ACARA Tells the Australian Mathematical Society to Get Stuffed

The period for submissions to ACARA on their draft mathematics curriculum closed on July 8. Our intention is to wind this up, and get to the backlogged mountains of nonsense, but there are at least a couple more posts that need to be done.

On July 2, The President of the Australian Mathematical Society,* Ole Warnaar, wrote to ACARA’s CEO, David de Carvalho. Ole has subsequently written an open letter to ACARA on what then occurred.

In his July 2 letter, Ole requested an extension of the “consultation period”, so as to enable “a proper process of engagement with the mathematics discipline”. This did and does seem to us to have been a confused and unwise request,** but de Carvalho, by being even more confused and less wise, and foot-shootingly arrogant, made sure that it didn’t matter.

De Carvalho responded to Ole pretty much immediately, noting that there had already been “extensive engagement with teachers, curriculum experts and professional associations”, that July 8 meant July 8, and that was it. In brief: Ole and the mathematicians he represented could get stuffed.

Ever an optimist, Ole arranged for him and VP Geoff Prince to meet with ACARA representatives, which occurred on July 5. This meeting confirmed, according to Ole, that

“mathematical scientists were not involved in any official capacity in the preparation of the revised curriculum”

Other than that, Ole’s description of the meeting, and of AustMS’s current stance, is vague. In brief, it seems that AustMS was told to get stuffed. Again. The exchange of letters and Ole’s summary of the meeting can be read here.

We will make just one point, which we have made before. De Carvalho may be 100% correct in what he wrote, But. It. Doesn’t. Matter. One. Jot.

There is all manner of well-practised ways to game “consultation”, and it would be bridge-buying naive to not suspect ACARA of having done so. But suppose not? Suppose ACARA went out in good faith and consulted widely, and honestly and intelligently and knowledgeably considered the feedback? Doesn’t sound likely, but let’s suppose that’s all true. It doesn’t matter.

What matters is, however it happened, that Australian mathematicians are not remotely on board with the draft curriculum. With the distinguishable exception of Chris Matthews,*** we are unaware of a single Australian Mathematician who has come out publicly with anything remotely like support for the draft. By contrast, many mathematicians, including a number of very prominent mathematicians, have come out strongly, calling for the draft to be delayed or to be withdrawn entirely: in the open letter; in AMSI’s submission; and now in AustMS’s futile pleading for some belated sense.

In the face of such strong opposition from mathematicians, from the “subject matter experts“, for ACARA then to bulldoze on with its review is fingers-in-ears madness. Which is just what one would expect.

 

*) The professional body for Australian mathematicians. You know, those guys that know maths and stuff.

**) We know Ole pretty well, and have co-taught with him. He is a very strong mathematician and a great guy. Ole made a dumb move here, but he was doing what he thought best in a dumb-dumb-dumb situation.

***) Chris Matthews reportedly advised on the curriculum, seems to us to have made a mess of things, and his contribution requires serious discussion. It is better done elsewhere.

Tony Guttmann’s Statement on the Draft Mathematics Curriculum

Tony Guttmann, AKA Mr. Very Big, is a member of or is associated with just about every mathematician organisation in Australia, excepting the Geelong Primary School Mathletics Squad.* Tony has signed the open letter and, much more importantly, has been working hard within the various organisations, arguing against the draft mathematics curriculum. He has been quoted in the recent, excellent reports of Rebecca Urban (Murdoch, paywalled).

As part of his efforts, Tony prepared a statement on the draft mathematics curriculum. With his kind permission, we have reprinted Tony’s statement here.

*) Membership pending.

 

COMMENTS ON ACARA’S DRAFT MATHEMATICS CURRICULUM

Tony Guttmann, AM, FAA, FTSE, FSIAM, FAustMS

As Australia is falling behind its international peers in basic mathematical skills, it is important to remedy this. A major problem is the lack of an adequate supply of trained mathematics teachers at the secondary level, and  the too-frequent occurrence of math-phobia among primary school teachers, which risks alienating their students from an appreciation of, and facility with, basic numeracy. This problem has been recognized for at least 40 years, and piece-meal attempts to address it have been made, but little has changed in four decades.

