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.




AAS Fellows Were Apparently Not Consulted in the Signing of the Joint Statement

A couple of days ago we wrote about the Australian Academy of Science squirming away from the March 31 joint statement, which they had signed. AAS effectively claimed that the joint statement was mere motherhooding on problem-solving, and “was not in response to” the draft curriculum.

AAS’s clarification wan’t much of a clarification; it was vague and evasive, made little sense on its own terms, and left plenty unexplained, In particular, there was no explanation of how AAS signed on to the joint statement or why, and whether NCMS – the body within AAS responsible for mathematics education policy – was consulted or had approved the signing.

In the past months, we have had many discussions about AAS and the joint statement. One person, who we understand to be truthful and to have a reasonably reliable sense of what happened, has given us the picture. In brief, and to quote them:

“the signing [of AAS onto the the joint statement of March 31] was by educational/administrative people within the AAS, and without consultation with fellows with expertise in the mathematical sciences.” [emphasis added]

We forwarded this exact quote to AAS, and provided AAS with ample opportunity to respond, to deny or to clarify the quote, or simply to indicate that they will respond in due course. AAS declined to acknowledge our email in any manner. As such, and until AAS provides some plausible correction, it seems reasonable to take the quotation as a statement of fact.

What the quotation implies is that the “Australian Academy of Science” having signed the joint statement has the rough authoritative value of the Shepparton Grammar Gazette.* As to why AAS is comfortable with this state of affairs and refuses to correct and clarify the record, and what mathematician fellows of AAS think of all this, one would have to ask them.


*) Such an evaluation would seem reasonable for any statement attributed to “AAS”. As it stands, we can see no way to determine whether any “AAS statement” has received the proper consideration of AAS’s deservedly respected fellows, or is merely the random thoughts of a random employee. Such an “academy statement” appeared in a woefully bad SMH column on July 8, responding to AMSI’s submission. (Guys, it’s pure optimism to expect you to do your job well, but you could at least think about the meaning of “maths experts”.) We have endeavoured to determine what the AAS statement means, and who within AAS wrote and/or approved the statement; AAS has not acknowledged our questions. As such, and until we receive any proper clarification, we regard the “AAS statement” within the SMH article to be of approximately zero value.

AAS Did Not Endorse the Draft Mathematics Curriculum

The title is accurate, although it requires explanation. But, first things first.

We’ve been sitting on details of this story for weeks, waiting for aspects to become clear. Or, mostly, waiting for the Australian Academy of Science to admit that they screwed up and to correct their screw up. There is still no clarity or admission, but there may never be. So, we will write what we know and are permitted to reveal.*

On March 31, the joint statement Why Maths Must Change was released to the world. Poorly argued, garishly colloquial and intrinsically poisonous, this statement was widely interpreted as an endorsement of the draft mathematics curriculum. Whether or not that is the case is farcically contentious.

The draft mathematics curriculum appeared on April 29, a month after the joint statement. The joint statement was also couched almost completely in general terms, of what the signers wished to see in the draft. All in all, permitting a semi-plausible deniability that the joint statement is an endorsement of the draft curriculum. Of course, to confirm what the joint statement means and implies, one would seemingly just need to ask the institutions that signed on.

Five institutions signed the joint statement, three of which were absolutely no surprise and of whose opinion we couldn’t care less on this issue. AAMT, which we understand is the ringleader here, is the Australian Association of Mathematics Teachers; we have never and will never expect a sensible statement from this group. ATSIMA is the Aboriginal and Torres Strait Islander Mathematics Alliance, and we know nothing of their general work. Aboriginal education is obviously a disaster, and we hope to learn more about various efforts to improve it. But, in regard to the joint statement ATSIMA seems, at strained best, just another teacher group. MERGA is the Mathematics Education Research Group of Australasia; it is the professional association of maths ed researchers, and it seems exactly the kind of group that Douglas Adams would have thrown onto Golgafrinchan Ship B.

That leaves the two puzzling signers, AMSI and AAS.** The Australian Mathematical Sciences Institute, Australia’s key institute for mathematics research, have now formally revised their position, effectively disowning the joint statement. In particular,  AMSI have called for ACARA to “halt the current review process”.

And then there was one.

The Australian Academy of Science is a highly prestigious organisation, with a few Fellows elected each year. The mathematician Fellows include Tony Guttmann and Alan Welsh, both of whom signed the open letter, and Ole Warnaar, the President of AustMS. As well as providing a cosy home for Very Big Shots, AAS has a number of outward reaching subgroups, including a schools education program, and the National Committee for Mathematical Sciences. NCMS is chaired by Alan Welsh, it also lists Ole Warnaar as a member, and has as its primary goal “to foster mathematical sciences in Australia”; as such, NCMS appears to be the main group responsible for AAS policy towards mathematics education.

