ACARA’s draft Mathematics Curriculum is out. Feedback can be given, in the form of survey only, until July 8.

We have had no time to look at the draft, although of course we will. Our posts on the review literature leading up to this draft are here, here, here, here and here.

We’ll be interested in what people note in the comments below. Please try to keep the comments focussed on substantive criticism (or praise), rather than unanchored abuse (even if deserved). For now, what matters is the detail.

Here are the relevant documents and links, as far as we can see:

- The main draft Mathematics page, including FAQ and an overview video (with transcript).
- The survey feedback page (with survey questions).

- An overview, What Has Changed and Why?
- Content comparison of current and draft F-6.
- Content comparison of current and draft 7-10.

- The current Mathematics Curriculum (added 28/05/21)

Again, we very much look forward to reading people’s comments. And, again, please keep it focussed. Comments may be about the curriculum generally, and of course may be critical, but should be dealing with the substantive issues.

**UPDATE (30/04/21)**

Thank you to everyone who has commented so far, and please keep the comments coming. We’ll be reading with keen interest, and we’re definitely intending to go through the Daft Curriculum with a fine-tooth comb. However, won’t look to be posting further on the curriculum for at least a few days.

In brief, the ACARA literature marathon has exhausted us. Plus, the Evil Mathologre is breathing down our neck: a deadline for *Son of Dingo* is looming, and 200 mini-Mathologer essays are about to come crashing down, demanding to be graded.

We’ll end here with a genuine and very interesting question:

*Will Alan Tudge take on ACARA? *

The Minister for Education is clearly serious, if largely misguided, about raising Australia’s educational standards. And, in particular, Tudge is presenting himself as Mr. Back To Basics. True, Tudge has given no indication that he understands what “the basics” are, but it is in his sights. So, what’s he gonna do with the Daft Curriculum and the people responsible for it? Whatever the hell this curriculum is, it is decidedly not going back to the basics.

There doesn’t seem to be any noticeable change to the content descriptors for 7 to 10.

Same sort of stuff thats been in before.

Some interesting “elaborations”. Are they compulsory or just ideas that could be done to teach a content descriptor? In NSW the syllabus is structured a bit differently and such this like elaborations are optional things a teach could do.

Just one elaboration that I never thought of: “exploring the conjecture that the area of a shape is the product of the average of the lengths of a pair of parallel sides and the distance between them”. Is this an actual conjecture?

I’ve heard of two atrocious changes in the content, although I haven’t confirmed either. I gather the major issues are the constructivist elaborations, and the elaborating of the content descriptions. Again, I’ve had no time to check.

Is one of the atrocious changes that associative, commutative and distributive laws are relegated to the algebra strand and are not in number in both primary and secondary curriculums? Seems like this will not be helpful in supporting primary teachers teaching arithmetic well (which I assume falls in the number strand).

Yes the elaborations can quite bizarre and unhelpful (even without constructivist flavouring). One example suggests finding the mode for a dataset of people’s heights.

Hi, Potii. I hadn’t heard of that change, but it indeed sounds like an atrocious change.

The original descriptor was in year 7 number: “Apply the associative, commutative and distributive laws to aid mental and written computation (ACMNA151)”, which is pretty good.

It’s now incorporated (?) in a year 7 algebra monster “create algebraic expressions using constants, variables, operations and brackets. Interpret and factorise these expressions, applying the associative, commutative, identity and distributive laws as applicable (AC9M7A02)”

I dug around a bit looking for what the curriculum says about solving linear equations. On another post, JF gave a list of some of his bugbears; one of mine is students coming into Year 11 Methods who can’t routinely solve linear equations which involve fractions and unknowns on both sides.

According to the draft curriculum, solving linear equations of the form ax + b = c is deemed too difficult for Year 7 (!) students, and should be left for Year 8 students. Following this, there is just very vague mention of solving linear equations in a few places in Years 9 and 10, but nothing specifically about the complexity of these equations. In fact, the only other specific thing the curriculum mentions is that linear equations involving algebraic fractions should be REMOVED from year 10, because it is “not essential for all year 10 students” and should be optional content for students aiming to do Methods / Specialist.