Australia has frequently sought inspiration from successful countries, such as Finland and Singapore. Unfortunately, their success is founded on a highly skilled and well-trained cohort of teachers, along with an appropriate curriculum. Australia lacks both.

One aspect of the Singapore curriculum is the application of mathematics to so-called “real world problems”. But this application only takes place after the mastery of basic skills. These are not learnt by trying to solve problems, and picking up the basic skills by some sort of osmosis.

So while the present Australian Mathematics Curriculum definitely requires review, ACARA’s current draft is systemically flawed, being based on this flawed premise of teaching through investigation, problem solving etc. While these have their place, the basic skills need to be there first, so that the focus can properly be on applying those skills to the problem at hand.

The power of mathematics, and our ability to learn and to apply mathematics, comes from its simplicity and its precision. Mathematics simplifies and abstracts the real world: from “three apples” to 3, from “three apples and five oranges” to 3a + 5b, and so on. With particular abstractions sufficiently understood, then, and only then, mathematics can feed back, to be applied to and to help us better understand the real world. This two-step process is long and sometimes difficult, but it is natural. A beautifully clear description of such an approach to mathematics education is given in the just-released UK Government’s Ofsted mathematics review.

The current ACARA approach is much more difficult and convoluted. The draft proposes that students learn fundamental mathematics, and come to understand the way it works, largely through “investigation” and “modelling” and “problem-solving”, much of it open-ended and poorly defined. Even if such investigations were totally within mathematics, this would be a flawed approach. What is critical to learning the arithmetic of fractions, for example, is practice on arithmetic with fractions. What the draft curriculum offers Year 6 students is a range of activities, heavy on vague modelling (pp 87-88). The draft curriculum is further flawed by situating “problem-solving” and the like in real-world scenarios (p 14). This may be where one eventually wants to apply mathematics, but it is not how one should attempt to learn the mathematics to be applied.

The strong emphasis on exploration in the draft curriculum leads to many other troubling issues. In brief:

1. The draft curriculum is difficult to read:

A consequence of the draft’s mixing mathematical content with applications is the loss of a simple and coherent structure. The framing is around thirteen “core concepts”, many of which are poorly defined and overlapping (p 15). In an apparent, and failed, attempt to make sense of this mix of concepts, the long introduction to the draft is prolix to the point of incomprehensibility (pp 1-16). Equally vague are the content descriptors in the draft, which are not infrequently a mix of the key facts/ideas/skills to be learned and the typically exploratory and ineffective methods proposed to learn them (p 27, for example).

2. The delaying and dilution of the “basics”:

Critical examples of this deficiency are the decisions to delay the learning of multiplication tables until Year 4 (p 64), and the solving of linear equations until Year 8 (p 115). ACARA’s arguments for these changes are quite unacceptable (pp 8-9). The dilution is also systemic. An emphasis on real-world modelling is a very poor mode for the practice of fundamental skills and, inevitably, it takes emphasis and precious time away from the proper practice of these skills. It denies students the opportunity to develop the fluency to apply the mathematics in a proper and rewarding manner.

3. The devaluing of mathematics:

For History or for English, the subject is largely taken to be its own worthy goal, but this is too seldom done for mathematics, and the idea is almost entirely ignored in the draft curriculum. The strong emphasis on premature exposure to real-world contexts squanders the opportunity for students to gain an appreciation of mathematics as its own beautiful discipline. In doing so, the draft also squanders the opportunity for students to gain a rich understanding of mathematics, which, in the long run, is what will best serve the students. Well-constructed problems within mathematics, and posed after the mastery of the appropriate basic skills, can be highly engaging, and can elevate students’ approach to the level of sophisticated mathematical thought. Such problems are barely hinted at in the draft curriculum.

The stated intention of the Curriculum review was for it to be modest, with an emphasis on “refining” and “decluttering” (p 1). The review, however, has been radical, the absolute antithesis of modest. Moreover, it is radicalism doomed to failure; every top-performing country on international mathematics tests has a fundamental emphasis on the mastery of basic skills, which the draft simply lacks (p 8, p 7). The draft curriculum is an abject failure, on its own terms and on any terms. The draft should be withdrawn, to make way for a fresh review, which includes the proper participation of discipline experts.

Melbourne,

18/6/2021.

