We’ve been trying to tone down the language on this blog. Honestly. But education reporters make it so damn hard.
To be fair, most of the reports of the passing of ACARA’s curriculum have been ok. Not good, not exhibiting much in the way of thought or memory or reflection, but ok. Sure, the reporters could have pointed out that the Wonderful New Curriculum is still secret, meaning nobody really knows whether the media releases are remotely accurate. They could have reported that the participants in ACARA’s final charade are still bound by ACARA’s insidious NDA and so have been cowed into not commenting. They could have reported that AMSI and AustMS have been silent, and most definitely have not signalled endorsement of the new mathematics curriculum. They could have pointed out that ACARA had screwed up royally, for years, and that the alleged improvements to the mathematics curriculum, if real and meaningful, only came about because of a massive campaign, a campaign which, until the very end, ACARA treated with utter contempt. But, after all, they’re education reporters; you can’t expect too much. Continue reading “A Bita Crap”→
Yesterday, ACARA’s draft curriculum was approved by the Ministers, as it was always going to be. The draft is, of course, still secret, since when did ACARA ever give a stuff about what anybody thinks? The draft is due to appear in a couple weeks. We shall be ready.
Until the draft is released, there is not a lot upon which to comment. We know some details of the reprehensible process of the last month, and we have been given some vague hints of the nature of the new curriculum. But, because of ACARA’s insidious NDA, and out of a respect for sources, there is little we have to write and less we are permitted to write. We know, however, what to be watching for, and we’ll be waiting. Continue reading “ACARA, Annotated”→
establish the formula for the area of a rectangle and use to solve practical problems
solving problems involving the comparison of lengths and areas using appropriate units
investigating the connection between perimeter and area for fixed area or fixed perimeter, for example, in situations involving determining the maximum area enclosed by a specific length of fencing or the minimum amount of fencing required to enclose a specific area
investigating the relationship between the area of a parallelogram and the area of a rectangle by rearranging a parallelogram to form a rectangle of the same area and explaining why all parallelograms on the same base and of the same height will have the same area
CONTENT (Year 7 Measurement)
establish the formulas for areas of triangles and parallelograms, using their relationship to rectangles and use these to solve practical problems using appropriate units
exploring the spatial relationship between rectangles and different types of triangles to establish that the area of a triangle is half the area of an appropriate rectangle
using dynamic geometry software to demonstrate how the sliding of the vertex of a triangle at a fixed altitude opposite a side leaves the area of the triangle unchanged (invariant)
using established formulas to solve practical problems involving the area of triangles, parallelograms and rectangles, for example, estimating the cost of materials needed to make shade sails based on a price per metre
CONTENT (Year 7 Measurement)
establish the formula for the volume of a prism. Use formulas and appropriate units to solve problems involving the volume of prisms including rectangular and triangular prisms
packing a rectangular prism, with whole-number side lengths, with unit cubes and showing that the volume is the same as would be found by multiplying the edge lengths or by multiplying the height by the area of the base
developing the connection between the area of the parallel cross section (base), the height and volume of a rectangular or triangular prism to other prisms
connecting the footprint and the number of floors to model the space taken up by a building
representing threefold whole-number products as volumes, for example, to represent the associative property of multiplication
using dynamic geometry software and prediction to develop the formula for the volume of prisms
exploring the relationship between volume and capacity of different sized nets used by Aboriginal and Torres Strait Islander Peoples to catch different sized fish
exploring Aboriginal and Torres Strait Islander Peoples’ water resource management and the relationship between volume and capacity
We decided ACARA’s psychedelic circle, which we discussed briefly here, was worthy of its own post. So, apart from the potential to trigger an epileptic fit, what is wrong with ACARA’s wheel?
ACARA labels their wheel as depicting
[the] relationship between the six strands and three core concept organisers
The six strands make up the inner wheel, and are explained here (pages 4-5). The three “core concept organisers” are the three colours on the wheel rim, with the categories and subcategories as pictured below, and which are explained here (pages 5-8).
Below are parts of de Carvalho’s speech that relate in some manner to the mathematics review, followed by our, mostly redundant, comments. What de Carvalho says is clear, and clearly ridiculous.
The data that we get from NAPLAN is important, but it is not a measure of overall school quality, and we need to remember that education is a complex multi-dimensional process where improvement does not rely on the rationalistic analysis of data and the application of associated managerial techniques.
“Rationalistic” is now a boogie-man word? That’s where we are? And once again, we have this idiotic selection: NAPLAN or touchy-feely. A pox on them both.
For the thousandth time, NAPLAN is garbage. Numeracy is garbage. And, while we’re at it, PISA is garbage. If there were decent national tests of arithmetic and mathematics, these would be a godsend; the subsequent “rationalistic analysis” would do more than anything else imaginable to lift Australian mathematics education. But, of course, courtesy of two very poxy houses, there’s not a snowflake’s chance in Hell of this occurring.
