On July 8, AMSI released its submission to ACARA, in which AMSI called for a halt of the mathematics curriculum review. On July 20, ACARA contacted AMSI, requesting a “consultation session” with AMSI, to enable ACARA “to address [AMSI’s] concerns”. That meeting was held on August 17. Prior to the meeting, ACARA forwarded to AMSI an agenda, together with a long document, Elaboration to Agenda Items. This Elaboration document amounted to a written response to AMSI’s submission, effectively a defense of ACARA’s draft mathematics curriculum.
The purpose of this post is to critique ACARA’s defense as presented in the Elaboration document. ACARA’s defense is extensive, and is astonishing in its nothingness. The self-indulgence of the Elaboration, its poverty of argument, its manipulativeness and special pleading, its level of plain falsehood, and its smug, unrelenting certainty, its unwillingness to offer any but the most trivial concession, is phenomenal.
We shall go through the Elaboration section by section. The analysis is necessarily long, since the Elaboration is classic Gish Gallop and demonstrating the Gish requires galloping alongside. Readers are advised to pour themselves a stiff drink and to get comfortable, with the bottle within easy reach; they might be here a while.
THE AMSI-ACARA MEETING
Before getting to the Elaboration, it is worth making some remarks about the AMSI-ACARA meeting. In brief, the prior arrangements pretty much guaranteed that the meeting would be a farce, and, reportedly, it was. From their first contact, ACARA was manipulative, condescending and passive-aggressive: the question of halting the draft curriculum was not on the agenda (which ACARA wrote) and was not to be discussed; there was a repeated reminder from ACARA that participants should be “respectful”; there was a reminder that the Terms of Reference had been “shared with AMSI via email on June 15 2020”, as if AMSI had been delivered a commandment from God, and ignoring ACARA’s own violations of the Terms of Reference; the Agenda began with and wasted much time on relative trivia, ignoring the clearly stated sense of AMSI’s submission.
Throughout, and mirroring the lordly manner that ACARA had affected with the leadership of the Australian Mathematical Society, ACARA’s clear framing was “ACARA talks, AMSI listens”, that ACARA would explain things to AMSI participants. This went as far as ACARA’s condescending and pushy “agree[ment] to take questions on notice” (bold in the original), to be submitted before the meeting. Then it went further.
The day before the meeting, participants were informed that they “will be asked to have their microphones on mute throughout the meeting”. ACARA had evidently decided upon the Guantanamo model of “consultation”. Adding to the Guantanamo flavour, those questions on notice that ACARA so boldly requested were not answered in the meeting and at least some of these questions, and presumably all of them, still have not been answered.
And then there is the Elaboration. This document was framed around the meeting Agenda and was represented, falsely, as to be the basis of the meeting. As a defense of the draft curriculum the Elaboration is laughable, and as a political or diplomatic move it was disastrous. The Elaboration convinced a number of AMSI participants that attempting to discuss anything with ACARA was pointless.
THE MEETING AGENDA
Since the Elaboration was framed around the meeting agenda, it is worth outlining this agenda. This structure also indicates the intent, and the actuality, of the AMSI-ACARA meeting:
0. Welcome (5 minutes)
1. Background to the Review (5 minutes)
2. Specific matters raised by AMSI (25 minutes)
3. General concerns raised by AMSI (20 minutes)
4. Optional content at Year 10 (15 minutes)
5. Other matters (10 minutes)
6. Summary and closing (10 minutes)
Note that the “general concerns” raised by AMSI, i.e. that draft curriculum is systemically awful, was allotted just 20 minutes, beginning 35 minutes into the meeting. Similarly, the “specific matters” on the agenda entirely ignored the very clear framing of this specificity in AMSI’s submission:
This section lists some of the specific concerns expressed by members. This list is not comprehensive, but rather is indicative of the wide range of concerns. [emphasis added]
Of course ACARA never bothered to enquire about AMSI’s wide range of concerns, and of course the wider range of concerns were never discussed. Such was the nature of the meeting that ACARA’s trashing of multiplication tables, for example, along with dozens of other serious issues, was not on the agenda.
1. BACKGROUND TO THE REVIEW
This was clearly intended to be a quick, manipulative and unanswerable puff for ACARA, combined with a preemptive framing to justify ACARA’s past and future conduct, and the stifling of proper debate. We consider the bullet points and sub-points in turn:
a) A mathematics curriculum for all Australian students in F-10
The “all” here is absurd and manipulative, and is played upon later to justify the general dumbing down and the specific de-algebra-ising of the draft curriculum. See 1.2.5, below.
b) Terms of Reference … Review Timeline
c) Evidence Base
Painting ACARA’s work as so, so professional. It is almost entirely nonsense.
(i) ACARA Program of Research (2015-2020)
(ii) OECD Education 2030 Project
From the same people responsible for the awfulness of PISA , but to which ACARA’s draft documents only appear to make vague reference. It is more of the “transferable 21st century skills” nonsense, which fits in with, and which ACARA quotes with, the Center for Curriculum Redesign nonsense (see below).
