Not the Volume of a Cone

ACARA is why we can’t have nice things.

Yesterday I decided to be a good guy for a change, and went about writing up Alfred Lodge’s derivation of the volume of a cone. While doing so, however, I thought to take a quick peek at how cones are covered in the new mathematics F-10 curriculum. Big mistake.

Continue reading “Not the Volume of a Cone”

The Volume of a Cone

A few days ago, we pulled on a historical thread and wound up browsing the early volumes of The Mathematical Gazette. Doing so, we stumbled across a “mathematical note” from 1896 by Alfred Lodge, the first president of the Mathematical Association. Lodge’s note provides a simple derivation for the volume of a cone. Such arguments don’t vary all that much but, however we missed it, we’d never seen the derivation in the very elegant form presented by Lodge. Here is Lodge’s argument, slightly reworded.

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A Bita Crap

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”

ACARA, Annotated

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”

And Thus it Ends

As it was always going to. The fix was always in. It just took time to fix the fix. Below is Minister Robert’s media release, grammar and all. UPDATE (01/04/22) Plus ACARA’s Media release, below below.

 

Minister Robert:

Education Ministers agree a new Australian Curriculum

Australian schools will have a new curriculum to teach after Education Ministers today endorsed the revised Version 9.0 of the Australian Curriculum.

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WitCH 78: Seeing Through De Carvalho’s Prism

Happy April Fools’ Day everyone. Guess which gang of fools is gonna get fooled, and guess which gang of fools is gonna do the fooling.

There’s not a whole lot of point to this any more, but it’s niggling. So we’ll post again on ACARA‘s thoughtful and classy CEO, David de Carvalho.
Continue reading “WitCH 78: Seeing Through De Carvalho’s Prism”

ACARA Crash 13: The Establishment Blues

(We had thought about destroying another song, but decided against it. Still, people should stop to the listen to the great Rodriguez.)

The following are content-elaboration combos from Year 6 and Year 7 Measurement.

CONTENT (Year 6 Measurement)

establish the formula for the area of a rectangle and use to solve practical problems

ELABORATIONS

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

ELABORATIONS

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

ELABORATIONS

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

 

WitCH 61: Wheel of Misfortune

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).

Being Carvalho With the Truth

There are bigger, stupider fish to fry, but this also needs to be done, and it’s now or never.

Earlier this week, David de Carvalho, the CEO of ACARA, gave a speech at The Age Schools Summit. flagging the Daft Australian Mathematics Curriculum (the spelling is correct). Our most recent WitCH is based on an excerpt of de Carvalho’s speech, but the entire speech — also condensed to an op-ed — is worthy of scrutiny. And so, here we are.

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.

An A+ for irony. If there is one central theme to the now decades of destruction to Australian education, it is an utter contempt for the past, the active denigration and wilful forgetting of Australia’s one-time educational excellence.

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.

That’s a lot of people. What could go wrong?

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.

Yes, …

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.

Yep, “five of the leading maths and science organisations” can endorse this poisonous twaddle. That’s where we are.

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.