So, how did AAS come to sign the joint letter, and does the joint letter constitute an endorsement of the draft curriculum?

We are in the midst of a protracted exchange with AAS, the key parts of which we include below. The exchange has been frustrating and absurd.*** it began on June 25, when we contacted AAS with a number of questions (see below). AAS’s reply came a week later, on July 2:

The joint statement was issued on 31 March before the public consultation period for the Australian Curriculum review, not in response to it. The statement noted the importance of the development of mathematical skills and the application of these skills to problem-solving. The Australian Academy of Science is reviewing the revised curriculum document that is out for consultation, in order to consider our response to it.” [emphasis added]

As the correspondence indicates, this reply was inadequate for a number of reasons, but we first dealt with the kernel of clear declaration contained within. In our reply on the same day, we wrote:

“I will begin with my second question, which the [AAS media] statement … does appear to answer. I take it that, as of July 2, AAS has not endorsed the proposed revisions to the mathematics curriculum, and in particular that AAS does not accept the joint statement of 31/3 to be any such endorsement.” [emphasis added]

We indicated to AAS our intention to write this, and we have given them ample to correct or clarify the above, and anything else. They have not responded.

So, with AAS’s statement of July 2, and with their so-far unwillingness to correct the natural interpretation of this statement, it should be accepted that, before July 2, AAS did not endorse the draft mathematics curriculum. It is implied by AAS’s stated public position that anybody suggesting otherwise is making stuff up.

Of course this is by no means the end of the story. AAS’s reasons for and manner of signing the joint statement are as yet totally unexplained. AAS’s actual position on the draft curriculum, earlier and now, are as clear as mud; AAS was most recently quoted in a July 8 article, but the quotation is slippery. We also have no idea whether AAS made a formal submission to ACARA, or who may have contributed to or signed off on this submission. We are endeavouring to clarify all this, and we hope to write more tomorrow.


*) We are seeking further knowledge and further permissions. Of course we will update this post or write a new post if and when either is forthcoming.

**) Notably, the Australian Mathematical Society, the professional association for Australian mathematicians, did not sign onto the joint statement. We do not know  whether AustMS was approached to sign, a remarkably tricky question to answer.

***) We have been instructed that any statement from AAS should be labelled as having come from “an Academy spokesperson”. We will just note that practicality determined we go through AAS’s media office. That office has been friendly and attentive throughout; it is not their fault that they’ve been instructed to pass on obfuscating nonsense.


Email to AAS, June 29

Dear [media person],

My name is Marty Ross. I just talked to you on the phone. I am a mathematician who takes an interest in and writes upon educational matters.

I am enquiring about a joint public statement that AAS signed, which was released on 31 March:

This is a “statement on [the] proposed mathematics curriculum”, and includes the line

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

It is therefore, and in total, not unreasonable to read the joint statement as an endorsement of the revisions currently proposed for the Australian mathematics curriculum. I think it is also fair to say that the statement has been widely understood in this manner, both by the general public, and by mathematics and mathematics education professionals.

Here are my questions to AAS regarding the draft revisions and the joint statement.

1) Was NCMS consulted before AAS signed on to the joint statement?

2) Does AAS endorse the proposed revisions to the Australian mathematics curriculum?

3) If not, does AAS intend to provide a media release to clarify and/or to correct the public record?

Thank you very much.

Kind Regards, Marty

Email from AAS, July 2

AAS replied with pleasantries, and the statement above, but nothing else.

Email to AAS, July 2 (and there has been no subsequent reply from AAS]

Dear [media person],

Thank you for your reply. I understand the manner in which I should attribute this statement and any subsequent statement from AAS.

Unfortunately, AAS’s statement [above] raises more questions than it answers. I will indicate my current understanding and ask (and re-ask) some questions. I will also indicate my current understanding, upon which I intend to write. AAS is welcome to clarify anything that I have written, and I sincerely hope that this is done, but I do not intend to wait another week for a response.

I intend to write on this Monday evening. Of course I will carefully consider anything AAS wishes to share before then, and I am happy to discuss this by phone if that is preferable.


I will begin with my second question, which the statement below does appear to answer. I take it that, as of July 2, AAS has not endorsed the proposed revisions to the mathematics curriculum, and in particular that AAS does not accept the joint statement of 31/3 to be any such endorsement.


Now, I will ask my first question again:

1) Was NCMS consulted before AAS signed on to the joint statement?

As it stands, my understanding is that NCMS was not consulted. I also note that AAS has ignored a direct question to confirm or to deny this.


Next, I will ask my third question again:

3) Does AAS intend to provide a media release to clarify or correct the public record?

As it stands, I have no indication that AAS intends to do so, and in particular to do so before public consultation on the draft revisions closes on July 8. As such, AAS has indicated no intention to take responsibility for the public interpretation of the joint statement of 31/3, and in particular for the bold statement that AAS signed on to, that “… the suggested revisions in the [mathematics] curriculum are … welcomed …”.