Stuff like this where ax + b = c is for year 8 and ax + b = 0 is for year 7 screams teaching without understanding.

Something the ACARA people are apparently trying to avoid.

Their curriculum is just blather.

As an aside, I was informed that our favourite VCAA mathematics manager was on the radio this morning (774 ABC Breakfast Show with Sammy J) blathering about changes to the maths curriculum. Did anyone hear any of it? I don’t know whether he was blathering about the draft Stupid Design or the ACARA Maths draft.

Nope, it was worse. It was de Carvalho. You can listen here (29 April at 1:44:40). The man is an idiot.

Thanks, SRK. The year 7 thing is one of the horrors I had heard. I hadn’t heard the Year 10 compounding of that horror. These people are fucking lunatics.

Un-friggin-believable. I have no words …

“Un-friggin-believable” is, in fact, a word, and the correct word.

“When and where are the single-digit multiplication facts (timetables) covered in the proposed F–10 Australian Curriculum: Mathematics?

These are explicitly covered at Year 4 in both the achievement standard and content descriptions for the number strand. Work on developing knowledge of addition and multiplication facts and related subtraction and division facts, and fluency with these, takes place throughout the primary years through explicit reference to using number facts when operating, modelling and solving related problems.”

This is shit.

Glen! Language! The expression is “fucking shit”.

In 1202, Fibonacci wrote Liber Abaci in which he introduces Europeans to the Hind-Arabic system of numerals and the associated arithmetic. I don’t have a copy handy, so I am working from memory. As I recall, in chapter 1 he introduces the reader to 1,2,3, … and of course 0 and place value. So we are at the beginning of arithmetic. Chapter 2 deals with multiplication. He expects the reader, by the end of the chapter, to be able to multiply two 6 digit numbers together without showing any working. The reader should be able to do in his or her head.

Only digital calculators allowed: he teaches you how to represent numbers up to 9999 using the fingers on two hands.

This is a great book; translated into English for the first time in 2002.

The draft curriculum states: “In contexts where chance plays a role, probability provides both experimental and theoretical approaches…”.

I don’t believe in “chance”. There is not some force called “chance” at work in the world. “It was pure chance” – what does that mean? The Romans would identify the goddess Fortuna as responsible for certain events. These days, the word “chance” is used to explain events that can’t be explained otherwise.

I have a question… why is “networks and planar graphs” now going to be a topic at Year 9/10?

Also, why is it also being added to the Specialist Mathematics curriculum in the new draft?

Genuinely curious if it is because someone wants to make money off it some how or if there is an actual logical reason behind it.

Networks and graphs are already in General Mathematics at Year 11. As the topic is presented in the text book, it is a litany of definitions (which goes with the territory in graph theory), accompanying rules with little justification, and pedestrian applications and exercises. I found the text book disappointing to say the least.

I’m well aware of this, but my question remains: WHY?

My answer is “fashion”. The study of graphs and networks is appealing in its simplicity. But this appeal is superficial because it does not become interesting until you get over the mountain of definitions which won’t happen in our schools. We seem to devote only a couple of weeks to any single topic.

There is also the issue that many teachers have never studied the subject and therefore do not read the text book critically: it contains many errors.

A few times I have worked in Hungary which is renowned for the strength of its mathematicians. There they have special events for their best high school students. I was told once that they don’t allow to be involved because he turns the students onto graph theory rather than mathematics. (He was alive when I last visited.)

Robin Wilson “Introduction to graph theory” is a good place to learn about the subject.

And also in Further Mathematics Unit 3/4.

My theory on its recent proliferation is the so-called ‘algorithmic thinking’ that is heavily influencing the draft Stupid Design and other curriculum documents (even though there is already a specific VCE subject called Algorithmics). And ‘algorithmic thinking’ is part of the larger ‘problem solving’ influence.

Thanks – I actually studies graph theory in my final year as an undergraduate so knowledge is not my issue – it is walking the fine line between going far enough in a topic to show students the purpose of the topic without going so far as to lose 80% of the class because it is beyond the comprehension of a pre-university student.