(iii) Extensive Literature Review
(iv) Cambridge University Collaborative Project
We have not looked carefully at this group, although a well-informed person that we trust described them as “slightly whacky”. Their role appears to have been mainly on statistics in the curriculum, which was, is and always will be absurd.
We address ACARA’s manipulation of the international test results in 3.1, below.
(vi) National and International Learning Progressions
It is unclear, but we’re assuming this refers to the curriculum comparisons, done as part of ACARA’s Program of Research. The overview to these comparisons is hammered here, and the Singapore comparison is hammered here. We also briefly refer to another, weird aspect of these comparisons in 2.1.1, below.
(vii) Center for Curriculum Redesign
These were ACARA’s hired guns for the “21st Century skills” nonsense, and they are not listed in the Elaboration. The question is, why not? CCR are a (pseudo)research organisation, and were presumably consulted at least as much as the Cambridge group, which is listed.
(d) Core Concepts and essential content
This jargon about jargon is repeated ad nauseam in the Terms of Reference, and in the associated Review Process Paper, as part of the push to “refine” and “declutter”. We discuss this here, and in 2.1.5 and 3.1, below.
(e) CRG and TRG
These refer to the F-10 Curriculum Reference Group and (presumably) “teacher reference group”, and corresponding F-6 groups, as indicated in the Terms of Reference. As discussed here, there is no indication that any group contains a single mathematician.
2. SPECIFIC MATTERS RAISED BY AMSI
2.1 DELAYED OR REMOVED CONTENT
2.1.1 Tell time to the half hour
This has been moved in the draft from Year 1 to Year 2:*
There is strong international evidence that fractions are introduced in many other countries (Singapore, NZ, Finland, British Columbia) later than the current Australian Curriculum: Mathematics.
What a ridiculous little hill to choose to die on. To begin:
- Introducing half a bloody clock is not the same as introducing fractions.
- The phrase “Strong international evidence” is pompous and absurd. The claim is either true or it is false.
- The claim is false.
The four “countries” listed are hardly indicative of “many other countries”, although, as we discuss below, they are indicative of something. But, in any case, let’s review how these “countries” introduce fractions.
- time to the half hour in Primary 1 (= first year of school ≈ Year 1 Australia).
- fractions of a whole in Primary 2 (done in Australia in Year 2).
- fractions as numbers and fraction notation in Primary 2 (Australia in Year 3).
- addition of “like fractions” (same denominator) in Primary 2 (Australia in Year 5).
The other three curricula are remarkably difficult to decipher. New Zealand seems to introduce fractions of a whole in Year 2 (= second year of school ≈ Year 1 Australia), and fractions as numbers (and, it seems, addition of like fractions) in Year 3. Finland seems to introduce fractions of a whole in Year 2 (= second year of school ≈ Year 2 in Australia). British Columbia*** seems to introduce fractions as concept, parts and numbers in Year 3 (= third year of school ≈ Year 3 in Australia).
A notable aspect of all three of the non-Singapore curricula is that they are so vague, so concerned with “it’s the vibe” Big Picture skills, it’s almost impossible to determine the underlying curriculum bones, if any. This is no coincidence; together with Singapore, these three “countries” were chosen for ACARA’s curriculum comparisons, and the three curricula fit perfectly with ACARA’s anti-curriculum sense of curriculum. Singapore doesn’t fit of course, but it was probably too obviously gaming things to pretend that all of Asia doesn’t exist; so, instead, ACARA simply gamed the comparison.
Anyway, dodgy comparisons with dodgy countries aside, what is ACARA’s argument for the delay?
This allows more time in Foundation and Year 1 for consolidation of basic knowledge about numbers before fractions are introduced.
Let’s concede this point. It obviously takes kids years to prepare for the concept of halfway around a clock.
Moving the reading of time to the half hour to Year 2 aligns this content with the introduction of fractions in Year 2 in the revised curriculum.
That doesn’t mean it makes any pedagogical sense and it clearly requires an argument. It would seem natural and obvious to introduce the simplest, staring-at-the-kid fraction idea before considering 1/n.
* The concept of half of a whole has similarly been moved from Year 1 to Year 2. This was not flagged by AMSI.
** The information is taken from Singapore’s 2012 curriculum, which ACARA employed in its comparative study. As of 2021, Singapore is implementing a new curriculum, of which only Year 1 is currently available. Telling the time to the half hour remains in Year 1 in the new curriculum.
2.1.2 Connections between fractions and decimal notation
This has been moved in the draft from Year 4 to Year 5:
There is strong evidence in the literature to support the introduction of decimals as an extension of the place value number system using division by ten
And 1 divided by 10 is, um, let’s think …
One also wonders if this “strong evidence in the literature” is as strong as the “strong international evidence” for when fractions are introduced. There is, however, strong evidence in the literature that ACARA loves to appeal to invisible authority.
(including in the current AC: M elaborations).
