Open Letter to ACARA and the ACARA Board

The following is an open letter to David de Carvalho, CEO of ACARA, and to the ACARA Board. regarding the draft mathematics curriculum. The home of the letter is here, you can sign up here, and the list of current signatories is here.

Disclosure: The letter was not my idea, and it is not my letter, but I had a hand in bringing the letter to fruition. As to why I think the letter is important, see here.

UPDATE (08/07/21)

The sign-up page for the open letter has now been closed. Greg Ashman, the boss of the open letter, will submit (or has already submitted) the letter and the list of signatories today, to ACARA and to the ACARA Board.

Greg Ashman deserves a huge thank you from the Australian maths ed world. Greg instigated the open letter, and managed it through, and it simply wouldn’t have existed without him. There are also a number of other, anonymous or semi-anonymous, people who deserve a very big thanks. Some for their persistent and incredibly irritating hammering on various drafts, and some for helping to sign up various Mr. Bigs.

And, a very big thanks to the hundreds of people who signed on to this strong and public declaration.


Open letter to Mr. David de Carvalho, CEO of ACARA, and the ACARA Board

On 29 April 2021, the Australian Curriculum, Assessment and Reporting Authority (ACARA) released its draft revisions to the Australian Mathematics Curriculum, with a consultation period ending on 8 July 2021. We are a group of mathematicians, mathematics educators, educational psychologists, parents and members of the public who take an active interest in mathematics education and in the curriculum. We agree that the Mathematics Curriculum desperately requires reform; it is repetitious, disconnected, unambitious and is lacking in critical elements. We are pleased that efforts to reform the curriculum are underway. We are profoundly concerned, however, with the structure of the current draft and with many of the proposed changes within.

The primary source of our concerns is the proposal to replace the four Proficiencies in the current Curriculum with the draft’s thirteen “Core Concepts”, grouped under three “Core Concept Organisers”. The Proficiencies – understanding, fluency, reasoning and problem-solving – are well-understood and provide a clear structure for teaching mathematics. In contrast, the Core Concepts are often poorly defined and overlapping, vary massively in scope and breadth, and their groupings into Core Concept Organisers, including the faddish “Mathematising”, are a mostly arbitrary and at times contradictory categorisation. The critical element of “thinking and reasoning”, for example, has somehow been reduced to just another concept among thirteen, sharing equal value with wordy descriptions of simple ideas. The end effect is a framework of little practical value as a guiding structure.

The Core Concepts are confused and confusing, but it is clear that they represent a push toward a central role for “problem-solving” and inquiry-based learning. Solving problems is obviously a core aspect of mathematical practice, is an important goal for mathematics education, and is already listed as one of the four Proficiencies in the current curriculum. The issue with the draft curriculum is that its “inquiries” are unanchored by clear and specific content, by underlying knowledge and skills. Moreover, the “problems” suggested to be “solved” are mostly exploratory and open-ended, effectively unsolvable and of questionable pedagogical value, and with little or no indication of the specific desired learning outcome. Insufficient attention is given to carefully constrained problems facilitating the practicing and subsequent extension of already mastered skills. Making things worse, the inclusion of inquiry methods in the content descriptors results in the descriptors being almost useless as determiners of actual content. This obscures the key ideas and basic skills to be learned, which are the foundational elements essential for any effective mathematical practice, including for problem-solving.

The draft is not so much pushing problem-solving as it is pushing for learning through activities referred to as “solving problems”, but which are actually ill-defined explorations. We do not believe that a curriculum document should mandate a specific method of mathematics teaching, and it is especially concerning that the draft curriculum is extensively mandating learning through “exploring” and “problem-solving”. There is strong evidence to indicate that methods without a proper balance that includes the explicit teaching of mathematical concepts are less effective, in particular for younger students grappling with new concepts and basic skills. The content of the mathematics curriculum, even for the lower years, is the result of millennia of human endeavour across cultures around the world – it is neither fair nor realistic to expect students to retrace this journey with a few pointers and inquiries in a few hours per week.

The emphasis in the draft curriculum on open-ended inquiry, without the systematic building of coherent knowledge, creates further serious issues. Some indication of these issues is provided in the following paragraphs, but many, many more examples could be given.