I like the fashion theory, but do wonder if there is an invisible hand from the logistics world pulling a few strings here.

Yes, there are always invisible hands. There were (not so) invisible hands pulling the strings to get all that statistical inference bullshit into the Methods and Specialist syllabus.

There are too many invisible hands with too much influence pulling too many strings.

I finally had a look. The first thing that really threw me was that

“Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (ACMNA178)” has been removed from Year 7.

I just taught this last week using a join-the-dots activity that I made (you joined the dots to make a picture) and I was really happy with how it went. The students found it challenging at the start, so it hadn’t been taught

thatmuch in primary school.And obviously they’re going to need to know how to plot points in order to “plot relationships on the Cartesian plane”. It’s the foundation for a lot of stuff to do with graphing functions right through to Year 12. Am I missing something – why would they remove plotting points from coordinates?

ETA: I looked a bit harder and found out they are meant to know it in Year 5. Oh, wait – they haven’t done negative numbers then so it’s not the whole plane. I’m not sure what to make of it. A lot of people don’t

reallyseem to get what they are doing when they graph points and functions, so I think it is worth repeating in Year 7 anyway. And it seems like they’re expecting students to just make the leap into graphing functions without learning how to plot negative coordinates explicitly?I also found this while looking for where it might be covered:

“approximating the coordinates of the points of intersection of the graphs of two functions using systematic guess-check and refine algorithms (AC9M10A07_E2)” and I don’t get it.

What exactly are they saying we’re supposed to teach?Curriculum documents always make me feel so stupid.You should conclude stupidity, but not your own.

That’s kind of you to say. But I feel silly because I found the explanation in the What’s Changed and Why document: “This is redundant as it is already covered in Year 6.”

So I checked, and apparently students do learn negative numbers in Year 6, which is weird, because I taught it this year as a “new” topic to Year 7 students who showed no great signs of having learned it already. And I’m still explaining negative numbers regularly to students when I give review problems and they haven’t all got the main points yet.

I think maybe the curriculum should have more clarity around the difference between students being introduced to something and them having mastered it. So for negative numbers and coordinates, I would expect to teach the same thing for a few years but the students would get better? I think that would be easier to understand for me. Having items listed just doesn’t make the distinction at all. The curriculum descriptions just get harder for me to understand as they say more and more complicated things about the same concepts, rather than just admit it takes time to learn the simple thing. I reckon a bit of redundancy would be just fine with me.

The expression “learned in Year 6” doesn’t mean what you think it means.

Indeed. The fact that it is ‘taught’ in Year 6 or whenever does not mean that it has been ‘learned’ at that level.

There is a lack of understanding in re-visiting basic facts and skills that have already been ‘taught’ to ensure that they are also learnt. Which is strange because the quadratic formula (for example) gets ‘taught’ in Yr 9, Yr 10, Yr 11 and Yr 12. The distinction in each year level being the level of mastery required (and hence the types of questions asked).

What does it mean when something is listed in a certain year level of the curriculum document? How is a teacher supposed to interpret it?

Good question, wst. You have to accept the fact that the curriculum documents published by DET etc. are complete shit, and then just do your best. In reality, from Yrs 7-11 (VCE Units 1/2) most teachers will depend solely on the textbook to interpret the curriculum for them, and essentially teach from the textbook. The better teachers will also fill in the gaps they see the textbook as having.

For VCE Units 3/4 – again, most teachers will depend on the textbook, and essentially teach from it. Better teachers will look at past exams questions for additional clarification and interpretation. The best teachers will do all these things and also fill in the remaining gaps using their own knowledge, experience and expertise. And unfortunately, some teachers will also rely on trial exams. I say unfortunately because some trial exams have content that is definitely NOT on the Stupid Design and this ends up worrying novice teachers of the subject and frustrating experienced teachers. For example, see here (Q3 in particular): https://mathematicalcrap.com/2020/09/25/mavs-trials-and-tribulations/

VCAA’s current daft Mathematics Stupid Design is a case in point for all of the above: it has more holes in it than a colander. I do not hold out any hope that the final copy will be an improvement, despite the feedback that is given to the clowns that extensive further clarification is required. Compare VCAA’s Stupid Design to the attached document from SACE (South Australia’s VCAA equivalent) in terms of knowing where you stand.