Final Day: Our Submission to ACARA

A reminder, today is the last day to make a submission to ACARA’s review of the draft mathematics curriculum. And, a further reminder, you can directly email your submission to ACARA via the yellow box half-way down this page.

Below is our submission to ACARA.

 

Dear ACARA,

The following is my submission, on ACARA’s draft revisions as part of ACARA’s review of the Australian Mathematics Curriculum.

My position is that ACARA should halt the review. Or withdraw it. Or whatever. Call the process whatever you like, but, please, ACARA should stop. ACARA must stop.

I am not going to argue for the existence of what I believe are the systemic flaws in the draft revisions. You will have had many such, very weighty, submissions, in writing and in person, and you would either treat these submissions with proper and respectful consideration or you would not. A further submission along these lines from me will add no perceivable weight.

What I will argue is that ACARA must stop, because ACARA does not have mathematicians, or at least sufficiently many mathematicians, even remotely on board with ACARA’s proposed revisions. One may argue how this state of affairs has come about, but one cannot argue with the simple fact: ACARA does not have sufficient backing from the community of Australian mathematicians.

Mathematicians’ voices are, of course, not the only voices that need to be heard. Mathematicians are not the rulers here. But mathematicians’ voices are key, and cannot be ignored. Mathematicians are, in the language of the review’s Terms of Reference, the subject matter experts. Any plan to implement a new mathematics curriculum, particularly a radically new mathematics curriculum, without the solid support of the subject matter experts is doomed to failure, or to absurdity, or to both.

Please listen to reality, and please stop the review process.

Kind Regards, Dr. Marty Ross

AMSI Calls for a Halt of the Mathematics Curriculum Review

The Australian Mathematical Sciences Institute has finalised and released its submission for ACARA’s consultation on their draft mathematics curriculum. For eccentric reasons, we haven’t properly read AMSI’s submission. (Seriously.) We understand that it is a good and strong statement. The second and key paragraph is

In early April, AMSI, together with some of its key partners, released a joint statement on the proposed new curriculum “Why maths must change”. AMSI initially endorsed the revised draft curriculum in our joint statement. However, there is now an opportunity to comment on the draft curriculum, and we have revised our position, following extensive consultation with representatives of our member organisations. Many members expressed concern, and indeed alarm, at numerous proposed changes. AMSI and its members believe that the new curriculum should be delayed, and we ask ACARA to halt the current review process.

Continue reading “AMSI Calls for a Halt of the Mathematics Curriculum Review”

What Are the Arguments FOR the Draft Mathematics Curriculum?

This one is a companion to our problem-solving treasure hunt, and again amounts to a competition. We have written roughly ten million words on what is wrong with the draft mathematics curriculum. And plenty of people, including a number of big shots, have signed the open letter calling for the draft curriculum to be withdrawn. But where are the arguments for the draft curriculum? There is undoubtedly support for the draft curriculum. In particular, we are aware of a decent amount of snark directed towards the open letter and this blog. What we are unaware of is any substantive arguments in favour of the draft mathematics curriculum. The only articles of which we are aware, we posted on here and here. The first article came out before the draft curriculum and doesn’t amount to a substantive defense of anything. The second article was written in direct response to the open letter, and is so weak as to warrant no response beyond the comments already posted. And, apart from these two articles we are aware of nothing. No blog posts. No tweets. No anything. Just an arrogant and vacuous dismissal of the draft’s critics.* And now to the competition:

What is the strongest argument FOR the draft mathematics curriculum?

To be clear, what we’re asking for are very specific examples of good things within the draft curriculum, examples of content and/or elaborations that are genuine plusses. So, for example, claiming “the focus on mathematising” as a good won’t win a prize. First of all because the suggestion is really stupid, and secondly because such a generalist statement provides no specific evidence of how the mathematising is good. If you really want to argue that the mathematising is a plus then the argument must be based around very specific examples. Similar to our problem-solving competition, the intention here is not to imply or to prove that there is nothing of value in the draft curriculum. Rather, the competition is intended to imply and to prove that there is very little of value in the draft curriculum. Your job is to try to prove us wrong. Answer in the comments below. The provider of the most convincing evidence will win a signed copy of the number one best-selling** A Dingo Ate My Math Book.   *) If anyone is aware of any article/post/tweet/anything in support of the draft curriculum, which also contains at least a hint of evidence, please let us know and we will seek to address it. **) In Polster and Ross households.  

