics, and come to understand the way it works, largely through “investigation” and “modelling” and “problem-solving”, much of it open-ended and poorly defined. Even if such investigations were totally within mathematics, this would be a flawed approach. What is critical to learning the arithmetic of fractions, for example, is practice on arithmetic with fractions. What the draft curriculum offers Year 6 students is a range of activities, heavy on vague modelling (pp 87-88). The draft curriculum is further flawed by situating “problem-solving” and the like in real-world scenarios (p 14). This may be where one eventually wants to apply mathematics, but it is not how one should attempt to learn the mathematics to be applied.

The strong emphasis on exploration in the draft curriculum leads to many other troubling issues. In brief:

1. The draft curriculum is difficult to read:

A consequence of the draft’s mixing mathematical content with applications is the loss of a simple and coherent structure. The framing is around thirteen “core concepts”, many of which are poorly defined and overlapping (p 15). In an apparent, and failed, attempt to make sense of this mix of concepts, the long introduction to the draft is prolix to the point of incomprehensibility (pp 1-16). Equally vague are the content descriptors in the draft, which are not infrequently a mix of the key facts/ideas/skills to be learned and the typically exploratory and ineffective methods proposed to learn them (p 27, for example).

2. The delaying and dilution of the “basics”:

Critical examples of this deficiency are the decisions to delay the learning of multiplication tables until Year 4 (p 64), and the solving of linear equations until Year 8 (p 115). ACARA’s arguments for these changes are quite unacceptable (pp 8-9). The dilution is also systemic. An emphasis on real-world modelling is a very poor mode for the practice of fundamental skills and, inevitably, it takes emphasis and precious time away from the proper practice of these skills. It denies students the opportunity to develop the fluency to apply the mathematics in a proper and rewarding manner.

3. The devaluing of mathematics:

For History or for English, the subject is largely taken to be its own worthy goal, but this is too seldom done for mathematics, and the idea is almost entirely ignored in the draft curriculum. The strong emphasis on premature exposure to real-world contexts squanders the opportunity for students to gain an appreciation of mathematics as its own beautiful discipline. In doing so, the draft also squanders the opportunity for students to gain a rich understanding of mathematics, which, in the long run, is what will best serve the students. Well-constructed problems within mathematics, and posed after the mastery of the appropriate basic skills, can be highly engaging, and can elevate students’ approach to the level of sophisticated mathematical thought. Such problems are barely hinted at in the draft curriculum.

The stated intention of the Curriculum review was for it to be modest, with an emphasis on “refining” and “decluttering” (p 1). The review, however, has been radical, the absolute antithesis of modest. Moreover, it is radicalism doomed to failure; every top-performing country on international mathematics tests has a fundamental emphasis on the mastery of basic skills, which the draft simply lacks (p 8, p 7). The draft curriculum is an abject failure, on its own terms and on any terms. The draft should be withdrawn, to make way for a fresh review, which includes the proper participation of discipline experts.



Final Day: Our Submission to ACARA

A reminder, today is the last day to make a submission to ACARA’s review of the draft mathematics curriculum. And, a further reminder, you can directly email your submission to ACARA via the yellow box half-way down this page.

Below is our submission to ACARA.



The following is my submission, on ACARA’s draft revisions as part of ACARA’s review of the Australian Mathematics Curriculum.

My position is that ACARA should halt the review. Or withdraw it. Or whatever. Call the process whatever you like, but, please, ACARA should stop. ACARA must stop.

I am not going to argue for the existence of what I believe are the systemic flaws in the draft revisions. You will have had many such, very weighty, submissions, in writing and in person, and you would either treat these submissions with proper and respectful consideration or you would not. A further submission along these lines from me will add no perceivable weight.

What I will argue is that ACARA must stop, because ACARA does not have mathematicians, or at least sufficiently many mathematicians, even remotely on board with ACARA’s proposed revisions. One may argue how this state of affairs has come about, but one cannot argue with the simple fact: ACARA does not have sufficient backing from the community of Australian mathematicians.

Mathematicians’ voices are, of course, not the only voices that need to be heard. Mathematicians are not the rulers here. But mathematicians’ voices are key, and cannot be ignored. Mathematicians are, in the language of the review’s Terms of Reference, the subject matter experts. Any plan to implement a new mathematics curriculum, particularly a radically new mathematics curriculum, without the solid support of the subject matter experts is doomed to failure, or to absurdity, or to both.