The delaying and devaluing of fluency, of “the basics”

The draft curriculum includes some particularly concerning Content descriptors, and rearrangement of material. The learning of the multiplication tables, for example, is first addressed only in Year 4, where it is framed in terms of “patterns” and “strategies”, with no emphasis on mastery. Similarly, the solving of linear equations such as ax + b =c, a foundational skill for all secondary school mathematics, is pushed in the draft from Year 7 to Year 8. There is simply no valid argument for these, and many other, dilutions and delays. Indeed, the draft curriculum has squandered the opportunity to address some glaring problems with the timing and emphasis of content in the current Curriculum.

The loss of natural mathematical connections

Mathematics in the current Curriculum consists of three strands, but the draft has split these into six strands. The very natural Number-Algebra strand, for instance, has become separate strands of Number and Algebra. This is unwieldy, effectively requires a redefinition of “algebra” and, most damagingly, it severs the critical pedagogical link between these two disciplines. Similarly, the strands of Measurement-Geometry and Statistics-Probability have been split into Measurement, Space, Statistics and Probability, for no benefit or good purpose.

Shallow conceptualisation

Notwithstanding ACARA’s repetitive claims to be promoting “deep understanding”, the draft’s overwhelming emphasis on investigation and modelling has resulted in many critical mathematical concepts being underplayed and, in certain cases, not even being named. In Algebra, for example, fundamental terms such as “null factor” and “polynomial” and “completing the square” rate not a single mention. To give an analogy, it is as if a curriculum on Politics failed to mention “sovereignty” or “citizenship” or “separation of powers”.

The devaluing of mathematics

The problem-solving, investigation and modelling that is advocated by the draft curriculum is very heavily weighted towards real-world contexts. Indeed, the definition of “Problem solving” provided in the draft Curriculum’s “Key considerations” section explicitly mentions solving problems relating to the “natural and created worlds”, and pointedly omits references to solving problems stemming from mathematics itself. This approach squanders an excellent opportunity for students to gain an appreciation of mathematics as a beautiful discipline, a discipline which can be its own goal. This devaluing of mathematics is starkly displayed in the description of, and in the very name of, the Space strand. Whereas Geometry is concerned fundamentally with the study of abstract objects and their properties, the Space content is heavily slanted towards the study of real-world contexts. Learning in genuine real-world contexts is much more difficult, because the real world is inevitably full of distractions that cloud the clear principle to be learned.

Mathematical errors and non sequiturs

Some errors in the draft are subtle, but many are not. There is no purpose, for example, in directing students to “investigate … Fibonacci patterns in shells”, since such patterns simply do not exist. Such errors and confusions would typically be caught during a proper review by mathematicians; their existence in the draft curriculum places into serious question the nature and the extent of ACARA’s consultation process.

Finally, we make two points about ACARA’s presentation and promotion of the draft curriculum.

Part of ACARA’s justification for the strong emphasis on problem-solving has been that the mathematics curriculum in Singapore, an education system that performs extremely well in the mathematics component of the Programme for International Student Assessment (PISA), places an emphasis on problem-solving. We seriously question whether the Singaporean sense of “problem-solving” bears even a remote resemblance to ACARA’s use of the term but, in any case, ACARA’s justification fails on its own terms. To begin, there are other education systems that also place a premium on problem-solving but that do not perform at anywhere near the level of Singapore in PISA mathematics. Further, whatever the role of problem-solving in the Singaporean curriculum, this curriculum is also very demanding in terms of fluency with basic skills; no comparable requirements exist in the current Australian Curriculum, and the draft curriculum only pushes to weaken these requirements. The further elimination and weakening of fundamental skills will contribute to the root cause of Australian students’ slipping in international comparisons: the students end up knowing less mathematics.

Secondly, an important aspect of ACARA’s review is that it was intended to be modest in scope, with a focus on “refining” and “decluttering”. The draft curriculum fails in both respects. The radical introduction of the Core Concepts structure and “Mathematising”, the separation into twice the number of strands, the multipurpose nature of the Content, is all the antithesis of modest. This new structure is, inevitably, much clunkier, with massively increased curriculum clutter. The draft curriculum is barely readable.

In brief, the draft curriculum is systemically flawed. It is unworkable, and it fails to capture or to promote the high standard of mathematical knowledge, appreciation and understanding that Australia’s schoolchildren deserve.