Well, yeah. One emphasises the division/multiplication by ten, because that’s why we’re here. But, how the hell do you then talk about 0.1 without identifying it with 1/10, and ditto for 2/10? And why the hell would you want to delay doing that?* Is there “strong evidence”, or any evidence that delaying making this connection is valuable, or sane?
This sequence of development builds on the partitioning of numbers into tenths, hundredths and making connections to content in measurement.
So, you’re gonna emphasise the size of these numbers before students consider and become familiar with the nature of these numbers. That sounds like a brilliant plan.
This allows more time for students to build an understanding of equivalent fractions and the multiplicative relationship of place value in Year 4.
Um, perhaps pondering 2/10 = 1/5 and the like might help build an understanding of “equivalent” fractions? Or, maybe the real point is that ACARA don’t give a damn about fractions, and the sooner they get the kids punching decimals into a calculator, the happier ACARA will be.
and then introducing percentages in year 5 rather than Year 6 allows for connections to be made between equivalent decimal and fraction representations of hundredths and percentages.
Yep, do it all at once. Great plan.
This sequence of learning is coherent and aimed at developing a strong understanding of place value, building solid fraction sense and developing proportional thinking.
Lots of “developing” and “building”. Not a hell of a lot of doing.
* Singapore, of course, converts back and forth between decimals and easy fractions as soon as decimals are introduced, in Year 4. The other curricula (NZ/BC/FIN) are so flaky it is difficult to tell what is when.
2.1.3 Solving simple linear equations
This has been moved in the draft from Year 7 to Year 8:
This feedback has been considered and is being addressed in the current revisions resulting from analysis of the public consultation feedback.
We’ll see. ACARA doesn’t seem quite ready to concede the point:
The critical aspect of Year 7 algebra has been becoming familiar with the explicit use of pronumerals, variables and formulas involving these.
Yes, but playing with nouns for a damn year is not the way to do it. Kids figure out how X works by seeing the way it works in equations, and you see what those equations mean by rearranging them.
This poses various challenges for many students within the full cohort, as indicated in the mathematics education research literature.
Again, a vague wave of the hand to what might be “indicated in the mathematics education literature” is simply meaningless. One might also consider confronting the “various challenges” of algebra, rather than running away from them.
Prior to the current Australian Curriculum: Mathematics, solving linear equation was a curriculum expectation within a band that covered Years 7 and 8. Typically, at Year 7 some form of process relating to problems involving ‘simple linear equations ’(that is, with positive integer solutions) and their solution by various approaches is used, subsequently leading to problems involving integer and rational solutions in Year 8.
Yes, the teaching of algebra is already way, way too weak in the current curriculum.
2.1.4 Solving linear equations with simple algebraic fractions, and solving simple quadratic equations
This material was removed from Year 10, but the Elaboration does not address AMSI’s specific objection to this removal. Elsewhere, ACARA claims that the material is “redundant as it is already covered in Years 8 and 9”. Which is absurd, and all the more absurd since the draft curriculum never uses terms such “perfect square” and “differences of two squares” when factorising. Algebra is paper thin in the current curriculum, and the draft makes it paper thinner.
2.1.5 Solving linear equations with algebraic fractions, operations with algebraic fractions
This material was removed from Year 10, because
it is seen as not essential for all students to learn in Year 10 … Including only content that is ‘essential’ was one of the non-negotiable principles for this review.
This is arguably the most poisonous passage in the Elaboration. ACARA’s claim is simultaneously false, misconceived, wrong in this specific instance and generally unworkable. Quadruple stupid with pike.
- It is simply false to claim that the inclusion of only “essential content” was “non-negotiable”. The Terms of Reference and Review Process Paper repeatedly refer to “essential” content in the form “focus on essential content” (emphasis added). Focus means focus. It does not mean obliterate everything else.
- The idea of including only “essential” content in a curriculum is self-evidently ridiculous. To really do this is to not write a mathematics curriculum, but a numeracy curriculum, which is exactly what ACARA has attempted, without anything like a mandate to do so. What is properly essential in a mathematics curriculum is to provide a coherent and small core of essential facts and skills, fleshed out by a very large selection of valuable and mutually reinforcing mathematical material which, to a decent extent, is open to disputable taste and fashion. Consider, for example, the following, newly introduced, Year 10 content:
apply computational thinking to model and solve algebraic problems graphically or numerically
Is this content essential? For whom? One might claim that it is valuable (or meaningless), but to claim that it is essential is absurd. In particular, to suggest that this new content is more valuable than developing an understanding and facility with algebraic fractional equations requires an argument, which ACARA has not even attempted to provide and which probably does not exist.
- A proper facility with algebra is incredibly powerful; if there is one category of content that is close to essential in a secondary school curriculum, it is algebra. Algebra is the language and the apparatus of mathematics and science, of all the modelling and investigation the draft writers so, so much want. The draft curriculum is continually undermining the already weak position of algebra in the curriculum, continually diluting it with “numerical” and “graphical” and “digital”. ACARA evidently sees no value in a strong facility with algebra, up to and probably including loathing the idea.
