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.
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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.
Sincerely,
Well done on the open letter
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.
Thanks, I will be encouraging my colleagues to sign.
I hope that it has a positive effect.
It probably depends a fair amount on mathematicians. Which is unfortunate.
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
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.
https://www.abc.net.au/radio/newsradio/open-letter-slams-changes-to-national-curriculm/13371700
(And who read this a while ago – https://www.dailymail.co.uk/news/article-9532117/Australia-warned-nation-cretins-education-minister-slams-new-curriculum.html?ns_mchannel=rss&ns_campaign=1490&ito=1490
“will become” …? )
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.
Thanks, Terry.
“The draft curriculum is barely readable” possibly says it all?
Thanks, Andrew. The unreadability suffices to require the draft be withdrawn. But there’s also plenty of awfulness hidden in the jungle of words.
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
Thanks, Dawn.
Excellent response to an unteachable curriculum designed by those with little real experience of the complexity of teaching
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.
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.
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:
https://www.acara.edu.au/about-us/our-governance/our-executive
https://www.australiancurriculum.edu.au/media/7113/mathematics-transcript.pdf – she’s working on a PhD in ‘Mathematics Education’.
And possibly unrelated, here is something interesting: https://www.acara.edu.au/news-and-media/acara-presentations
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.
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!
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.
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.
Well written letter, totally agree!
Thanks, Robyn.
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
Hear, hear. We certainly don’t need a gang of fools whose sole motive is to impress everyone with their wokeness.
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.
The strong links to indigenous perspectives is because the results for indigenous students are low.
They feel that creating a curriculum filled with topics that link to their Aboriginality will provide a relatable context for them to learn maths…. But if that is indeed the case, what of the students who don’t connect with the indigenous concepts?
Let’s just teach proper maths concepts and then we can link to, and solve, whatever investigative problem we wish.
Thanks, Calam. I’m honestly not sure that concern for indigenous students is the primary motivation. It seems to me the motivation is at least as much out of concern that *all* Australian students gain an appreciation of indigenous culture.
Both concerns seem to me to be valid and important. But laying it on that thick, and making stuff up, is clearly not going to do anything for anybody.
Yes, well said, much better than I was able to express it.
I always thought it was silly to try and force cross curricular priorities. At best, it simply redistributes the time spent learning each subject. At worst, a teacher may give up time teaching their curriculum area to teach the cross priorities in the hopes that other teachers will do the same and they don’t, meaning your students have lost time in your content area.
Would you want their English teacher spending time teaching them how to read graphs and their math teacher teaching them how to structure essays anyway?
As an out of field math teacher myself, I worked hard to understand the content and then try to distill that process and knowledge to my students.
I always felt like a failure when the students would struggle to grasp simple concepts through the creative, inquiry-based learning approaches that we were encouraged/assessed on using.
I would see colleagues focusing on teaching the basics through explicit teaching models, and knew that is exactly what my students needed, but I was too afraid to go against the teaching methods we were told to use and which my lessons got assessed on.
I think the best approach is explicit teaching of the basic concepts, teasing out responses from students when you can have those brief moments of inquiry/student intuition and, practicing the basic concepts and then extending their knowledge through creative problem solving requiring them to try out using their existing knowledge in new ways. They will now have a sufficient amount of knowledge of the topic area to possibly explore other applications relating to their own interest/perspectives.
Thanks again, Calam. I’ve spent very little time thinking about the cross-curriculum stuff, but I think I probably agree. Even if the priorities were both well-chosen and properly-honestly addressed, the effect is probably just to muddy subjects and disciplines, with no tangible benefit.
Hi Callam.
Thanks for your posts. You’ve raised excellent points. I agree with all of them.
I’m very curious about the following:
“I would see colleagues focusing on teaching the basics through explicit teaching models, and knew that is exactly what my students needed, but I was too afraid to go against the teaching methods we were told to use and which my lessons got assessed on.”
and have some questions:
Who told you what teaching methods to use?
Who was assessing you?
Why were your colleagues allowed to use explicit teaching (and so going against the teaching methods you were told to use)?
I’m guessing this happened during a teaching placement while you were a pre-service teacher, and that the people telling you what methods to use were the so-called ‘education experts’ who lectured you (and maybe your mentor, who probably didn’t want to seem ‘old-fashioned’ in the eyes of your lecturers) …?
It happened when I was on contract trying to impress the profilers who we would have come in as part of our professional development plan or make sure I was doing what is jammed down our throats at PDs when HoDs or deputy’s would walk through.