The Australian mathematics curriculum requires proper review. Such a review, however, must be undertaken without a pre-ordained outcome, and with the proper participation and consultation of discipline experts. Indeed, ACARA’s own terms of reference for the review specify that the content changes are to be made by subject matter experts, namely mathematicians. It is difficult to imagine that this was the case.

We urge ACARA to remove the current draft mathematics curriculum for consideration and to begin a proper and properly open review, in line with community expectations and with Australia’s needs.


41 Replies to “Open Letter to ACARA and the ACARA Board”

  1. What a great letter. I wish I could write a letter even 10% as good.

    Really great job Mystery Writer and Marty. I hope that ACARA reads it carefully and takes the appropriate actions.

  2. Marti,

    I liked your ” Burke and Wills ” anology on NewsRadio yesterday morning when the open letter got a few minutes of prime time. Hopefully D de C was tuned in and taking notes

    Steve R

    1. Thanks, Steve. I also used it on a Sydney radio interview. On the Sydney interview, I also used a great one David Treeby thought up for inquiry learning of the basics: It’s not so much putting the cart before the horse, as it is killing the horse and expecting the cart to drive itself.

  3. Good interview on the ABC. Well done Marty.

    You don’t learn to play football just by playing lots of football matches in the real world.

    1. Thanks, Andrew. The unreadability suffices to require the draft be withdrawn. But there’s also plenty of awfulness hidden in the jungle of words.

  4. Understanding the basics of maths is not being taught to our grandchildren, tgry can’t work out change ir even tell time. We must provide basic education in maths and English as tgat is where the basic problem solving skills come from. The Basics nit stupid concepts

  5. Excellent response to an unteachable curriculum designed by those with little real experience of the complexity of teaching

    1. Thanks, Patricia. I’m not sure the draft curriculum is unteachable, but it appears pretty unlearnable. I can see a teacher giving the little kids some nonsense to explore, and as long as no one cares whether anything is actually learned, we’re all fine.

  6. Brilliant, are any of the ACARA team actually educators? Whatever happened to reading, writing and arithmetic basic principles? Can they explain why Australia have dropped so far behind other nations. Please leave out politics, educate students then they can make their own decisions when they leave school.
    Very concerned grand parent.

    1. Hi Sandy. It’s impossible to know the credentials of the ACARA team because the people on the team are not known. It’s a secret.

      For what it’s worth, the following links might be relevant to you first question: – she’s working on a PhD in ‘Mathematics Education’.

      And possibly unrelated, here is something interesting:

    2. Hi, Sandy. As John said, the method by which ACARA produces the curriculum is very opaque. Yes, they have a lead writer (for whom I feel genuinely sorry), and paid consultants, but they also have all sorts of “consultation” with “key stakeholders”. Whatever the process amounts to, ACARA has put forward an undeniably radical curriculum. Not that “radical” need be bad. But in this case it is bad, and it is being supported merely by puff words, not evidence of any sort.

  7. It’s about time the maths curriculum was overhauled. There is too much emphasis on non-maths issues and not enough on the basics.

    Once maths has been corrected move on to other subject which are full of wokisms. Enough is enough!

    1. Yes, it’s getting overhauled. Again. By the same people. Again.

      And in a few years time, when standards are still dropping, it will get overhauled. Again. By the same people. Again.

      Getting the people who create the problem again and again to fix the problem again and again – the quintessence of stupidity.

    2. Thanks, Carol. I am not sure “wokism” is an important aspect of the draft mathematics curriculum (or the current curriculum). There is that aspect to consider, and I hope to get to it, but it pales in importance to the lack of basics and related issues.

  8. I think its wonderful and important to teach Aboriginal studies but this is a mathematics curriculum. 115 times ‘aboriginal’ appears in this mathematics curriculum review. Not hard to do the maths and conclude that the authors have lost touch with what our children need and deserve to simply just appreciate and learn mathematics in a way that will allow them to compete with the rest of the world. Throw this away and start again with someone whose only concern is to teach mathematics

    1. Hear, hear. We certainly don’t need a gang of fools whose sole motive is to impress everyone with their wokeness.

    2. Thanks, Wayne. The 115 is probably, in effect, a serious undercount. There is something pretty ridiculous going on here, although, as I indicated in reply to Carol above, I don’t think it comes close to the most important flaw in the draft.