Please listen to reality, and please stop the review process.

Kind Regards, Dr. Marty Ross

AMSI Calls for a Halt of the Mathematics Curriculum Review

The Australian Mathematical Sciences Institute has finalised and released its submission for ACARA’s consultation on their draft mathematics curriculum. For eccentric reasons, we haven’t properly read AMSI’s submission. (Seriously.) We understand that it is a good and strong statement. The second and key paragraph is

In early April, AMSI, together with some of its key partners, released a joint statement on the proposed new curriculum “Why maths must change”. AMSI initially endorsed the revised draft curriculum in our joint statement. However, there is now an opportunity to comment on the draft curriculum, and we have revised our position, following extensive consultation with representatives of our member organisations. Many members expressed concern, and indeed alarm, at numerous proposed changes. AMSI and its members believe that the new curriculum should be delayed, and we ask ACARA to halt the current review process.

Continue reading “AMSI Calls for a Halt of the Mathematics Curriculum Review”

What Are the Arguments FOR the Draft Mathematics Curriculum?

This one is a companion to our problem-solving treasure hunt, and again amounts to a competition. We have written roughly ten million words on what is wrong with the draft mathematics curriculum. And plenty of people, including a number of big shots, have signed the open letter calling for the draft curriculum to be withdrawn. But where are the arguments for the draft curriculum? There is undoubtedly support for the draft curriculum. In particular, we are aware of a decent amount of snark directed towards the open letter and this blog. What we are unaware of is any substantive arguments in favour of the draft mathematics curriculum. The only articles of which we are aware, we posted on here and here. The first article came out before the draft curriculum and doesn’t amount to a substantive defense of anything. The second article was written in direct response to the open letter, and is so weak as to warrant no response beyond the comments already posted. And, apart from these two articles we are aware of nothing. No blog posts. No tweets. No anything. Just an arrogant and vacuous dismissal of the draft’s critics.* And now to the competition:

What is the strongest argument FOR the draft mathematics curriculum?

To be clear, what we’re asking for are very specific examples of good things within the draft curriculum, examples of content and/or elaborations that are genuine plusses. So, for example, claiming “the focus on mathematising” as a good won’t win a prize. First of all because the suggestion is really stupid, and secondly because such a generalist statement provides no specific evidence of how the mathematising is good. If you really want to argue that the mathematising is a plus then the argument must be based around very specific examples. Similar to our problem-solving competition, the intention here is not to imply or to prove that there is nothing of value in the draft curriculum. Rather, the competition is intended to imply and to prove that there is very little of value in the draft curriculum. Your job is to try to prove us wrong. Answer in the comments below. The provider of the most convincing evidence will win a signed copy of the number one best-selling** A Dingo Ate My Math Book.  

*) If anyone is aware of any article/post/tweet/anything in support of the draft curriculum, which also contains at least a hint of evidence, please let us know and we will seek to address it.

**) In Polster and Ross households.  

Update (29/07/21)

We’ve finally ended this. The winner is really nobody, but we’ve awarded it to John Friend. See here for details.


Does the Draft Mathematics Curriculum Contain Any Problem-Solving?

We’ve written about this before, and the point is obvious. But, it’s apparently not sufficiently obvious for some wilfully blind mathematicians. So, let’s go again. Plus, there’s a prize for the best comment.*

ACARA is playing people with a cute syllogism.

  • Problem-solving is good.
  • The draft curriculum contains lots of problem-solving.
  • Therefore the draft curriculum is good.

Yep, the syllogism is flawed from the get go. But in this post we want to focus on the second line, and we ask:

Does the draft mathematics curriculum contain any problem-solving?

Certainly the draft curriculum contains a hell of a lot of something. As we’ve noted, the draft refers to “investigating” or some variation of the word 298 times. And, students get to “explore” and the like 236 times, and they “model” or whatever 264 times. That’s a baker’s ton of inquiring and real-worlding, which some people, including some really clueless mathematicians, regard as a good thing. Ignoring such cluelessness, what about genuine mathematical problem-solving?