Stage 2 Specialist Mathematics Subject Outline (for teaching in 2021)

Thank you. That’s really informative. I like how the SACE curriculum guide has all the examples and mathematical specifics. It’s much clearer to me than all the words that VCAA use. (Sometimes I wonder if maybe the VCAA people just don’t know how to use LaTeX?)

I was reading this thinking I would fill out the survey but maybe it’s not my place because I don’t know enough yet.

I’m sure the VCAA people know how to use Latex. The reason VCAA’s Stupid Design is shit is because the VCAA people responsible for this stuff cannot give straight answers. They prefer to obfuscate and create an environment of ambiguity and confusion. It makes them feel powerful and important. It’s all about control.

There are a number of very simple things that can be done to improve teaching standards and teacher training, including getting rid of:

1) the parasitic Vampires,

2) the 2 year Monstrosity of Teaching,

3) inept subject Managers at VCAA.

PS: You clearly know enough to know that the various curriculum documents are falling well short of achieving what they’re meant to achieve …

PPS: I had said in my feedback on the daft Stupid Design that it should follow the SACE model. But I may as well try to piss into a hurricane.

WST, I’d have to double check, but from memory that bit is included under solving systems of linear equations. I don’t quite know what they are getting at, but perhaps it’s something like: (1) Draw two graphs, to scale. (2) From your graphs, estimate a point of intersection. (3) Check your guess by substituting into both equations. (4) If you are wrong, adjust your guess and then check again.

I’ve never heard of anyone actually teaching this as a method for solving simultaneous linear equations, so I don’t know why it’s there. I’ve always ignored anything in curriculum documents referring to “guess and check”. (Perhaps these methods have some use in some contexts; school maths isn’t one of them).

How nightmarish. That’s just going to scare the students into thinking systems of equations are hard to solve.

Oh, thank you. 🙂 That kind of makes sense. I suspect ACARA are thinking you’re doing it with a calculator or Geogebra or something (it’s next to something about technology).

A mantra that is often used is “Stage not age”. Students should learn something when they are ready for it. Expecting all students of a certain age to be ready to learn something is nonsense. I have often asked: What size shoe should a 12 year old wear? Somebody gave me a good answer: One that fits.

Terry, that truism has been turned to bullshit. It is now an excuse to not expect, much less demand, anything from anyone at any level. Until you get to VCE, when you find out that it’s too late. (And you find out that VCE is garbage, but that’s off the point here.).

Not so far off the point though Marty.

If the final exams/courses are rubbish, then perhaps a rubbish 7 to 10 curriculum is the way to prepare them for it…?

Thanks to everyone for the comments and discussion and flags of nonsense.

SRK, or anyone, can you point to “guess and check” in the draft (or current) curriculum? I guess this occurs with factoring polynomials (pretty reasonably for quadratics and pretty contrivedly for highers), but is it anywhere else?

After having written about ten million words on this, and waiting for someone else to pull some fucking weight, I’m trying to stay away this week, and to put out some of the many other fires. I’ll have one more no-surprise WitCH, and then back next week. But I am reading the comments, and I’ll use them when I look very carefully at the Daft AC.

The only place I could explicitly find a reference to “guess and check” is in Year 10, the content descriptor for AC9M10A07 is “apply computational thinking to model and solve algebraic problems graphically or numerically”. One of the elaborations is “approximating the coordinates of the points of intersection of the graphs of two functions using systematic guess-check and refine algorithms”. Another of the elaborations is to use a bisection algorithm to approximate the locations of roots of quadratics.

The VCE study design for Methods also mentions solving equations and systems of equations “numerically”, and this is mentioned alongside solving “algebraically”. I’m not quite sure what the intended contrast is, but if it’s not some kind of guess-and-check or trial-and-error-ish method, I’m not sure what it could be.

Could VCE be talking about finding roots to

by iterating Newton’s method? That’s not a system of equations, but still….

