ACARA Crash 18: Errors in the Draft Mathematics Curriculum

The following is a list of errors – and possible/arguable errors – in the draft mathematics curriculum. Commenters are invited and encouraged to suggest additions, and deletions.

By “error” we mean a statement or instruction that is factually wrong or that makes no logical/mathematical/everyday sense. Some of the listed “errors” are clear-cut, while others are less so. Of course the fact that a statement/instruction made no sense to us does not prove that it makes no sense; we’ve attempted to be fair, being tough on the improper use of technical terms while giving weird phrasings a good-faith pondering in context. Nonetheless, there may well be reasonable interpretations that we have missed. (Of course phrasing that is difficult to interpret has no place in a curriculum document, but that is a separate category of sin.) As well, it is not always clear whether to characterise a statement as an error or simply a really dumb idea, but we’ve tried to stick pretty closely to “error”, leaving the noting of really dumb ideas to our other ninety-eight posts.

The list follows. The majority are elaborations. There are a few content descriptors, for which associated elaborations are indicated by a further indentation. Again, commenters are encouraged both to suggest additions to the list, and to argue for deletions from the list.

Continue reading “ACARA Crash 18: Errors in the Draft Mathematics Curriculum”

ACARA CRASH 17: Algebraic Fractures

The following are Year 10 Number-Algebra content-elaborations in the current curriculum:


Apply the four operations to simple algebraic fractions with numerical denominators


expressing the sum and difference of algebraic fractions with a common denominator

using the index laws to simplify products and quotients of algebraic fractions


Solve linear equations involving simple algebraic fractions


solving a wide range of linear equations, including those involving one or two simple algebraic fractions, and checking solutions by substitution

representing word problems, including those involving fractions, as equations and solving them to answer the question

And what does the draft curriculum do with these?


And, why?

Not essential for all students to learn in Year 10.

God only knows how one develops fluency with expressions that cease to exist.

ACARA CRASH 16: Unlevel Playing Field

Each Year’s content in the draft curriculum begins with a Level description, and each of the thirteen Level description begins with the exact same sentences:

The Australian Curriculum: Mathematics focuses on the development of a deep knowledge and conceptual understanding of mathematical structures and fluency with procedures. Students learn through the approaches for working mathematically, including modelling, investigation, experimentation and problem solving, all underpinned by the different forms of mathematical reasoning. [emphasis added]

Yep, “an equal focus on building fluency“, no doubt about it.


And the Winner Is …

Definitely not Sydeney.

OK, in a futile attempt to unPonzi our blogging scheme, we’re closing off our four competitions.* The winners are indicated below, and any winner who has not died of old age should  email us to receive their prize, a signed copy of the best-selling** A Dingo Ate My Math Book.***

Continue reading “And the Winner Is …”

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.