Doh!
Let’s start at the very beginning
A very good place to start
When you read you begin with A B C
When you count you begin with 1 2 3, establishing an understanding of the language and processes, and which you use to quantify, compare, order and make correspondences between collections.
It’s just possible that Julie Andrews will singlehandedly take down ACARA.
We’re desperately trying to find the time to give the Daft Australian Curriculum the comprehensive hammering it deserves. Until we can get to that, we’ll keep things rolling with a series of short(ish) posts: ACARA Crash (pronounced with a thick Italian accent). We’ll start at the very beginning … with Foundation, the Prep year or whatever you want to call it.
What’s the very first thing you want to teach (or confirm the knowledge of)? Yep, you want the kids to know the numbers, their symbols and their names, and you want them to be able to count. You want the kids to have a sense of ordering, and the language to capture it.
It’s pretty straightforward, and fun. Sing some counting songs, practise writing the words and the numerals, watch out for those reversed 5s. Maybe go to an antique shop and grab some coloured blocks to play with. There are things to be learned, practice to be done, the understanding of ordering to be gained. But there’s just not a whole lot need be said about this practice. ACARA, of course, believes otherwise.
Following on from its (bloated) content on number names and its (badly misplaced and bloated) content on quantifying, ACARA has their content descriptor on counting:
“establish understanding of the language and processes of counting to quantify, compare, order and make correspondences between collections, initially to 20, and explain reasoning (AC9MFN03)”
There is a fundamental rule of teaching: say less. Make every word count, and if nothing needs to be said then say nothing. It is a rule that ACARA (and all education princelings) desperately needs to learn.
What is the point of ACARA’s word swamp? In what conceivable sense can it be considered “refining” or “decluttering”? What does it clarify to anyone? How is it in any way better than a bare bones content description:
Teach the little monsters to count.
Ok, you might want to tweak the wording, but for content, that is pretty much it. None of ACARA’s blather is required or remotely helpful. It is much, much worse than the corresponding content in the current Australian Curriculum.
Content is meant to be the bones, the clear and solid structure. If you want meat then sure, have meat. But if you don’t want to lose sight of the bones — and you really, really don’t — then put the meat in the damn meat section, in the elaborations. And of course, ACARA has plenty more meat in the elaborations; it will come as no surprise that their meat is off.
Most of ACARA’s counting elaborations are benign, just standard classroom exercises and token (but ok) Aboriginal material. Ten elaborations is more a textbook chapter than elaboration, but individually they’re not intrinsically bad. The problem is with what there isn’t, and it is a massive problem.
After counting, what sense of number do you want Foundation kids to attain? The answer is in the question: you want them to begin to develop a sense of number. Beyond the Four Horsemen and the Third Man, you want the kids to develop a sense of fourness and threeness, numbers as quantity, and the prelude to proper arithmetic. That is abstract and not easy, which is why it is important to begin with the hints early on.
The current Australian Curriculum, is not strong on this, but the draft curriculum is way, way worse. The stage is set right at the start, by ACARA’s “Level description” for Foundation mathematics:
The Australian Curriculum: Mathematics focuses on the development of deep knowledge and conceptual understanding of mathematical structures and fluency with procedures. Students learn through the approaches for working mathematically, including modelling, investigation, experimentation and problem solving, all underpinned by the different forms of mathematical reasoning. As students engage in learning mathematics in Foundation year, they:

 explore situations, sparking curiosity to investigate and solve everyday problems using physical and virtual materials to model, sort, quantify and compare
 begin to bring some mathematical meaning to their use of familiar terms and language when they pose and respond to questions and explain their
 look for and make connections between number names, numerals and quantities and through active learning experiences, compare quantities and shapes, using elementary mathematical reasoning
 build confidence and autonomy in being able to make and justify mathematical decisions based on quantification and direct comparisons
 learn to recognise repetition and apply this to creatively build repeating patterns in a wide range of contexts
 begin to build a sense of chance and variability when they engage in playbased activities, imagine and think about familiar chance events.
For Foundation year? “Deep knowledge and conceptual understanding”? Have you gotten them to count backwards yet? Have you bothered to try to explain what a number is?
This is nonsense, of course, but it is also poison. Pretty much all of the Number strand in the Foundation Year is on “modelling” and “Problems” and “practical situations”, and there’s a lot of it. There’s barely a hint of numbers as numbers, and what hint there is, is certain to be dissolved and forgotten in the ocean of inquiry.
Sure, you expect young kids to be playing with things more than ideas. They will add three blocks to four blocks many times before they add 3 + 4. But there are better and worse activities to suggest and encourage this abstraction; ACARA’s are much worse, and deliberately so. The writers don’t want it. Fundamentally, they don’t want mathematics.
What the draft curriculum makes clear, already at the Foundation level, is that the curriculum writers, deep in their hearts, hate mathematics. They hate the abstraction at the heart of mathematics and proper mathematical thought. They might love what mathematics can do, assigning numbers here and there, but their sense of mathematics is wadepool deep. Real mathematics, they hate.
This hatred glows brightly from almost every line. Almost never is the opportunity grasped to display the internal beauty and power of mathematics. Almost never is mathematics promoted as its own end, as its own good. It is clearly unimaginable to the writers. Mathematics is just a tool, the annoying but necessary “m” in STEm.
This is not just cultural philistinism, it is ACARA shooting its own philistine feet. Without a proper appreciation of mathematics and the source of its power, all of ACARA’s realworld games are, well, just games. 13 years of pointless games, that’s what’s on offer.
There is plenty more nonsense in Foundation draft: we haven’t even mentioned the “Algebra”. But that’ll do. We’ve never paid much attention to the Foundation curriculum. We figured the damage mostly began around Year 2, and up until now that is probably true. But no more: ACARA’s draft begins with a perfectly awful Foundation for the greater awfulness to come.
“establishing an understanding”
or
“getting used to”?
Us humans get used to more than we understand.
A really excellent point.
I recall helping a neighbour’s daughter with her mathematics; she was about 8 years old and struggling with mathematics.
Eventually it stuck me that, although she could count 1,2,3,4 …, she had no idea that 1 < 2 < 3 < 4 …
She thought that 1,2,3,4, … was like a,b,c,d, …
No wonder mathematics did not make much sense to her.
No wonder did not make much sense to me … I always thought a < b < c …
Now that’s funny.
How do you suppose that happened?
A new development:
https://apps.apple.com/au/app/photomath/id919087726
Geez. All Hail the Techno God.
I saw this today and posed the problem to find by writing it on a paper napkin – we were in a restaurant. It gave the answer “Not available in terms of elementary functions” – or something like that.
“There is a fundamental rule of teaching: say less.” I spent a month teaching in a university in Shanghai and several mathematics professors came to my classes to see how I teach. One of my habits is not to talk while I am writing on the board because I figure that students cannot copy and listen at the same time. In any case, many teachers say exactly what they are writing while they write it. The Chinese professors told me that they were amazed at this.
In teaching in a secondary school, I aim to allocate at least 50% of the lesson to allowing students to work on mathematical problems.