It was a dark and stormy curriculum; the jargon fell in torrents—except at occasional intervals, when it was checked by violent gusts of puffery which swept up the streets (for it is in Australia that our scene lies), rattling along the schooltops, and fiercely agitating the scanty flames of thought that struggled against the darkness.
Yeah, yeah, a mixed metaphor, or something, but it’s really late and we’re really tired. Anyway, the point is that the writing in the Daft Mathematics Curriculum sucks, and the Introduction really sucks. Like Bulwer-Lytton level of sucking. And, of course, embedded in the suckingness, there is the awfulness.
We’ll get back to hammering the Content-Elaborations as soon as possible, since that’s where the rotten meets the road. Someone, however, has to write something about the godawful Introduction. Which is much easier said than done. The damn thing is sixteen pages. Sixteen Bulwer-Lytton pages. By way of comparison, the introduction to the Current Curriculum is three short, to-the-point pages. (Such modification is what David de Carvalho likes to refer to as “refining” and “decluttering”.)
OK, sure, “mathematising” may be a brilliant new concept.* Nonetheless, someone has to be plenty pleased with themselves to believe that their shiny new toy warrants five times the introduction. And, yes, the ACARA writers are indeed pleased; the Introduction is dripping with smug satisfaction, declarations of the wonderfulness of their new scheme. It goes without saying that this continual self-congratulation really assists the overall flow.
Alright, time to hold our noses and dive in. We’ll take it section by section.**
RATIONALE (p 1)
This section is mostly florid motherhooding: “deep learning” and “creative” and so forth. One sentence, however, is worth noting, as it is a portent:
“Throughout schooling, actions such as posing questions, abstracting, recognising patterns, practising skills, modelling, investigating, experimenting, simulating, making and testing conjectures, play an important role in the growth of students’ mathematical knowledge and skills.”
This is explicitly advocating an experimental/”problem-solving” approach to learning mathematics. Yes “Practising skills” and “abstracting” are there (learning facts is not), but they are just two “actions” in a very long list. Moreover, it is simply false to claim that the rest of these “actions” can play more than a trivial role in “the growth of students’ mathematical knowledge and skills”. Unless, that is, ACARA reinterprets “skills” to include the skill of modelling and so forth. Which ACARA can do, but which then also means ACARA is playing a cup and balls trick with their terminology.
FUNDAMENTAL STRUCTURE (pp 2-5)
Each year level of the Draft Curriculum contains
*) Year Level Description – “overview of the learning”
*) Achievement Standards – “expected quality of learning”
*) Content items – “essential knowledge, understanding and skills”
*) Elaborations on each Content item – “suggestions and illustrations”
The content and companion elaborations are organised under six “strands“:
*) Number, Algebra, Measurement, Space, Statistics, Probability.
This replaces the current structure of three double strands — Number-Algebra and so forth — and it is self-evidently ridiculous. It ignores and thus weakens the critical connection between number and algebra. It also means that to have “Algebra” in primary school, ACARA simply has to make stuff up; they have to redefine “algebra” to be pattern-hunting or whatnot.
This is then not simply a case of having the same stuff under different labels. Once algebra is separated from number, it discourages semi-algebraic approaches to arithmetic, and to arithmetic problems. It discourages taking natural conceptual steps from arithmetic to algebra, which can be done, and should be done, in primary school.
The numerous strands also makes it easier for ACARA to push the overhyped Statistics and, more generally, ACARA’s real-world fetishism. This comes out most clearly in the splitting of the current double strand of Measurement-Geometry into Measurement and Space.
Why “Space”? Why not Geometry? The description indicates exactly why:
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.
Bulwer-Lytton sits up in his grave, and tips his hat.
The point of this, and the clear awfulness of this, is Geometry, the mathematical consideration of abstract objects, has been trivialised to a tiny element of real-world investigation. Space includes a ton of what would currently be thought of as coming under Measurement, effectively airbrushing Geometry out of existence. And, then, what is the Measurement strand? Well, it’s pretty much just measurement, just quantifying, which is a fine, correct use of the word. Except that as a strand of mathematics it’s pretty damn trivial.
STUFF OVERLYING THE SIX STRANDS — CORE CONCEPTS (pp 5-8)
This is the stuff underlying ACARA’s hideous wheel, and it is when things get truly appalling.
The Core Concepts are intended to replace the four “proficiencies” in the Current Curriculum:
*) Understanding, Fluency, Reasoning, and Problem-Solving. (Current Curriculum)
The current proficiencies aren’t that helpful in practice, since at least the first three proficiencies are much more intermingled than is suggested.*** Still, the current proficiencies are fundamentally coherent. No longer …
The three “Core Concepts” are those blue arcs surrounding the six strands:
*) Mathematical Structures, Mathematical Approaches, Mathematising.