To possibly allow AAS to clarify this in part, please let me ask a follow-up question:

4) Does AAS intend to make its response to the proposed revisions publicly available, and if so will that be before or after the closing of public submissions on July 8?

As it stands, I note that AAS has not indicated that they intend to make their submission to ACARA publicly available, although that would presumably help clarify the joint statement of 31/3.


Finally, I will note and inquire about two puzzling aspects of AAS’s statement below.

AAS notes that the joint statement was “not in response to [the public consultation period for the Australian curriculum review]”. This sentence makes no sense as written. The joint statement is advocating, and in one line applauding, certain aspects of a curriculum. It is also clear that the proposed curriculum revisions have turned out to be very strongly in line with what the joint statement was advocating/applauding. The statement also appeared on 31/3, presumably long after the draft revisions had taken shape.

5) What was the purpose of the joint statement?

6) Was the person/persons from AAS who agreed to AAS signing the joint statement aware of the nature of and/or detail fo the draft revisions? If so, how?

As it stands, I can conceive of no other purpose for the joint statement other than as preemptive support for the draft revisions, from people sufficiently aware of the nature of those revisions.

The other puzzling aspect is that the joint statement “noted the importance of the development of mathematical skills …”. However, the phrase “mathematical skills” is never used in the joint statement. The term “skills” is used six times, and on my reading all six uses are concerned with the skill of applying mathematics to problem-solving, not what is typically referred to by mathematicians and teachers as “mathematical skills”.

7) Will AAS indicate precisely what they mean by “mathematical skills”, and how the joint statement notes the important of the development of these skills?


Thank you again. as I indicated, I  look forward to any further clarification AAS may be provide, and I am more than happy to discuss this by phone. Also as indicated, I intend to write upon this Monday evening.

Kind Regards, Marty

ACARA Tells the Australian Mathematical Society to Get Stuffed

The period for submissions to ACARA on their draft mathematics curriculum closed on July 8. Our intention is to wind this up, and get to the backlogged mountains of nonsense, but there are at least a couple more posts that need to be done.

On July 2, The President of the Australian Mathematical Society,* Ole Warnaar, wrote to ACARA’s CEO, David de Carvalho. Ole has subsequently written an open letter to ACARA on what then occurred.

In his July 2 letter, Ole requested an extension of the “consultation period”, so as to enable “a proper process of engagement with the mathematics discipline”. This did and does seem to us to have been a confused and unwise request,** but de Carvalho, by being even more confused and less wise, and foot-shootingly arrogant, made sure that it didn’t matter.

De Carvalho responded to Ole pretty much immediately, noting that there had already been “extensive engagement with teachers, curriculum experts and professional associations”, that July 8 meant July 8, and that was it. In brief: Ole and the mathematicians he represented could get stuffed.

Ever an optimist, Ole arranged for him and VP Geoff Prince to meet with ACARA representatives, which occurred on July 5. This meeting confirmed, according to Ole, that

“mathematical scientists were not involved in any official capacity in the preparation of the revised curriculum”

Other than that, Ole’s description of the meeting, and of AustMS’s current stance, is vague. In brief, it seems that AustMS was told to get stuffed. Again. The exchange of letters and Ole’s summary of the meeting can be read here.

We will make just one point, which we have made before. De Carvalho may be 100% correct in what he wrote, But. It. Doesn’t. Matter. One. Jot.

There is all manner of well-practised ways to game “consultation”, and it would be bridge-buying naive to not suspect ACARA of having done so. But suppose not? Suppose ACARA went out in good faith and consulted widely, and honestly and intelligently and knowledgeably considered the feedback? Doesn’t sound likely, but let’s suppose that’s all true. It doesn’t matter.

What matters is, however it happened, that Australian mathematicians are not remotely on board with the draft curriculum. With the distinguishable exception of Chris Matthews,*** we are unaware of a single Australian Mathematician who has come out publicly with anything remotely like support for the draft. By contrast, many mathematicians, including a number of very prominent mathematicians, have come out strongly, calling for the draft to be delayed or to be withdrawn entirely: in the open letter; in AMSI’s submission; and now in AustMS’s futile pleading for some belated sense.

In the face of such strong opposition from mathematicians, from the “subject matter experts“, for ACARA then to bulldoze on with its review is fingers-in-ears madness. Which is just what one would expect.


*) The professional body for Australian mathematicians. You know, those guys that know maths and stuff.

**) We know Ole pretty well, and have co-taught with him. He is a very strong mathematician and a great guy. Ole made a dumb move here, but he was doing what he thought best in a dumb-dumb-dumb situation.

***) Chris Matthews reportedly advised on the curriculum, seems to us to have made a mess of things, and his contribution requires serious discussion. It is better done elsewhere.

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.