Update (29/07/21)

We’ve finally ended this. The winner is really nobody, but we’ve awarded it to John Friend. See here for details.  

One Week to Email Submissions on the Draft Curriculum

Submissions on ACARA’s draft mathematics curriculum close next week, on July 8, And, note, you do not have to use ACARA’s sheep-herding submission form. You can email your comments to ACARA, via the yellow “Email submissions and comments” button, near the bottom of ACARA’s consultation page. (We could include the email link here, but somehow that feels incorrect.)

Should you submit something? Yes, you should, for the same reason that you should vote against ScoMoFo in the next election. The point isn’t that your action is likely to change anything; the point is that it feels good. So, if it feels good to simply submit the open letter, then do that. But you should submit something.

Not convinced? Then maybe the following will help convince you. ACARA’s consultation page encourages feedback with the following line:

The online survey includes open fields to allow you to provide general comments about what you think we have improved and what you think needs further improvement.

So, either 1) what they’ve improved, or 2) what needs further improvement. On the off chance you believe something might fall into a third category, perhaps you might want to let ACARA know about it.

Does the Draft Mathematics Curriculum Contain Any Problem-Solving?

We’ve written about this before, and the point is obvious. But, it’s apparently not sufficiently obvious for some wilfully blind mathematicians. So, let’s go again. Plus, there’s a prize for the best comment.*

ACARA is playing people with a cute syllogism.

  • Problem-solving is good.
  • The draft curriculum contains lots of problem-solving.
  • Therefore the draft curriculum is good.

Yep, the syllogism is flawed from the get go. But in this post we want to focus on the second line, and we ask:

Does the draft mathematics curriculum contain any problem-solving?

Certainly the draft curriculum contains a hell of a lot of something. As we’ve noted, the draft refers to “investigating” or some variation of the word 298 times. And, students get to “explore” and the like 236 times, and they “model” or whatever 264 times. That’s a baker’s ton of inquiring and real-worlding, which some people, including some really clueless mathematicians, regard as a good thing. Ignoring such cluelessness, what about genuine mathematical problem-solving?

The draft curriculum refers to “problem(s)” to “solve” 154 times. But what do they mean? When, if ever, is the draft referring to a clearly defined mathematical problem that has a clearly defined answer, and which is to be solved with a choice of clearly defined mathematical techniques? To the extent that there are any such “problems”, do they rise above the level of a trivial exercise or computation? In the case of such trivial “problems”, is the label “problem-solving” more than a veil-thin disguise for the mandating of inquiry-learning?

In brief, is there more than a token amount of the draft’s “problem-solving” that is not either real-world “exploring/modelling/investigating” or routine exercises/skills to be taught in a ridiculously inappropriate inquiry manner?

Perhaps genuine mathematical problem-solving is there, and we are honestly curious to see what people have found or can find. But, we’ve found essentially nothing.

And so, to the competition. Find the best example of genuine, mathematical problem-solving in the draft curriculum. Answer in the comments below. The most convincing example will win a signed copy of the number one best-selling** A Dingo Ate My Math Book.

 

*) Yes, yes. we have those other competitions we still haven’t finalised. We will soon, we promise. As soon as we’re out of this ACARA swamp, we’ll be taking significant time out to catch up on our massive tidying backlog.

**) In Polster and Ross households.

 

Update (29/07/21)

We’ve finally ended this. The winner is, hilariously, Glen. See here for details.

 

 

ACARA CRASH 14: Backward Thinking

This one we really don’t get. It concerns Foundation and Year 1 Number, and was pointed out to us by Mr. Big.

We began the Crash series by critiquing the draft curriculum’s approach to counting in Foundation. Our main concern was the painful verbosity and the real-world awfulness, but we also provided a cryptic hint of one specifically puzzling aspect. The draft curriculum’s content descriptor on counting is as follows:

“establish understanding of the language and processes of counting to quantify, compare, order and make correspondences between collections, initially to 20, and explain reasoning” (draft curriculum)

“explain reasoning”. Foundation kids.