Even ignoring the garishness of “mathematising”, the entire thing is absurd. What can “mathematising” mean other than to deal with a “mathematical structure” with a “mathematical approach”. How is “mathematising” anything other than the verb form of the noun phrase “mathematical approaches”? Why is “abstraction” a structure, rather than abstracting as an approach? Why is “generalising” an “approach” rather than “generalisation” a structure? How is “thinking and reasoning” a separate approach? Are the other approaches unthinking and unreasoned? What does “manipulating mathematical objects” mean? Do the other approaches not involve manipulation of anything? Why bother asking any questions at all about something so self-evidently meaningless? Where’s our vodka?
In twenty years of investigating educational absurdity, this diagram and its description out-absurds anything else we’ve seen. By a mile.
STUFF OVERLYING MATHEMATICS — GENERAL CAPABILITIES (pp 8-10)
Everything in the (not just mathematics) Curriculum is supposed to promote the General Capabilities:
*) Numeracy, Literacy, Critical and Creative Thinking, Digital Literacy, Ethical Understanding, Personal and Social capability, Intercultural Understanding. (Current and Draft Curriculum)
The Draft makes no mention of the last two general capabilities, which, given what comes next, is a little odd. Of course, whatever their intrinsic worth, the general capabilities can readily be used as an argument for real-world problem-solving and the like. Of course, that is exactly what is done.
Numeracy needs no comment, since it is already perverting everything, to the point where Arithmetic barely exists. Similarly, Digital Literacy is obvious: why think think when you can push a button and watch a movie? As for the others: Literacy is about communicating problems and real-world contexts; Critical and Creative Thinking is press-ganged into serving problem-solving; Ethical Understanding amounts to gathering and analysing data on whatever needs ethicising.
MORE STUFF OVERLYING MATHEMATICS — CROSS-CURRICULUM PRIORITIES (pp 10-11)
Everything in the (not just mathematics) Curriculum is supposed to promote the Cross-Curriculum Priorities:
*) Aboriginal and Torres Strait Islanders, Asia, Sustainability (Current and Draft Curriculum)
The Draft ignores Asia, for God knows what reason. Sustainability is what you’d expect, the “modelling” of this or that. And, predictably, the description of Aboriginal and Torres Strait Islander mathematics is strained, embarrassing and plain silly:
[Aboriginal and Torres Strait Islander Peoples] tend to be systems thinkers who are adept at pattern and algebraic thinking, …
Go on, pull the other one.
For example, within the probability and statistics strands, stochastic reasoning is developed through Aboriginal and Torres Strait Islander instructive games and toys.
Huh. They pulled the other one.
We really wish well-meaning clowns would cease this tendentious nonsense and instead focus on the stopping of aboriginals being beaten up by racist cops.
Just to be clear, the A and TSI description in the Introduction is ridiculous, but it is not half-way as ridiculous, nor a tenth-way as damaging, as ACARA’s Core Concepts nonsense. It’s easy to make fun of this stuff, and it should be made fun of, but it is not even close to the main game.
MATHEMATICS AND OTHER SUBJECTS (pp 11-12)
There is nothing exceptionally notable here. It is just another opportunity taken to push the real-world contexts of mathematics, exactly as was done with the General Capabilities.
MORE STUFF OVERLYING THE SIX STRANDS — KEY CONSIDERATIONS (pp 13-16)
This is the last section, and it is very weird. And very bad. It seems to be attempting to serve the same purpose as the Core Concepts, but with no proper connection to the Core Concepts nor, as far as we can see, to anything else in the Curriculum documentation. It’s as if the Core Concepts section didn’t exist, or someone realise/admitted that the Core Concepts section was meaningless.
in any case the Key Considerations are:
*) Understanding, Fluency, Reasoning, Problem-Solving, Experimentation, Investigation, Mathematical modelling, Computational Thinking, Computation algorithms and the use of digital tools of mathematics.
Note that the first four Key Considerations are exactly the four Proficiencies in the Current Curriculum — what the Core Concepts are meant to be replacing. But, then we have five more Considerations, all shoving us towards modelling, real-world contexts, computers and whatnot. The purpose of this is obvious, and it is bad.
There are minor changes in wording from the first three Proficiencies in the Current Curriculum to the corresponding Considerations. The new wording is generally worse, including an annoying amount of self-promotion, but is basically ok. The problem is with the rest of the Key Considerations.
The Proficiency on Problem-Solving is extensively reworded in the corresponding Consideration, with explicit linking to the next four (new) Considerations. Embedded in it is ACARA’s definition of Problem-Solving:
Students formulate and solve problems when they: apply mathematics to model and represent meaningful or unfamiliar situations; design investigations and plan their approaches; choose and apply their existing strategies to seek solutions; reflect upon and evaluate approaches; and verify that their answers are reasonable.