- Any attempt to define a broad category of “essential content” is doomed to farce. Communities and schools and teachers and students are simply not sufficiently cookie-cutter uniform for any such scheme.
But, of course, it is not just ACARA that hates algebra:
This was strongly supported by the members of the reference groups.
Those would be the reference groups hand-picked by ACARA, and seemingly not containing a single mathematician. The “this” is ambiguous but, in any case, is absurd. Teachers and curriculum administrators do not have a privileged opinion on what is or is not “essential” in a curriculum.
2.2 CONTENT ADDED
In its submission, AMSI objected to the inclusion of some specific new content in Years 7-10. The objection was not to the intrinsic merit of this material, but to the consequent effect upon the curriculum as a whole:
No clear argument is made that these topics are more important and relevant than material that is being removed from this part of the curriculum. Moreover, the impact of these changes on pathways to senior secondary mathematics curricula is not spelled out. Despite the mandate of the review to declutter, members were concerned that the changes suggested in the draft curriculum have increased the breadth of the material covered.
The Elaboration simply ignores AMSI’s central, stated concern for the solidity and the coherence of the curriculum, merely arguing, poorly, for the merits of the new content topic by topic. The Elaboration is also silent on a double-violation of the Terms of Reference: there is nothing in the Terms of Reference to license the inclusion of such new content; and, such inclusion violates the clear intention for the review to declutter the curriculum.
2.2.1 Logarithmic Scale
This material was added to Year 10.
Logarithmic scales complement understanding of exponential growth and are pervasive in measurements contexts in the physical, biological, medical and social sciences.
The Covid-19 pandemic has seen them used extensively in the popular media. Hence this is seen as ‘essential content’ for the F-10 mathematics curriculum.
The “hence” is nonsense, and “seen” by whom? Valuable, perhaps; essential, no.
Note that the approach for all students in Year 10 is graphical only, with any extension into the laws of logarithms at the discretion of teachers.
At which point one realises that the entire topic in the draft is dilettantish nonsense. A “graphical only” approach to logarithms, or anything, contradicts the very meaning of “approach”: the draft is not approaching the topic, it is standing back and gazing. Teaching logarithms properly, fundamentally algebraically, is fine and good, and close to “essential”. But, ACARA is not interested in the hard and meaningful work of algebraic mastery, and proper, memorable understanding. Their “graphical only” nonsense is flimsy and immediately forgettable, and thus pointless.
2.2.2 Error and Approximation
Understanding and capacity with approximation and appreciation of error have been identified as critical to numeracy.
This is meaningless. Identified by whom? Understanding and capacity to what degree?
Essential numeracy skills are specified in ACARA’s National Numeracy Progression (NNP).
Once again, waving the magic wand of “numeracy” to argue for the supplanting of mathematics. The term “approximation” appear just twice in the NNLP (not NNP) and the term “error” appears exactly once, in the phrase “error in media reports”. That is quite the mandate.
This is based, at least in part, on the importance of these ideas in many workplaces.
How many is “many”? Is this material “essential” for students who might be seeking an education rather than training?
The mathematics curriculum has been designated by ACARA as the ‘home’ of the mathematical knowledge that underpins numeracy. Hence this mathematical content is necessary to underpin students’ numeracy as represented in the NNP [sic].
The “hence” is weird, and meaningless.
Estimation and approximation and error are progressively developed in the curriculum, being able to know when calculation are reasonable in context is important,
Again, “important” does not equal “essential”. This concern for approximation is primarily driven by ACARA’s massive over-concern for real-world application and pseudo-application, at the expense of exactness and mathematical fundamentals.
and an area for which the current curriculum has received some criticism in being deficient.
For about the fiftieth time, this is meaningless. “Some criticism” from whom?
This material is complementary to effective computation, and its application across the curriculum.
Yes and no. Exact computation, which is the heart of a mathematics curriculum, is exact: approximation plays no role. Furthermore, any suggestion that “computation” is already “effective” in the current curriculum is laughable, and the draft curriculum would make it way worse. Students do not, and will not, have the proper sense of and facility with computation to make the approximation meaningful.
2.2.3 Networks and Planar Graphs
This material was added to Years 9-10.
Networks and planar graphs are one of the key representations of certain kinds of relations and have many applications in contemporary society. Various mathematicians (including members of the AustMS) have argued for inclusion of such material as fundamental.
There are also various mathematicians (including members of the AustMS) who have argued publicly that the draft curriculum is a disaster; ACARA hasn’t paid a hell of a lot of attention to them. Who are the “various mathematicians” who argued for the network/graph material, and in what forum? Did these various mathematicians argue this after considering the cost of including this material, or did they just wing it?
To suggest networks/graphs has value is fine, that it is “fundamental” is a stretch, and that it is “essential”, which ACARA is declaring to be the standard, is absurd.