OK, let’s not get distracted; we’ve already bashed this nonsense. Here, we’re interested in the accompanying elaborations. There are ten of them, which one would imagine incorporates any conceivable manner in which one might wish to elaborate on counting. One would be wrong.

The corresponding content descriptor in the current Mathematics Curriculum is as follows:

“Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point” (current curriculum)

Notice how much more “cluttered” is the current descriptor… OK, OK stay focussed.

The current descriptor on counting has just (?) four elaborations, including the following two:

“identifying the number words in sequence, backwards and forwards, and reasoning with the number sequences, establishing the language on which subsequent counting experiences can be built” (current curriculum, emphasis added)

“developing fluency with forwards and backwards counting in meaningful contexts, including stories and rhymes” (current curriculum, emphasis added)

The point is, these elaborations also emphasise counting backwards, which seems an obvious idea to introduce and an obvious skill to master. And which is not even hinted at in any of the ten elaborations of the draft counting descriptor.

Why would the writers of the draft curriculum do that? Why would they consciously eliminate backward counting from Foundation? We’re genuinely perplexed. It is undoubtedly a stupid idea, but we cannot imagine the thought process that would lead to this stupid idea.

OK, we know what you’re thinking: it’s part of their dumbing down – maybe “dumbing forward” is a more apt expression – and they’ve thrown backward counting into Year 1. Well, no. In Year 1, students are introduce to the idea of skip-counting. And, yep, you know where this is going. So we’ll, um, skip to the end.

The current Curriculum has two elaborations of the skip-counting descriptor, one of which emphasises the straight, pure ability to count numbers backwards. And the draft curriculum? There are four elaborations on skip-counting, suggesting in turn the counting of counters in a jar, pencils, images of birds, and coins. Counting unadorned numbers? Forget it. And counting backwards? What, are you nuts?

OK, so eventually the draft curriculum seems, somehow, to get around to kids counting backwards, to look at “additive pattern sequences” and possibly to solve “subtraction problems”. The content descriptors are so unstructured and boneless, and the elaborations so vague and cluttered, it is difficult to tell. But how are the kids supposed to get there? Where is the necessary content description or elaboration:

Teach the little monsters to count backwards.

If it is there, somewhere in the draft curriculum, we honestly can’t see it. And if it is not there, that it is simply insane.

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

 

What if You Hate this Blog

Having put out a few fires, I will return to posting on the draft curriculum. (The open letter can still be signed, here.) But, first, a meta-post on the draft.

It was brought to my attention that a Professor who might have otherwise contemplated signing the open letter did not even consider signing, because the open letter is seen to be “associated with” my ACARA page. The Professor decided that they could not “endorse” the style of criticism that I (and perhaps some commenters) provide there. I am sure the Professor is far from alone. So, how to respond?

Dear Professor, and Others,

I will try to make this simple.

(1) If you agree with the open letter then maybe you should just sign the letter. If not, not. Why is this hard?

(2) The open letter is not mine. I was involved in its production, but it is not my letter. It is no one’s letter. It is a letter stating a point of view, and with a request for ACARA and the ACARA Board to withdraw the draft curriculum. In particular, the letter is not hosted on this blog, and the idea that signing the letter somehow amounts to an endorsement of me or my blog is absolutely absurd. Signing the letter is an endorsement of the letter. That’s what “endorse” means. See point (1).

(3) I have provided the ACARA page (and the draft curriculum page) as assistance, in the unlikely event that someone couldn’t make their way through ACARA’s documentation. You are of course free to ignore my page entirely, and to use other sources. The fact that there are no other sources may be a bit of a hurdle, but I’m afraid that is your problem to solve. In any case, it is up to you to decide how to evaluate ACARA’s draft curriculum, and to act accordingly. See point (1).

(4) I can understand why you may find this blog, and me, distasteful, or worse. I can understand there are good and popular arguments, even just in my own self-interest, for why I should write in a different style. I believe I can defend myself and my blog, but this is not the place to do it. It is not the place to do it, because my blog is not the issue here. The issue here is the draft curriculum and the open letter. See point (1).

See, it’s not really that hard, is it?

Kind Regards, Marty

p. s. See point (1).