Glen, that’s explicitly in the study design for Mathematical Methods Unit 2 (the second half of year 11, roughly equivalent to HSC’s Advanced Mathematics).

I have a theory about the development of the revised curriculum.

In recent years, Australian students have been performing badly in PISA mathematical assessments [1]. The government thinks we should do better.

How do we improve our performance in PISA assessments? Well, like any other form of assessment, students should be prepared for PISA mathematical assessments.

“The PISA assessment focuses on young people’s ability to apply their knowledge and skills to real-life problems and situations.” [1, p. xiv]

The road-map is clear. Design a curriculum that concentrates on problem-solving and modelling. This is the way to improve our PISA scores.

Had they started with TIMSS, which assesses quite different aspects of learning mathematics, they would have another road-map.

Reference

[1] PISA 2018: Reporting Australia’s Results. Volume I Student Performance by Sue Thomson, Lisa De Bortoli, Catherine Underwood and Marina Schmid (Australian Council for Educational Research) under contract with the Commonwealth of Australia as represented by the Department of Education who is the copyright owner of the material.

Terry, i think you’re on to something, although perhaps it’s more a general sympathetic idiocy.

There is no question that (foolishly) worrying about PISA will skew away from the much saner TIMSS. (Although, I also have an uninformed suspicion that TIMSS is becoming less sane.) There is also no question that the draft, and the hired clowns CCR, are immersed in the PISA Kool Aid. But, also, mathematics education completely generally has gone nutso with inquiry learning and exploration, and just full-blown garbage.

Is there a single maths ed academic in the country who is vaguely sane, and who is vaguely doing good? I honestly cannot identify a single such person. As I keep saying, and have competitioned, everything they do appears to me either trivial or false. I cannot think of a single maths ed academic who is acknowledging and fighting against the systemic perversion of mathematics education. And, many are fighting to make it actively more perverse.

Terry, that’s a pretty good theory. It makes sense. Although the question is then was PISA rather than TIMMS chosen as motivating the curriculum roadmap. Maybe it just boils down to wanting a cheap and simple solution to a complex problem. Related to this, I’m sure the soundbite of ‘problem-solving’ was also attractive.

As the 2014 letter I posted here (https://mathematicalcrap.com/2021/06/02/open-letter-to-acara-and-the-acara-board/#comment-9464) clearly displays, ACARA has been selling its snake-oil since at least 2014.

The only reason why ‘problem-solving’ is such a focus in this Daft curriculum is the misrepresented notion that it’s the basis of the Singaporean curriculum.

The only known member of the Daft curriculum panel is a person who’s career is based on inquiry-based learning. It would be interesting to know who the remaining panel members are (were, hopefully …) so that their credentials could be assessed. I suspect that water finds its own level with these sorts of panels. When all you have are hammers, everything looks like a nail. A biased panel will always produce a biased report.

John, I think you said it clearer than me. One might see PISA as the focus, but then that focus was chosen for a reason. And, the reason is a general perversion in maths ed.

Regarding Singapore, I’m not convinced the ACARA whatevers honestly believe that the draft is remotely Singaporean. The curriculum comparisons appear so obviously gamed, I think they knew what they were doing.

Hmmm …

To quote Graham Greene: “Innocence is like a dumb leper who has lost his bell, wandering the world, meaning no harm.”

I can forgive innocence (whilst still condemning it).

What is unforgivable (and deserves our utter contempt) is if ACARA and its assorted gang of clowns “knew what they were doing”.

My guess is that they have fooled themselves into believing their own bullshit. It’s amazing how often that happens.

Of course they have. They are well-meaning ideologues.

I think you mean idiotlogues. Be that as it may, the real criminal is whoever stacked the review panel with such people, making the current Daft curriculum inevitable. Hopefully the title of this blog is a prediction of the near-future …

John, I think that’s the wrong way to think about it. They are obviously going to select their writers and insider consultants from the world of mathematics education. Who might they choose that’s not a nitwit?

It seems to me that PISA and TIMSS have quite different purposes. They can be evaluated only to the extent to which they achieve their purposes.

The purpose of PISA is bullshit. Are we done now?