It seems the VCAA has just released their draft of the new study design for Mathematics:

- The current (pre-COVID) study design (pdf) is here.
- The draft for the new study design (word) is here.
- The key changes overview (work) is here.
- The link for feedback (
**until March 9, 2021**) is here.

We haven’t yet looked at the draft, because we’re scared. But, don’t let that stop others. May the discussion and the throwing of brickbats begin.

They’ve introduced logic and proof to Spesh 3&4, which doesn’t actually look too bad.

To make room for it, they’ve removed mechanics, which I have mixed feelings about. (I think removing probability and statistics would have been a better choice.)

They’ve *brought back* logic and proof … Back in the 90’s Specialist consisted of core topics plus a couple of modules you could choose from. Logic and proof was one of those modules (mechanics was another). It was a similar model to the current Further Maths.

I’ll be asking VCAA to make available all those old Specialist exams from the 90’s that had logic and proof questions. The question is, will VCAA comply? If anyone can find an old Checkpoints from that era, those questions would have been collated.

It’s interesting to note that one of the SACs of shit in BOTH Methods AND Specialist now has to focus on the data analysis, probability and statistics area of study. And it’s worth 20% of the students result. So who are the goons in the shadows calling the shots here …? The Australian Bureau of Stooges?

It’s no Carlton Draft, that’s for sure. More Victoria Bitter.

I’ve had a look at the changes and one funny thing that JF may be thinking about is “the median is no longer required for continuous random variables”… I seriously can’t help but feel that a certain *event* helped push that decision across. Other than that, the whole study design is going to take a while to process, especially with the introduction of Foundation Maths Units 3 & 4.

lol. Yes, that entered my mind too. But then you’d need to delete *all* the content that a certain *event* affected, starting with the trigger itself … (Much better to delete all the people associated with the *event*)

No, I don’t think it was pushed by the *event*. I think it was deleted because it was considered surplus to requirements for whatever reasons (unfortunately that doesn’t happen to some VCAA staff and their stooges).

Bob, I’m on your side. The writing has been on the wall for a few years now that mechanics was on the way out, being steadily diluted with various deletions. I have no problem with the statistics if it was mathematical statistics not this stupid bullshit recipe driven hypothesis testing. Imagine the immediate difference if that shit was replaced with stuff like moment generating functions etc. The logic and proof (which used to be one of the optional modules in Specialist Maths back in the 90’s) looks good on paper and I’m happy that proof by induction has been added. But I’d love to hear the motivations and rationale for these changes. And the lack of details in the Study Design is concerning. The devil will always be in the detail (or lack thereof) and there’s going to be a lot of ambushing of teachers and students – especially since the exam writers will no doubt be applying their own interpretation of the vague Study Design statements. There is a lot more stuff to be taught than I think many people will realise.

FR, I agree with all your comments. It’s very interesting indeed.

Sai, the explicit inclusion of the logistic equation is very interesting. I don’t know why that would be done, it’s just another DE that can arise in the context of population growth etc. I think it’s a knee-jerk reaction to the events of 2020. Subsets of the complex plane is hidden in a key skill dot point – typical VCAA deception. This really makes me angry because it should be clearly stated in the Area of Study descriptions. Re: Points of inflection – I doubt these fools see the importance of clarity here. In fact, they are so stupid they don’t see the importance of clarity anywhere except when it’s redundant (logistic equation). I have no problem with the Vectors section. I was expecting cross-product last time – there was a big push by Michael Evans, for some reason he wants students to be able to find the equation of planes in 3-d. I guess he got his way this time.

And yes, the SACs of shit carrying more weight is very troubling.

Conclusion:

1. The Specialist Units 3&4 proposed syllabus has been written by people who won’t have to teach it. Teaching it properly in 10 months is going to be virtually impossible (unless you cheat by using Specialist Units 1&2 to lay the explicit groundwork).

2. The lack of DETAILS and CLARITY is insane and insulting. Teachers will be left guessing – as always – how much to teach. Because anything goes. Take proof by induction – There is no limit to the contexts and types of questions that could be examined.

3. As always, it’s the teachers that will be left carrying the can. There will be an even smaller pool of teachers willing and able to teach Specialist Maths with this proposed Study Design.

I’ve only had a brief look and had some initial reactions, and I’ll have to think more carefully over the weekend and start formulating a response to VCAA.

But just on the point about sketching subsets of the complex plane: this is now explicitly mentioned in the complex numbers area of study for Unit 2 Specialist Mathematics, and now Units 1&2 SM are prerequisites for Units 3&4.

Yeah, this has opened up a huge can of worms. It’s going to *significantly* add to the teaching load of Specialist 3&4 because of course all that Specialist Units 1&2 stuff will have to be reviewed. There has been no thought put into the reality of teaching this Study Design.

Agreed. There’s no way that all of the circular functions content for SM (trig identities, reciprocals, inverses) can only be taught in Units 1&2 and be assumed that the students have mastered it.

And the notion that Year 11 classes have time in their schedule to include two weeks of “mathematical investigation” *per Unit* on top of all the content is hilariously out of touch.