This is because the essential nature of education is that it involves a sense of historic continuity and conversation between generations, between teachers and their students, where a learner is engaged in the process of becoming a well-rounded human being …
This conversation between the generations is the basis of the curriculum.
Up to now, we have been working with 18 teacher and curriculum reference groups established to support the review, made up of 360 teachers and curriculum authority representatives from across Australia, as well as consulting with our peak national subject bodies and key academics. I’ve also had discussions with the staff from 24 primary schools across the country.
But on Thursday, we begin public consultations on the proposed revisions to the Foundation to Year 10 Australian Curriculum.
No, you aren’t. You are permitting people to fill in a survey, which, presumably, will never see the light of day. In no manner does this sham hold ACARA publicly accountable to publicly available opinion.
I’ve heard some stakeholders say that we should be “taking a chainsaw to the curriculum”, but chainsaws are not particularly subtle, and can leave an awful mess behind.
What is currently wrong with the Australian Curriculum is also not subtle. We’d go for dynamite, but a chainsaw would do in a pinch.
We need to avoid perpetuating a false dichotomy between factual knowledge and capabilities such as collaboration and critical thinking.
You can’t engage critically and creatively on a topic if you lack the relevant background knowledge …
Go on, …
So the ability to recall facts from memory is not necessarily evidence of having genuine understanding.
A very cute straw man, but please continue.
A student might, for example, memorise the formula for calculating the length of the hypotenuse if given the length of the other two sides of a right-angle triangle, but do they understand why that formula, known as Pythagoras’ theorem, works every time? The process of discovering that for themselves, with the assistance of the teacher, is what makes learning exciting. And it’s what make teaching exciting. Seeing the look of excitement on the face of the student when they experience that “aha!” moment.
Ah, so that’s what you’re getting at. You nitwit.
This example is so monumentally, multidimensionally stupid, it has its own post.
Some learning areas have only required some tidying – but others have required more focus. Maths for example has required greater improvement and updating.
If we look at our PISA and our TIMSS results, Australian students are not bad at knowing the “what”, but we are not as strong at “why” of mathematics, …
This is, to use the technical term, a fucking lie. It is an absurd, almost meaningless dichotomy. And you forgot the “how”, you idiot. But in any case Australian students absolutely suck at the “what”, and the “how”, and ACARA damn well knows it.
This is THE lie. This pretence, that Australian maths students are doing just fine on the basic knowledge and skills, is why it is absolutely impossible for ACARA to revise the mathematics curriculum in a meaningful manner. This is why, without even needing to read it, you know the Draft Curriculum is a farce.
… this joint statement from five of the leading maths and science organisations in the country is an indication of the level of interest out there about the curriculum.
Again – knowledge and capabilities being acquired together.
Mate, it doesn’t work that way. More often than not, and particularly in primary school, your precious “capabilities” are just getting in the damn way. You can wish it all you want, but learning mathematics just doesn’t work that way.
It should be noted that the current Australian Curriculum in Mathematics already includes four Proficiency Strands: understanding, fluency, problem-solving and reasoning. The issue has been that these proficiencies have not been incorporated into the Content Descriptions, which is what teachers focus on.
So the major change we have made in the proposed revisions to Maths is to make these proficiencies more visible by incorporating them into the Content Descriptions.
In other words, you are changing the Curriculum content, and you are pretending that these changes are simply an innocent act of tidying up. Do you imagine anyone believes you?
It is also important to note that in proposing these revisions, ACARA is not making any recommendations about pedagogical approaches.
So that Pythagoras nonsense back there was just for the Hell of it? There’s a technical term for this. What was it again?
I expect we will see a stirring of the passions.
So you’re ok with passions. How do you feel about white-hot fury?
No doubt some will argue the proposed revisions don’t go far enough, while others will say they go too far, …
Of course it never crossed your mind that people might say, accurately, that you’re going in entirely the wrong fucking direction.
This discussion and civil debate is a good thing.
It is not a discussion, it is a fait accompli, and there is no benefit here in being civil. What is called for is complete and utter contempt.
Yesterday, David de Carvalho, the CEO of ACARA, gave a speech at The Age Schools Summit. de Carvalho used his speech to set the stage for ACARA’s imminent launch of the draft of the revised Australian Curriculum. (See here.)
We shall take a more careful look at de Carvalho’s speech in the near future. For now, we’ll settle with a WitCH, an excerpt from de Carvalho’s speech:
“So the ability to recall facts from memory is not necessarily evidence of having genuine understanding.
