Maths Experts Do Not Reaffirm Support For Curriculum Changes

A few weeks ago, the Sydney Morning Herald published a report by Lisa Visentin and Anna Prytz, with the pithy title,

Maths experts reaffirm support for curriculum changes as leading group sounds alarm

The “leading group” refers to AMSI, which indeed sounded the alarm, calling for a halt of ACARA’s review of the mathematics curriculum. The claim, however, that “maths experts” reaffirmed support for the curriculum changes is, in a word, bullshit. Obviously AMSI did not do so, but also, to a reasonable approximation, no one did.

Continue reading “Maths Experts Do Not Reaffirm Support For Curriculum Changes”

ACARA CRASH 17: Algebraic Fractures

The following are Year 10 Number-Algebra content-elaborations in the current curriculum:

CONTENT

Apply the four operations to simple algebraic fractions with numerical denominators

ELABORATIONS

expressing the sum and difference of algebraic fractions with a common denominator

using the index laws to simplify products and quotients of algebraic fractions

CONTENT

Solve linear equations involving simple algebraic fractions

ELABORATIONS

solving a wide range of linear equations, including those involving one or two simple algebraic fractions, and checking solutions by substitution

representing word problems, including those involving fractions, as equations and solving them to answer the question

And what does the draft curriculum do with these?

Removed

And, why?

Not essential for all students to learn in Year 10.

God only knows how one develops fluency with expressions that cease to exist.

ACARA CRASH 16: Unlevel Playing Field

Each Year’s content in the draft curriculum begins with a Level description, and each of the thirteen Level description begins with the exact same sentences:

The Australian Curriculum: Mathematics focuses on the development of a 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. [emphasis added]

Yep, “an equal focus on building fluency“, no doubt about it.

 

ACARA CRASH 15: Digital Insertion

Continuing to try to rid ourselves of ACARA irritants, the following are the “calculator” elaborations from Year 1 – Year 6 Number and Algebra (sic):

YEAR 1

using the constant function on a calculator to add ten to single digit numbers, recording the numbers to make, show and explore the patterns in a 0 – 100 chart

with the use of a calculator, exploring skip-counting sequences that start from different numbers, discussing patterns

modeling skip counting sequences using the constant function on a calculator, while saying, reading and recording the numbers as they go

Continue reading “ACARA CRASH 15: Digital Insertion”

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.

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).

 

Education Fires Back Again

There is another contribution from the Education community:

How to do the sums for an excellent maths curriculum

This one does not directly address the open letter, although, given the framing and the links, it is difficult to not see the article as an intended rebuttal. Again, we know little of the authors, and we have not read the article with any attention. We’ll be interested in what commenters think. (Ball-not-man rules still apply.)

UPDATE (10/06/21)

Glen has pointed out that the article is from April 21. So, it is definitely not in response to the open letter. However, the article came out soon after the ridiculous, pre-emptive strike statement from AMSI, AAS and others, and in its first sentence the article links to the reporting of this statement. Whatever merits it might have, the article is not an innocent reflection on educational method.

UPDATE (10/06/21)

As indicated by SRK, there is now (in effect) a response from John Sweller.

Maths Ed Fires Back

Today in The Conversation there is an article firing back at the open letter to ACARA:

The proposed new maths curriculum doesn’t dumb down content. It actually demands more of students

We haven’t read the letter, and we don’t know the authors, or of the authors. We’ll try to read the article and comment on the article soon, modulo home schooling and general exhaustion. For now, people can comment below (respectfully and on-topic and on-the-ball-not-the-man). We’ll be interested in what people think.

 

UPDATE (28/6/21)

We’ve finally had the time to read this article. The comments below suffice, and we’re not going to waste our or others’ time with a detailed critique. .

Seriously, that’s the sum of the defense of the draft curriculum? That’s all they got?