What most struck me is the “Mathematical Investigation” (1 – 2 weeks) in the Unit 1&2 studies. No doubt this is meant to impact SAC 1 for units 3&4 in some way.

Feels a bit awkward, but I guess we will wait and see exactly how schools implement this into the (over)crowded curriculum.

Specialist Units 1&2 becoming fully prescribed is interesting also, but for a different reason. Graph theory being introduced (looks a lot like Networks module from FM…) is also an interesting one.

But most of all, I find it interesting that Specialist 3&4 is now assuming knowledge of Specialist 1&2 AND Methods 1-4 (Specialist 1&2 has, to my knowledge NEVER been a prerequisite for Specialist 3&4 in the past).

I do feel the Specialist 1&2 course is becoming a bit more “methodsy” in this draft, which is a pity, in my opnion.

Now that I’ve had a bit of time to investigate the new study design, I’ve had a look through SM 3 & 4, and wow, there are quite a few changes. In order, we have:

The first area of study is now discrete mathematics, particularly logic and proof. This seems to involve logic statements, such as implication, equivalence, contrapositive and so on, in addition to the quantifiers ∀ and ∃. What’s really interesting is that one could be tested on proofs from areas such as graph theory (a proof of something such as Prim’s algorithm generating a minimal spanning tree would be fascinating to see), boolean algebra (perhaps simplifying statements such as X*X+Y*X or proving something), matrices, sequences and series.

The second area of study seems to be unchanged (it used to be the first area of study) under the topic of functions, relations and graphs. Although I don’t see any of the dot points relating to relations…

Area of study 3 (complex numbers) seems to now lack argand diagrams and sketches of complex subsets unless I’m mistaken and cannot read.

Calculus is where things get more interesting. Unsurprisingly, no clarification on the concavity debacle, however, I am very surprised to find that IBP has now made its way into the study design. (About damn time). Under differential equations, it so happens that the logistic differential equation is explicitly listed which is unusual but interesting…

Under the 5th area of study (the study of vectors), there seem to be quite a few changes. First off, the cross product has been introduced, along with the determinant form which is something that should have been here a long time ago. Vector and cartesian equations have been expanded as well, now with explicit mention of the vector equation of a straight line in . Following this, systems of linear equations have been expanded to learning Gaussian elimination along with interpretations of a consistent/inconsistent system of equations.

As for probability, no obvious changes are present.

It seems as though there’s a lean towards linear algebra from what I can see so far. What I’m more interested in is the first area of study. Another thing is that that SAC’s carry more weight now (SAC = 40%, E1 = 20%, E2 =40%)…

The complex subsets stuff is hidden in the Key Skills:

“represent regions of an Argand diagram using complex relations”

WHY is the Logistic Equation given its own separate dot point? It’s simply a model of population growth and an example of a separable differential equation. Is it to be studied as a special type of separable differential equation (the different types of solutions, equilibrium solutions etc.) What is the broader context meant to be here? It’s explicit inclusion is moronic and probably a stupid knee-jerk reaction to COVID-19.

Seems like they’ve added quite a few things to Specialist 3-4, along with the Logic and Proof unit, which apparently can apply to anything from Units 1-4.

From my first pass I found: cross products, matrices for systems of linear equations (that’s a whole unit, row reduction etc.) integration by parts, surface area of solids of revolution.

Also some typical VCAA vaguery about using pseudocode in Outcome 2, as well as this in the Key Skills: “Interpret and apply algorithms in a variety of contexts including the use of pseudocode for representation”

All of that in, with Mechanics out and nothing else I can find explicitly removed.

I’m actually liking the new Vectors and Matrices material. Although it does feel like the course it taking a bit swing towards the “pure” rather than “applied” end of the spectrum. A lot more like the IB HL curriculum in many ways (and they could do a lot worse than emulate the IB HL Mathematics course…)

Specialist Maths Area of Study 5 is a mess:

How can the determinant representation of the cross product be taught when matrices as a topic is not part of the Methods or Specialist syllabus. This is yet another example of some random bit of matrix theory being included (see use of matrices for transformations in Maths Methods) without formally including the study of matrices in the syllabus.

Ditto for systems of linear equations.

The use of matrices is sprinkled throughout both Methods and Specialist and yet matrices are not included as a topic in the Study Design. Matrices should be formally included in Maths Methods and ‘systems of linear equations’ should also be moved to Maths Methods.

And how can proof include matrices in Area of Study 1 when matrices as a topic is not included in the Study Design?

The random use of matrices in Methods and Specialist is fucked.

A major change has been the introduction of Foundation Mathematics, Units 1-4.

Victorian students now have the choice of four mathematics subjects: Specialist Mathematics, Mathematical Methods, General Mathematics, and Foundation Mathematics.

General Mathematics seems to have replaced Further Mathematics.

With the abolition of VCAL, I imagine that Foundation Mathematics replaces Numeracy which was in VCAL.