The draft curriculum refers to “problem(s)” to “solve” 154 times. But what do they mean? When, if ever, is the draft referring to a clearly defined mathematical problem that has a clearly defined answer, and which is to be solved with a choice of clearly defined mathematical techniques? To the extent that there are any such “problems”, do they rise above the level of a trivial exercise or computation? In the case of such trivial “problems”, is the label “problem-solving” more than a veil-thin disguise for the mandating of inquiry-learning?

In brief, is there more than a token amount of the draft’s “problem-solving” that is not either real-world “exploring/modelling/investigating” or routine exercises/skills to be taught in a ridiculously inappropriate inquiry manner?

Perhaps genuine mathematical problem-solving is there, and we are honestly curious to see what people have found or can find. But, we’ve found essentially nothing.

And so, to the competition. Find the best example of genuine, mathematical problem-solving in the draft curriculum. Answer in the comments below. The most convincing example will win a signed copy of the number one best-selling** A Dingo Ate My Math Book.


*) Yes, yes. we have those other competitions we still haven’t finalised. We will soon, we promise. As soon as we’re out of this ACARA swamp, we’ll be taking significant time out to catch up on our massive tidying backlog.

**) In Polster and Ross households.


Update (29/07/21)

We’ve finally ended this. The winner is, hilariously, Glen. See here for details.



ACARA CRASH 14: Backward Thinking

This one we really don’t get. It concerns Foundation and Year 1 Number, and was pointed out to us by Mr. Big.

We began the Crash series by critiquing the draft curriculum’s approach to counting in Foundation. Our main concern was the painful verbosity and the real-world awfulness, but we also provided a cryptic hint of one specifically puzzling aspect. The draft curriculum’s content descriptor on counting is as follows:

“establish understanding of the language and processes of counting to quantify, compare, order and make correspondences between collections, initially to 20, and explain reasoning” (draft curriculum)

“explain reasoning”. Foundation kids.

OK, let’s not get distracted; we’ve already bashed this nonsense. Here, we’re interested in the accompanying elaborations. There are ten of them, which one would imagine incorporates any conceivable manner in which one might wish to elaborate on counting. One would be wrong.

The corresponding content descriptor in the current Mathematics Curriculum is as follows:

“Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point” (current curriculum)

Notice how much more “cluttered” is the current descriptor… OK, OK stay focussed.

The current descriptor on counting has just (?) four elaborations, including the following two:

“identifying the number words in sequence, backwards and forwards, and reasoning with the number sequences, establishing the language on which subsequent counting experiences can be built” (current curriculum, emphasis added)

“developing fluency with forwards and backwards counting in meaningful contexts, including stories and rhymes” (current curriculum, emphasis added)

The point is, these elaborations also emphasise counting backwards, which seems an obvious idea to introduce and an obvious skill to master. And which is not even hinted at in any of the ten elaborations of the draft counting descriptor.

Why would the writers of the draft curriculum do that? Why would they consciously eliminate backward counting from Foundation? We’re genuinely perplexed. It is undoubtedly a stupid idea, but we cannot imagine the thought process that would lead to this stupid idea.

OK, we know what you’re thinking: it’s part of their dumbing down – maybe “dumbing forward” is a more apt expression – and they’ve thrown backward counting into Year 1. Well, no. In Year 1, students are introduce to the idea of skip-counting. And, yep, you know where this is going. So we’ll, um, skip to the end.

The current Curriculum has two elaborations of the skip-counting descriptor, one of which emphasises the straight, pure ability to count numbers backwards. And the draft curriculum? There are four elaborations on skip-counting, suggesting in turn the counting of counters in a jar, pencils, images of birds, and coins. Counting unadorned numbers? Forget it. And counting backwards? What, are you nuts?

OK, so eventually the draft curriculum seems, somehow, to get around to kids counting backwards, to look at “additive pattern sequences” and possibly to solve “subtraction problems”. The content descriptors are so unstructured and boneless, and the elaborations so vague and cluttered, it is difficult to tell. But how are the kids supposed to get there? Where is the necessary content description or elaboration:

Teach the little monsters to count backwards.

If it is there, somewhere in the draft curriculum, we honestly can’t see it. And if it is not there, that it is simply insane.