Education Fires Back Again

There is another contribution from the Education community:

How to do the sums for an excellent maths curriculum

This one does not directly address the open letter, although, given the framing and the links, it is difficult to not see the article as an intended rebuttal. Again, we know little of the authors, and we have not read the article with any attention. We’ll be interested in what commenters think. (Ball-not-man rules still apply.)

UPDATE (10/06/21)

Glen has pointed out that the article is from April 21. So, it is definitely not in response to the open letter. However, the article came out soon after the ridiculous, pre-emptive strike statement from AMSI, AAS and others, and in its first sentence the article links to the reporting of this statement. Whatever merits it might have, the article is not an innocent reflection on educational method.

UPDATE (10/06/21)

As indicated by SRK, there is now (in effect) a response from John Sweller.

Maths Ed Fires Back

Today in The Conversation there is an article firing back at the open letter to ACARA:

The proposed new maths curriculum doesn’t dumb down content. It actually demands more of students

We haven’t read the letter, and we don’t know the authors, or of the authors. We’ll try to read the article and comment on the article soon, modulo home schooling and general exhaustion. For now, people can comment below (respectfully and on-topic and on-the-ball-not-the-man). We’ll be interested in what people think.

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.

 

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,

The ACARA Page

Honestly, it wasn’t our intention to write three hundred posts on ACARA and their appalling draft mathematics curriculum. But, we did. Given that we did, it seems worthwhile having a pinned metapost, so that anybody who wants to can find their way through the jungle. (There’s probably a better way to do this, with a separate blog page or whatever, but we can’t be bothered figuring that out right now.)

So, here we are: the complete works, roughly in reverse chronological order, and laid out as clearly as we can think to do it. It includes older posts and articles, on the current mathematics curriculum (which also sucks) and NAPLAN (which also also sucks).

 

Open Letter

Open Letter to ACARA and the ACARA Board (02/06/21)

 

The Draft Curriculum

This is mainly the current, ACARA Crash series, on specific aspects of the draft curriculum.

 

Education Fires Back Again (10/06/21 – article from education academics)

Maths Ed Fires Back (09/06/21 – a response to the open letter)

ACARA Crash 12: Let X = X (02/06/21 – algebra in Year 7 Algebra)

ACARA Crash 11: Pulped Fractions (01/06/21 – fraction arithmetic in Year 7)

ACARA Crash 10: Dividing is Conquered (29/05/21 – division in Year 5 and Year 6)

ACARA Crash 9: Their Sorrows Will Multiply (28/05/21 – multiplication in Year 5 and Year 6)

You Got a Problem With That? (27/05/21 – problem-solving)

ACARA Crash 8 – Multiple Contusions (25/05/21 – multiplication tables in Year 4 Algebra)

ACARA Crash 7 – Spread Sheeet (24/05/21 – primes in Year 6 Number)

ACARA Crash 6 – Crossed Words (23/05/21 – word-hunting)

ACARA Crash 5 – Completing the Squander (22/05/21 – quadratics in Year 10 Optional)

ACARA Crash 4 – The Null Fact Law (21/05/21 – quadratics in Year 9 Algebra)

ACARA Crash 3 – Fool’s Gold (16/05/21 – golden ratio in Year 8 Number)

ACARA Crash 2 – Shell Game (15/05/21 – Fibonacci numbers in Year 6 Algebra)

ACARA Crash 1 – The Very Beginning (12/05/21 – counting in Foundation Number)

ACARA Crash 0 – It Was a Dark and Stormy Curriculum (18/05/21 – introductory material in the draft)

WitCH 61: Wheel of Misfortune (05/05/21 – Core Concepts and Organisers)

How Do You Solve a Problem Like ACARA (03/05/21 – problem-solving)

The ACARA Mathematics Draft is Out (summary page of draft documents)

 

Warm Up for the Draft Curriculum

Posts on public commentary, just prior to or with the draft’s release.

De Carvalho, AMSI and that Other Singapore (30/04/21 – comments by ACARA’s CEO and AMSI’s DIrector)

Being Carvalho With the Truth (30/04/21 – speech by ACARA’s CEO)

WitCH 60: Pythagorean Construction (28/04/21 – Pythagoras from ACARA CEO’s speech)

Leading By Example (15/04/21 – comments by AMSI’s Director and others)

Why Mathematics Education Must Change (12/04/21 – statement by AMSI, AAS and others)

ACARA is Confronted With the Big Ideas (17/03/21 – leaked review documents)

 

Curriculum Review

Posts on ACARA’s review documents, leading up to the draft.

Australia v Singapore (28/04/21 – ACARA’s curriculum comparison)

The Key to ACARA’s Universe (27/04/21 – ACARA’s Key Findings from curricula comparisons)

Massing Evidence (20/04/21 – more on the Literature Review)

ACARA’s Illiterature Review (11/04/21 – ACARA’s Literature Review)

 

The Current Australian Curriculum

Obtuse Triangles (25/06/2017 – Pythagoras in Year 9)

A Zillion and One Things to Talk About (18/06/2012 – statistics)

Irrational Thoughts (03/05/2010 – irrational numbers)

The Times Tables They Are A Changin’ (22/04/2010 – multiplication tables in draft curriculum)

New Draft Curriculum a Feeble Tool, Calculated to Bore (04/30/2010 – draft curriculum)

Summing Up a Failure (23/02/2009 – prelude to draft curriculum)

 

NAPLAN

The NAPLAN Numeracy Test Test (19/03/19 – numeracy)

NAPLAN’s Latest Last Legs (13/03/2019 – public criticism of NAPLAN)

We was Robbed (07/10/2018 – former ACARA CEO)

NAPLAN’s Numeracy Test (24/05/2018 – FOI application)

NAPLAN’s Numerological Numeracy (15/08/2017 – NAPLAN data)

NAPLAN’s Mathematical Nonsense, and What it Means for Rural Peru (13/07/21 – NAPLAN question)

Accentuate the Negative (27/05/2017 – NAPLAN problem)

NAPLAN in Kafkaland (12/05/2014 – FOI request)

NAPLAN, numeracy and nonsense (13/05/2013 – NAPLAN problems)

The best laid NAPLAN (09/05/2011 – numeracy)