For those keeping track, this is definitely not Singapore.
The last five Considerations are predictable and need no comment, except for Computational Thinking. This is described as follows:
The Australian Curriculum: Mathematics aims to develop students’ computational thinking through the application of its various components, including decomposition, abstraction, pattern recognition, modelling and simulation, algorithms and evaluation.
Framed as such, Computational Thinking is no different from standard aspects of Mathematical Thinking, except for the inclusion of “modelling and simulation” — which is jammed in even thought it doesn’t remotely fit — and “algorithms and evaluation”.
The point is then given away in the next line:
Computational thinking provides the strategic basis that underpins the central role of computation and algorithms in mathematics and their application to inquiry, modelling and problem solving in mathematics and other fields.
“The central role of computation and algorithms in mathematics”.
Clearly, the point is not to promote Computational Thinking. The point is to promote computing.
There is a strong push for this type of content, usually under the title “Algorithmic Thinking”. It can, rarely, refer to nice investigations of algorithms for solving mathematical problems. In this form, and only in this form, Algorithmic Thinking has a natural and minor place in a mathematics curriculum.
But that is not what is going on here. What is going on here is the turning of mathematics into an experimental subject and a computer science subject, in order to write crappy little programs to run on crappy little models. It is not a mathematics education and it is not remotely good.
We’re done. Thank Christ.
*) It’s not.
**) It’s a minor complaint in the scheme of things, but it is worth noting that the section labels and subsection labels have almost indistinguishable fonts, making it almost impossible to keep track of where one is. How a bunch of guys who cornered the market on Neon could even stuff this up, God only knows.
***) The fourth proficiency as well, if one has a Singaporean view of “problem-solving”
9 Replies to “ACARA Crash 0: It Was a Dark and Stormy Curriculum”
I’m one of the very few people who has actually read “Paul Clifford”, the Bulwer-Lytton novel which begins “It was a dark and stormy night” – it’s actually a hoot.
The biggest take-home message for me from this garbage is the intellectual dishonesty (and I made this same point in a previous comment somewhere) – there’s nothing about mathematics as such. The definition of “shape” is so broad, so unfocused, so diffuse, that it is essentially meaningless. (The “essentially” there may be deleted, of course.) And it doesn’t say anything about what students actually learn, or how they learn it.
This leaves a nasty taste in the mind; you feel you need a cleansing shower after reading it.
I think Marty prefers vodka on ice (hoping not to dredge up too many memories of *that* MAV conference) instead of a shower, but the point remains valid.
On ice, off ice, whatever. Just keep it coming.
(And yes, very fond memories of making kilofools of MAV fools.)
Imagine what would happen if you took a class of kids and you taught them under the traditional model:
2.Basic skills and practice
3.Layering of higher skills on top of initial examples with graded practice problems
4. Abstraction and theory (to add conceptual foundation to the skills and methods)
5. Geometric and graphical aspects of a concept
6. Algorithmic abstraction and programming
7. Applications and problem solving
Depending on the topic, these steps may not be in the right order but a thoughtful educator would take that into consideration anyway.
Those kids would have the world at the touch of their fingertips and I would delight in teaching them at university level.
Out of all of that what is ACARA’s ideal model? From what I read of it (and my oh my what a turgid read it is)
ACARA wants a lot of (1), a little bit of (2), NONE of (3) and (4), a tad of (5)- but only by button mashing on a CAS, a bit of (6), heaps and heaps of (7) but with none of the underpinnings required for that to be possible.
Our students will be like a genetically modified KFC chicken. Full of artificial growth hormones (i.e. false confidence coming from calculator use) but not enough bone structure for them to be able to walk on their own i.e. actually do non-trivial problem solving.
And after the implementation of this there will be anguished wailing of why our students are doing even worse than before in PISA and TIMMS. On David De Carvalho’s tombstone will read the epitaph “We’re just as good as Singapore”.
Attached is my effort to connect mathematics in Year 9 with local Aboriginal people.
Thanks, Terry. Were there any Aboriginal students in the class? What did the students, Aboriginal or otherwise, think of the exercise?
There were no Aboriginal students in the class. The students took to the mathematical exercise like ducks to water.
I inferred that they knew very little about the Dja Dja Wurrung people before the lesson. I had some interesting materials to share with them. At least they would have taken the map home. My hope was to plant a seed of interest in the Dja Dja Wurrung people while also doing an exercise on area and perimeter of complex shapes.
I think that’s excellent, and none if it entailed pretending that the Dja Dja Wurrung people are intrinsically great at algebra.