      I’m not arguing that the draft should include the amount of ATSI material that it does, and a number of the elaborations appear very forced. But mostly this material could be ignored if a teacher chose to do so. And, a maths teacher has to take their real-world examples from somewhere; if a few (not a hundred) of these are taken as genuine illustrations of under-appreciated ATSI technological culture, I think that is a good thing.

      1. It doesn’t matter who the letter is addressed to. My point is that you could easily substitute 2021 for 2014 on this letter. How can ACARA possibly say with a straight face what it’s said in 2021, given what it says in this 2014 letter?

        1. Sorry, John. I should have given it more time, but I’ll still ask you to do my homework for me. What do you see as the contradiction, or whatever, between 2014 and 2021?

          1. Look at how 2014 ACARA are describing the curriculum its rolling out (todays current curriculum). Now look at what 2021 ACARA are saying about it’s Daft Curriculum. Do you see the irony?

            2014 ACARA are saying the now current curriculum is high quality and mathematics education is going to be better off with it. 2021 are saying that its Daft curriculum is high quality and mathematics education is going to be better off with it. Do you see the irony? 2021 ACARA are quoting the 2014 letter almost word for word.

            Replace 2014 with 2021, put the letter in a time capsule, open in 2028 and compare with what 2028 ACARA are saying …

  9. ACARA appear to be confused about the subject they refer to.
    Mathematics is mathematics. It is not history or cultural studies.

    1. Thanks, David. See my reply above to Wayne, regarding ATSI material. I’ll just add a quick note on the history (and, implicitly, cultural studies).

      Mathematics is a human endeavour and it has a human history. That history can be fascinating and enlightening, and if elements of this history were included in a school mathematics curriculum, that would be a great thing. Not as the main game, and not to promote a cultural relativism, but simply to make the often difficult learning of mathematics more human and relatable. Since, for example, the ancient Greek geniuses didn’t have any proper concept of fractions, is it any wonder that an 8YO kid is gonna struggle? It seems to me like a very good thing to say to such a kid.

  10. It appears AMSI is backtracking on its previous support of the Australian curriculum and have asked for a halt to the review process.

    The director Tim Marchant said AMSI had backed the curriculum before the draft had been formally released. The change in support is a result of significant member backlash. Alan Tudge seems supportive of AMSI’s newfound position which is a excellent sign. AMSI has made a submission to ACARA which will be made public today, though it doesn’t appear to be released yet. There must have been a lot going on behind the scenes for this to have precipitated. Hopefully we can get meaningful change out of this, though it would require consistent engagement and input from the big shots.

    An editorial on the topic (with some colourful comments from readers):

    1. Good news, indeed. Let’s see how many others (like MAV) start jumping on the bandwagon now. The scramble will be on to cover up their past obsequiousness.

      Re: “The director Tim Marchant said AMSI had backed the curriculum before the draft had been formally released.”

      Does this mean AMSI backed something that they hadn’t actually seen? If so, they’re a bigger bunch of irrelevant fools than I thought.

      Re: “There must have been a lot going on behind the scenes for this to have precipitated.”

      Well, and I know Marty will deny his role, the contributions of Marty (and Greg Ashman and others) has been of inestimable value. Maybe ACARA can include its calculation as part of an open-ended, inquiry based, problem solving activity in its next daft curriculum. Assuming it’s allowed to go anywhere near one – I wouldn’t trust ACARA to write a curriculum for teaching dogs how to piss on a tree.

      Unfortunately the articles you’ve alerted us to are behind a paywall.

      1. John, however it happened, obviously AMSI (and AAS) screwed up by signing onto that joint statement. But it is a massive move for AMSI to now come out against the draft curriculum. Focus on the positive.

        1. OK, true enough. Others, who should be doing much more, will probably maintain their neutral stance, which is simply gutless obsequiousness. AMSI is big enough to admit its mistake(s), so congratulations to them and more power to its arm in this fight.

          1. Thanks, John. AMSI deserve congratulations. It is very difficult for such an organisation to come out strongly in this way, and it’s really difficult if it gets off on a very wrong foot.

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