2.3 “SHAPE” AS A STRAND NAME
AMSI argued that “Geometry” is preferable as a strand name, which is of course correct and is of course a trivial issue. Much more important is the idiotic decision to split three strands into six. And, much, much more important is the awfulness of the Space strand.
The team has proposed the term “Space” as a broader characterisation of the field.
Which is the real problem: the Space strand is no longer geometry. This, and the systemic awfulness of the draft curriculum, is captured by the draft curriculum’s definition of the Space strand:
Space develops ways of visualising, representing and working with the location, direction, shape, placement, proximity and transformation of objects at macro, local and micro size in natural and created worlds. It underpins the capacity to construct pictures, diagrams, maps, projections, models and graphic images that enable the manipulation and analysis of shapes and objects through actions and the senses. This includes notions such as continuity, curve, surface, region, boundary, object, dimension, connectedness, symmetry, direction, congruence and similarity in art, design, architecture, planning, transportation, construction and manufacturing, physics, engineering, chemistry, biology and medicine.
Euclid may have looked upon beauty bare, but it’s difficult to imagine anyone writing an ode to the monstrosity above. The description of the Number Strand at least refers to “mental constructs”, even if the constant push there is to consider, instead, physical and graphical representations, but ACARA don’t even pretend for the Space Strand.
It should be noted that the National Statement on Mathematics for Australian Schools (1991) used Space as a strand name.
Well, 1990, but who’s counting?
Subsequently the term was used in mathematics curricula in this country for two decades, without any apparent confusion with astronomy including NAPLAN Minimum standards – numeracy.
NAPLAN, the grand program to test “numeracy” rather than mathematics, is offered as the all-wise determiner of mathematical terminology.
Yes, some people have called geometry-like stuff “space”. And most people call geometry-like stuff “geometry”. “Space” is an idiotic name, which is only appropriate as the title of the draft strand because the strand content is idiotic to match.
3. GENERAL MATTERS RAISED BY AMSI
3.1 PISA AND TIMSS
AMSI’s submission referred to a number of “challenges” for the teaching of school mathematics. The only such “challenges” directly relevant to the draft curriculum are professional development – see 5.2, below – and Australia’s performance on PISA and TIMSS. ACARA, of course, concerns itself with PISA:
While the past two cycles of TIMSS have indicated improvement in Australia’s performance at Years 4 and 8 respectively, …
This is false, and misleading. The 2011–2015–2019 Australian TIMSS mathematics scores were 516-517-516 for Year 4 and 505-505-517 for Year 8. Theses figures indicate no improvement in Year 4 scores. And, the entire improvement in Australia’s Year 8 scores in 2019 turns out to be due to improvement in NSW. It is worth noting that NSW has been the state most actively hostile to ACARA and the national curriculum.
… more can be done.
To say the least. TIMSS appears to be a very good test, but the scores (and rankings) must be interpreted with great care. The scores are scaled, so that 500 is the average of the participating countries, and 100 corresponds to one standard deviation (which is less than the gap between Australia and Singapore, at both Year 4 and Year 8). Of course, countries come and go, and get better and worse. If, for example, the whole world is getting dumber, which is arguable, TIMSS would not indicate this.
The quickest way to get a sense of what TIMSS tests, and what the test tells us, is through the sample items and results from TIMSS 2011 for Year 4 and Year 8. (Corresponding sample items for later years have not been made publicly available, but there are a few 2019 “benchmark” items here.) It indicates, for example, that of Australia students near the end of Year 8 just 45% could recognise the prime factors of 36, and just 45% could recognise that 4/14 = 6/21, and just 31% could write 3 5/6 to two decimal places. (The corresponding results for Singapore were 79%, 83% and 73%). And on and on. Independent of Australia’s ranking, the TIMSS scores indicate that the situation is woeful, and it is crystal clear that the draft curriculum will make things very much worse.
On a deeper analysis into Australia’s average performance in PISA by process domains, Australian students perform close to the OECD average at employing style tasks and above the OECD average at interpreting results back into a context, however, tasks requiring students to formulate is where we fall well below the OECD average.
Without references, this is meaningless. And, once again, PISA is appalling.
This is one of the reasons for the increased and more explicit focus on mathematical modelling in the revised AC: M, providing opportunity for students to learn how to formulate.
If you want a kid to play piano sonatas well then, sure, you concentrate upon a few sonatas. But you don’t have 200 sonatas and no scales or exercises. Plain common sense suggests, and the evidence is, if you want kids to do well at PISA you don’t have them endlessly explore and model: you teach them (Table D2 and the references to it). The top ten countries for PISA 2018 were China, Singapore, Macau, Hong Kong, Taiwan, Japan, South Korea, Estonia, Netherlands, Poland. How many of these ten countries have a mathematics curriculum anything like Australia’s draft curriculum? Indeed, what country anywhere has anything like Australia’s draft curriculum, and what makes that country a role model? And, seriously, that much modelling and investigation, just out of concern for PISA scores? It was ACARA’s literature review that whined, weirdly and ignorantly, about such international “league tables”. Ironically, in this instance ACARA should pay attention to their own whining.