A student might, for example, memorise the formula for calculating the length of the hypotenuse if given the length of the other two sides of a right-angle triangle, but do they understand why that formula, known as Pythagoras’ theorem, works every time? The process of discovering that for themselves, with the assistance of the teacher, is what makes learning exciting. And it’s what make teaching exciting. Seeing the look of excitement on the face of the student when they experience that ‘aha!’ moment.”
And when we understand a topic, it is easier to recall the facts because they are no longer just random bits of information but are organised into intelligible ideas. Not only do we know where the dots are, but we know why they are there and how to join them.”
Just a reminder, this is a WitCH. So, what specifically is crap about de Carvalho’s Pythagoras suggestion?
To guide the discussion, below is (arguably) the simplest, algebra-free proof of Pythagoras, which, undeniably, all students should see. Where does/should this proof fit in with the teaching of Pythagoras, and where does de Carvalho’s suggestion fit in with either of these?
It is extremely helpful of De Carvalho to have selected such a fundamentally flawed example. If he had chosen more judiciously it would be more work to counter, to make the case here against inquiry-based learning. De Carvalho having chosen almost an anti-example, however, makes clear that ACARA’s inquiry push is nothing like a reasoned best-choice approach in given situations, and much more a religious fundamentalism: inquiry is, simply by being inquiry, the preferred method.
De Carvalho contrasts the WHAT of Pythagoras — the equation — with the WHY, the proof (or proof-like evidence for) that equation. Putting aside for the moment De Carvalho’s atrocious suggestion for getting to the WHY, we’ll first note that De Carvalho has failed to ask two fundamental questions:
HOW does Pythagoras’s theorem work?
WHY2 do we teach Pythagoras’s theorem?
The first question is about the HOW of the mechanics of dealing with the equation : manipulating for the unknown, taking roots and so on. This HOW is not glamorous, and not intrinsically difficult, but it is fundamental. Of course the application of Pythagoras’s theorem, including the mechanics, is in the draft curriculum (beginning in Year 8), but De Carvalho’s casual airbrushing of the HOW is a tell.
(As a side note, we’re pleased to see that the single stupidest line in the Australian Curriculum is still there, in the Pythagoras elaborations.)
And now, the second question: WHY2 teach Pythagoras’s theorem? There are two strong answers to this question, both of which, in different ways, demonstrate that De Carvalho has no understanding of his example.
The first reason, the WHAT to teach Pythagoras is because it is so important: it is the fundamental formula for distance in Cartesian (and Euclidean) geometry.
The second reason, to teach the WHY of Pythagoras’s theorem is because it is a historical icon and because it is so beautiful. The proof illustrated above is gorgeous, it can easily be learned by a primary school student, and it should be learned, by all students, as one learns a poem. (One can of course extend this to be a third reason, to teach other proofs and the nature of geometric proof.)
Here is why these reasons show De Carvalho’s example to be so empty:
The two reasons for teaching Pythagoras are almost totally disconnected.
Hunting for a proof is the absolute worst way to appreciate the beauty of Pythagoras.
Arguing for the WHY, De Carvalho notes,
And when we understand a topic, it is easier to recall the facts …
And of course, as a general point, De Carvalho is correct. In regards to Pythagoras, however, De Carvalho is simply wrong. Pythagoras is one of the easiest equations to learn, and students simply don’t need the WHY to know WHAT it is and HOW it works. Secondly, the WHY doesn’t help with the recall whatsoever. Pythagoras is a theorem about areas, and its application in school is always to distances. The idea that a longer proof about areas will help students recall and understand the use of a simple formula about distances is utterly ridiculous.
As for appreciating the beauty of Pythagoras: if you are given a beautiful poem then you simply teach the poem. It is absurd to think that De Carvalho’s “discovering that for themselves” — which, anyway, will almost certainly be faked — will give students any proper appreciation of Pythagoras. All it can do, and inevitably what it will do, is obscure the simple beauty.
There are zillions of examples of the WHY being critical to understanding the WHAT, and there are even examples where the WHY should replace the WHAT altogether. There are examples where a limited form of inquiry is worthwhile in discovering the WHY and the WHAT. Pythagoras, however, is none of none of these. Pythagoras is only an example of ACARA’s constructivist dogmatism, and of De Carvalho’s ignorance.
We’ve posted on the general nature of PISA’s mathematics questions here and here, and the main point is the sheer awfulness of what is being tested. One question, however, seemed worthy of special note. The following is the first of the PISA 2012 test questions included in this document of past questions, followed by a guide to its grading.
As Number 8 and Potii pointed out, notation of the form AB is amtriguous, referring in turn to the line through A and B, the segment from A to B and the distance from A to B. (This lazy lack of definition appears to be systemic in the textbook.) And, as Potii pointed out, there’s nothing stopping A being the same point as C.