My colleagues were all permanent and I guess either had less of a care factor for ‘getting in trouble’ or were adamant enough that this was how they were going to get the best out of their students…..or maybe they were just old fashioned and resistant to change 😅
It’s very deflating constantly feeling like you’re not good at what you do because what you do doesn’t work….when actually It’s because it just plain doesn’t.
Different topics lend themselves to be taught in different ways. Inquiry is a marvellous part of learning. Having a question opens the students minds, ready to receive knowledge. Though that process can happen in the form of ‘how can we solve this?’ “Here, I’ll show you…..step 1 is this…because….”
Hi Calam.
That would have been my second guess. Schools give a lot of money to con-artists selling snake oil, and when schools invest heavily in something …
Most schools regularly invest in steaming piles of shit wrapped in shiny paper. Reasons include:
1) Wanting to look innovative and cutting edge, wanting to market themselves as practitioners of “world best pedagogical practice”. As the old saying goes: “An ounce of image is worth a pound of performance”. Schools are obsessed with image.
2) To climb up the greasy pole your resume has to show that you led a whole school initiative in something. People with ambitions to climb the slimy pole are therefore easy targets for con-artists selling snake-oil. And the people higher up the pole encourage this to happen because then they can tick the box for “building capacity in the system”.
3) People higher up the food-chain are easily dazzled by shiny new things. They are like small children in a sandbox who find a new toy. Usually the ‘toy’ is a poisonous spider.
4) You have ‘Learning Specialist’ (a new category created under the current EBA to provide greater opportunity for promotion) that have to justify their position (and schools have to justify the position too). So they get given some snake-oil to implement in the school. Often this snake oil will involve taking teachers out of the classroom so that they can participate in what the snake-oil is promising. Given how much time students have spent without face-to-face teaching over the last few years, I would have thought taking teachers out of the classroom was a really bad idea. But some schools clearly think otherwise.
5) The idiots in DET mandate this to occur in schools. DET takes ideas that are good on paper and implements them so poorly that the good idea becomes a terrible idea.
No-one could say that having a professional development plan is a bad idea. It’s a good idea. But it becomes a terrible idea when it’s implementation gets corrupted with all the snake-oil that consequently gets shoved down teachers throats. The con-artists can’t believe their good luck. You’re one of the thousands of victims every year of swallowing the poison pushed down your throat of ‘fear’. It’s much easier when your position is permanent and you have years of experience to tell the poisoners to go apt themselves.
Your colleagues were clearly a lot smarter, and/or had more integrity, than the idiots who bought the snake oil. You did the best you could under difficult circumstances. I totally agree that it’s
“very deflating constantly feeling like you’re not good at what you do because what you do doesn’t work….when actually It’s because it just plain doesn’t.”
However, current circumstances are ideal for teachers to start pushing back (although the spineless AEU in Victoria obviously thought differently – I hope the members decisively vote against what’s being offered). Schools are struggling to fill positions. Now is the time to demand better. A puddle is deeper than Merlino’s so-called ‘teacher pool’. But most teachers won’t because they are sheep. They don’t want to rock the boat. They mistakenly think that they don’t have enough time to stand up for themselves, to demand a better curriculum, less bullshit etc.
Short-term contracts coupled with professional development plans is a disincentive to enter the teaching profession. It’s a sure-fire recipe for causing poor teaching and teacher burn-out. I wonder if the so-called ‘experts’ on the initial teacher education review panel
( https://www.dese.gov.au/quality-initial-teacher-education-review )
will consider this (probably not. I know people on that review and I’ve got to say that, at least one of them is the very last person I would have thought cared squat about how a new teacher was treated).
I stumbled across the letter below. Read the content first and then look at the date.
Click to access Cover_letter_-_Statement_for_the_Review_-_210314.pdf
I don’t know whether to laugh or cry or do both.
The enemy of my enemy is still my enemy.
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?
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?
Look at how 2014 ACARA are describing the curriculum its rolling out (todays
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
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 …
Very good point.
ACARA appear to be confused about the subject they refer to.
Mathematics is mathematics. It is not history or cultural studies.
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.
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.
https://www.theaustralian.com.au/nation/retreat-signalled-on-maths-overhaul/news-story/4aa14b89044ae7a28583ccb858a97fb9
An editorial on the topic (with some colourful comments from readers):
https://www.theaustralian.com.au/commentary/editorials/maths-skills-need-to-be-upgraded/news-story/ffa6e6eb45a486f65cf426dabde185d1
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.
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.
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.
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.
Thanks, studyroom. I’ve now posted on it here.