3.2 MORE TIME SPENT ON DEVELOPING UNDERSTANDING
The figures about performance in PISA demonstrate that what is currently in place is not working well.
No, PISA is irrelevant. But, to suggest that things aren’t working well is an understatement.
The proposed curriculum draws on research about students’ learning of mathematics to incorporate coherent, progressive development of content and mathematical skills.
And once again, the invisible “research” from the invisible researchers.
An important further consideration has been connecting learning in different areas of mathematics.
It is not even clear what this means, but it sounds very wrong. The way to learn arithmetic is to do arithmetic. The way to learn algebra is to do algebra. Over connecting, particularly in the early years, is simply distracting and confusing.
Some of these sequences are demonstrated above in response to specific feedback in the AMSI submission.
And what demonstrations they were. ACARA’s responses to the specific issues above ranged from weak to ridiculous.
In the instances where ‘more time is taken’ the trade-off is deeper, richer and more robust understanding that underpins mathematical knowledge and skills.
Absolutely no evidence is provided for this, and common sense, and Singapore, suggests that it is ridiculous. Knowledge and the skills are what you hang the understanding on. Without the framework of knowledge and skills, the “understanding” is thin and easily evaporates.
Addressing declines in PISA scores for 15-year old’s will be built on these foundations.
Just plain nonsense. There is simply no evidence provided that anything ACARA is suggesting will make this happen. And your grammar sucks.
3.3 CORE CONCEPTS
The review teams in all curriculum areas have developed and used Core Concepts as a framework for identifying essential content … For mathematics, this has been through Core Concepts for the discipline and associated Core concepts in each of the six strands.
Framing the curriculum around thirteen “core concepts” of which “thinking and reasoning” is just one, ACARA has gamed the determination of “essential content”. And, there is no way in hell that such a radical overhaul is consistent with the emphasis on “refine” and “declutter” in the Terms of Reference.
It is ACARA’s position that The Core Concepts are not another layer of the curriculum with which teachers will need to engage.
It is entirely irrelevant what “ACARA’s position” is, and it is entirely irrelevant whether the core concepts are a “layer”. The core concepts are there, and no reason is indicated for why they are there nor what teachers are supposed to do with them.
There has been feedback from other sources that indicates that what has been included in the draft curriculum about the Core Concepts has lacked clarity for many respondents.
Unbelievably arrogant. The Core Concepts haven’t “lacked clarity for many respondents”; the Core Concepts lack clarity. This is Exhibit A that ACARA is utterly incapable of admitting error. Exhibits B-Z is ACARA’s entire response to AMSI.
There has been feedback … [that] has caused the team to undertake a major overhaul of this material to address issues that have been identified. It is intended that much more – and clearer – information about the nature and role of Core Concepts will be included in the curriculum documentation.
Much more information? Dig up, stupid.
In any case, it doesn’t matter, since the damage has already been done. The “core concepts” were used to determine, very badly, the “essential content” of the draft curriculum.
On the matter of the term “mathematising”, it is a surprise to us that it “is a concept with which (AMSI’s) highly qualified educators have no experience.”
Maybe you should get out more. Meet some people. Perhaps some mathematicians.
Mathematising (or its US equivalent “mathematizing” also associated with mathematisation) is a term that is widely used in the mathematics education literature.
That does not prove that the concept is clear or useful.
The term mathematizing (mathematising) was introduced by the Dutch mathematician Hans Freudenthal …
The guy who gave us constructivism. Great.
… as a component of Realistic Mathematics Education (RME) … It has also been associated with particular learning approaches …
Yes. And perhaps these approaches warrant no time or respect.
identified in the literature as an essential component to building number sense and Numeracy capabilities.
This ‘mathematising” is an “essential component”? Prove it. Referencing “the literature” means nothing.
3.4 THE EMPHASIS ON PROBLEM-SOLVING, INQUIRY, MATHEMATICAL MODELLING AND COMPUTATIONAL THINKING
Concepts, knowledge, skills, and processes are all important and well represented in the revised curriculum, as a detailed reading will show.
No they aren’t, and no it won’t. The knowledge and skills are there, weaker and slower than before, which was already weak and slow. And, now it is swamped by everything else.
There is an explicit focus on what it means to ‘do’ mathematics. In the current curriculum the so-called Proficiency strands were the vehicle for this. These strands were separate from the content … and there has been extensive feedback to ACARA that they were not evident in many classrooms.
And this “extensive feedback” was from whom? Even isolated away from the content, the proficiencies in the current curriculum have screwed things up. There is already insufficient facts and skills taught, upon which to hang the glorified “understanding”.
The decision was taken to embed the intent of the proficiencies into the Content Descriptions and Achievement Standards. …This is a deliberate change that is based on evidence.
Based on what “evidence”? ACARA has not just embedded the proficiencies, which is awful; they have also changed the “proficiencies”. ACARA has embedded modelling and investigation and exploration.
It has been guided and is strongly endorsed by the review’s reference groups.
The reference groups that contain no mathematicians.
This ‘embedding’ means that the processes need to be explicitly taught, learnt and assessed.
It means nothing of the sort. It means that each content item is presented to the teacher as a big, lumpy stew of concepts and facts and skills and approaches, and the teacher will inevitably pick out more of some and less of the other. Three guesses what will get chosen least.
To illustrate just how the learning will be perverted, consider the “need” to learn the multiplication tables in Year 4. In the current curriculum this appears as
Recall multiplication facts up to 10 × 10 and related division facts
The expression “multiplication facts” is misleadingly vague, but the command is clear enough. And, currently, the command is typically ignored. The vast majority of students enter secondary school without properly knowing their tables. This is the inevitable consequence of the maths ed establishment’s contempt for the value of factual knowledge, a contempt reinforced by constantly hammering the “proficiencies”.
recognise, recall and explain patterns in basic multiplication facts up to 10 x 10 and related division facts. Extend and apply these patterns to develop increasingly efficient mental strategies for computation with larger numbers
The “recall” of “multiplication facts” is there, but it is jungled. It is obvious that the recall will be demoted. Teachers are being given explicit license to get kids to find “patterns” and “recognise” stuff and develop “strategies” and “explain” things; it is inevitable that the “recall” will be given lip service, at best. There’s not a chance in hell that more than a minority of students will properly learn their tables.
The draft Level Descriptions, for every Year, say exactly how much ACARA cares for “concepts, knowledge, skills and processes”, and how they imagine/pretend this will be learned:
The Australian Curriculum: Mathematics focuses on the development of deep knowledge and conceptual understanding of mathematical structures and fluency. 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]
Yeah, that’ll do it.
3.5 OPEN-ENDED INQUIRY
Whilst it can be useful for students to engage in open-ended inquiries at some times, this is a pedagogical matter for teachers and teaching. It is ACARA’s view that curricula should not in general privilege any particular pedagogy(ies).
Once again, “ACARA’s “view” is entirely irrelevant. What is relevant is what ACARA has done, and whether ACARA has a mandate to have done it. It is also not that inquiry being open-ended by design is the key problem: even if some inquiry task includes a reasonably specific intended answer, inquiry is in its nature open-ended. Open-ended answer or not, this is inquiry-based learning, and ACARA is mandating it.
The Content Descriptions identify the content that should be taught and learnt.
Yes. But ACARA has consciously gamed the core concepts to be heavily weighted on investigation and modelling and problem-solving, and ACARA has consciously embedded ACARA’s interpretations of ACARA’s core concepts in the content. Such investigations are, by their nature open-ended. Referring to all this as “content” does nothing to alter the nature of the activity.
It will be very useful to identify and discuss specific examples in Content Descriptions that are seen by AMSI as promoting “open-ended” pedagogical approaches.
Even if there were none, it wouldn’t change the reality of what ACARA is pushing. But, since you asked, here is a quick sample:
Year 3 Algebra:
describe, follow and create algorithms involving a sequence of steps and decisions to investigate numbers including odd and even numbers and multiples of 2, 3, 5 and 10 using computational thinking to recognise, describe and explain emerging patterns (AC9M3A04)
Year 4 Probability
explore the relationships between outcomes in games and other chance situations and identify whether the chance of one outcome occurring will or will not be affected by the occurrence of other outcome(s) (AC9M4P02)
Year 5 Number
solve problems involving addition and subtraction of fractions with the same denominator, investigating different strategies, including using different representations (AC9M5N06)
Year 6 Algebra
use algorithms and digital tools to explore factors and multiples and apply computational thinking to recognise, interpret and explain emerging patterns (AC9M5A03)
Year 7 Algebra
apply computational thinking and digital tools to construct tables of values from formulas involving several variables, and systematically explore the effect of variation in one variable while assigning fixed values for other variables (AC9M7A05)
Year 8 Probability
use observations and design and conduct experiments and simulations to explore and identify complementary and mutually exclusive events (AC9M8P03)
The Content Elaborations are optional and not part of what needs to be taught and learnt.
Really? So, just to be clear the following Year 7 content is “essential”?
apply computational thinking to design and create an algorithm that will sort and classify shapes
But, the following Year 7 elaboration is optional?
solving problems involving lowest common multiples and greatest common divisors (highest common factors) for pairs of natural numbers by comparing their prime factorization
And, since the concepts of “lowest common multiple” and “greatest common divisor” only appear in this one elaboration, then these concepts never need be taught or learnt? And just to be totally clear, since the only content descriptor on the addition of general fractions indicates absolutely no method to do so, ACARA is fine with how this is elaborated upon, they’re fine with whatever the teacher might concoct, possibly without a single mention of lowest common multiples, as long as the teacher deems it “efficient”?
In any case, the “optional” nature not provide ACARA with license do whatever the hell they want. It does not excuse ACARA from flooding the draft with a certain type of elaboration.
They are intended to provide insights and options for teachers when planning their teaching of the content in the related Content Description.
ACARA’s “insights and options” are overwhelmingly concerned with one obsession. This “just making a suggestion” line is dishonest and offensive.
To the extent that some of these may suggest ‘open-ended’ approaches
“Some”? Hundreds. The overwhelming majority of elaborations having nothing to do with the “teaching of the content” but, rather, are on applying the content to some investigation, more often that not to some contrived real-world scenario. This is obviously advocating, steam-shovelling, a particular inquiry mode of education, and it is obscene to refer this massive shovelling as “optional”.
– or indeed any other specific approach to the content – is a natural consequence of their purpose. However, it must be emphasised that teachers can reject any or all of the suggestions in the Content Elaborations as that material is not part of the prescribed curriculum.
This is most easily done by rejecting the entire draft curriculum.
3.6 MASTERY AND FLUENCY
Attention to developing mastery of and fluency with mathematical procedures is at least as strong in the draft curriculum as it is in the current one.
The attention is so strong that the term “mastery” does not appear a single time in the draft curriculum. Or the current curriculum, which is also awful. But at least the current curriculum is less flooded with superfluous nonsense. More attention to inquiry and modelling inevitably means even less attention to skills.
There is an expectation that students building a robust knowledge, understanding and fluency of procedures throughout the curriculum.
ACARA may have this “expectation”, but they are doing nothing to achieve this expectation.
The achievement standards across the Year levels specify expectations for fluency and mastery of procedures. For example we have:
ACARA’s accompanying list is absurd. Of course the words of fluency are in the draft curriculum. Most of them. Eventually. But that doesn’t mean anybody will read or pay attention to the words, since they are drowned out by gamed core concept words, and since they are not reinforced by the gamed elaborations.
To select just one of every example, ACARA lists the following Year 7 achievement standard:
use all four operations in calculations involving positive fractions and decimals
What exactly is this “standard”? How are students expected to “achieve” this standard? The single related content descriptor is no great help:
carry out the four operations with fractions and decimals and solve problems involving rational numbers and percentages, choosing representations that are suited to the context and enable efficient computational strategies (AC9M7N06)
What exactly, for example, is to be mastered on the multiplication and division of fractions? Keeping in mind that the concepts of greatest common divisor and least common multiple, and the associated techniques, are apparently optional. This is what the connected elaborations suggest:
choosing an appropriate numerical representation for a problem so that efficient computations can be made, such as 12.5%, 1/8, 0.125 or 25/1000 [sic] (AC9M7N06_E2)
developing efficient strategies with appropriate use of the commutative and associative properties, place value, patterning, multiplication facts to solve multiplication and division problems involving fractions and decimals, for example, using the commutative property to calculate 2/3 of 1/2 giving 1/2 of 2/3 = 1/3 (AC9M7N06_E3)
exploring multiplicative (multiplication and division) problems involving fractions and decimals such as fraction walls, rectangular arrays, algebra tiles, calculators or informal jottings (AC9M7N06_E4)
makes computations efficient such as 12.5% of 96 is more efficiently calculated as 1/8 of 96, including contexts such as, comparing land-use by calculating the total local municipal area set aside for parkland or manufacturing and retail, the amount of protein in daily food intake across several days, or increases/decreases in energy accounts each account cycle (AC9M7N06_E6)
using the digits 0 to 9 as many times as you want to find a value that is 50% of one number and 75% of another using two-digit numbers (AC9M7N06_E7)
Not a single elaboration is even remotely concerned with teaching or learning, much less mastering, the traditional techniques. This is appalling, and such “mastery” of nothing is repeated ad nauseam. The draft curriculum contains almost no proper standards, and it mandates almost no content, suggests almost no appropriate elaborations, to achieve the trivial pseudo-standards that dominate.
4. OPTIONAL YEAR 10 CONTENT
It is not entirely clear why this section is here, or how it relates to AMSI’s submission. It is obvious, as AMSI has hinted, that the dumbing down in the draft curriculum amounts to an even worse preparation for senior mathematics than the current, very poor, offering. The idea that this lack of preparation can somehow be address at the last minute, with the current “10A” or the draft “option 10” material or whatever, is absurd. It is not clear what the practical difference is between option 10 and 10A, but it does’t matter; both are flimsy bandaids, farcically insufficient to cover the gaping wounds.
5. OTHER MATTERS
5.1 CHAMPIONING MATHEMATICS
AMSI and ACARA patting each other on the back, because both care so, so deeply about Australian mathematics education.
5.2 PROFESSIONAL DEVELOPMENT
Yes, it’s needed. A pity that neither AMSI nor ACARA has the vaguest clue what is needed, or how to obtain it.
5.3 CROSS-CURRICULUM PRIORITIES
These are important, and AMSI support is welcome and acknowledged.
They are not important; they are absurd, and everybody knows it. But everybody is too polite or too intimidated, or too occupied with ACARA’s greater sins, to say so.
6. SUMMARY AND CLOSE