Numeracy in VCAL was enjoyable to teach because there was no specified syllabus, just broad guidelines of what the teacher should be trying to achieve. A teacher had a great deal of freedom to be imaginative and creative. It seems likely that Foundation Mathematics will be as dominated by a final examination as are the other mathematics subjects. The baby has been thrown out …

As we have an Australian Curriculum, and the new Victorian Curriculum looks more like the new proposed curriculum for NSW, why don’t we just combine the curriculum for NSW with that of Victoria and have one set of examinations?

Because NSW has standards, and because NSW knows that everything VCAA touches turns to shit.

It all looks pretty ordinary and what you’d expect; the changes are relatively minor and perhaps will make for a better all-round syllabus. But as we know all too well, any syllabus can be ruined by poor teaching, uninspired textbooks, and loathsome assessments. The VCAA seem excellent at making the teaching and assessing as woeful as possible, as we have seen far too many times. I’ll not be holding my breath for a sudden increase in mathematical excellence and excitement in Victorian schools.

I completely agree. Confining my opinion to Specialist, here are my main concerns:

1. The SACs of shit still exist AND have been given more weighting. I don’t think you’ll find more than a handful of teachers that think this is good. Good job, VCAA – Let’s make sure students are non-stop stressed the entire year.

2. There is too much to get through in 10 months or less, particularly since:

a) there is an expectation that revision starts at least a week or two before Term 3 ends.

b) everything in Specialist 1&2 is examinable and therefore must be revised and consolidated.

3. The lack of detail. To give you an idea of what’s missing in the proposed Stupid Design, look at what it says for Logic and proof. Then read the attachment (it’s the last section of the study design equivalent from the late 80’s when it was VCAB not VCAA – a classic case of when the B-team did it much better than the A-team …) Note also the amount of time suggested … for Logic and proof in this curriculum document.

Imagine how much more clarity and certainty teachers and students would have if the muppets who wrote the proposed Stupid Design did their job properly and modelled it along the lines of the attached VCAB document. I think VCAA has a vested interest in keeping the Stupid Design as vague as possible. Plus, VCAA is just too lazy and too dumb to do the job properly.

The proposed Stupid Design, like its predecessors, reads as if written by muppets who don’t have to teach from it. The end of 2022 will be a good time to retire for many teachers – that exodus of experience will not be easily replaced and will further exacerbate the shortage of specialist teachers of mathematics.

*Ahem* Here’s the attachment.

VCAB Mathematics A and B – Accrediation 1986-190 – Part 3

And here’s the 2021 SACE ‘Study Design’ – I really like how the right hand column provides examples and clarification. This is the sort of model that VCAA should be forced by over-whelming feedback to adopt. It’s not perfect but it provides much clearer instruction and advice to teachers than the currently proposed Stupid Design.

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

OK… does anyone else feel this is a bit contradictory?

Page 6: “Study of Specialist Mathematics Units 3&4 assumes concurrent study or previous completion of Mathematical Methods Units 3&4.” Then in the table, line 5 suggests Mathematical Methods Units 1 and 2 can be followed by Mathematical Methods Units 3&4 with Specialist Mathematics Units 3&4.

BUT… Page 107: “Specialist Mathematics Units 3&4 assumed familiarity with the key knowledge and skills from Mathematical Methods Units 1&2; the key knowledge and skills from Specialist Mathematics Units 1&2 and concurrent study or previous completion of Mathematical Methods Units 3&4.”

So… a student does not have to study Specialist Units 1&2 but can be examined on the material in it???

Re: So… a student does not have to study Specialist Units 1&2 but can be examined on the material in it???

Yes.

At my school we sometimes have a student going into Yr 12 who has not done Specialist Units 1&2 but wants to do Specialist Units 3&4. We do not allow this unless the student has achieved excellent academic results in all of his/her subjects (not just Maths Methods). It is then made crystal clear the topics from Specialist Units 1&2 that the student must study before Term 1 of the next year starts. The enrolment in Specialist is then provisional on the results of his/her first assessment at the start of Term 1 (a result of at least 70% is required).

Such exceptional students exist but are rare. But it will be much harder to allow students to do this from 2023 because they will have to know *everything* from Specialist Units 1&2 as opposed to a handful of key ‘cherry-picked’ topics.

By the way, I’m assuming the new Stupid Design will be rolled out incrementally, either starting with

1) Units 1&2 in 2022 and then Units 3&4 in 2023, or

2) Units 1&2 in 2023 and then Units 3&3 in 2024.

The idiotic and therefore most likely scenario will be for VCAA to roll out all units in 2023, which would make an exam that can include ANY of the Specialist 1&2 pretty unfair … (and forces teachers to roll out Units 1&2 in 2022 anyway). There has been no clarity on any of this. Again, because the proposed Stupid Design reads like it has been written by muppets who won’t be teaching from it and therefore haven’t even thought of this.

My reading is that it all starts in January 2023 (as it says on page 4).

Units 1 to 4. Same time. Just like 2016.

Yes. That lack of common sense makes perfect sense coming from VCAA. They don’t give a flying f$c% about the schmucks in the trenches who have to actually make this shit operational.

I’ve read and re-read the document over the last couple of days (because sitting in a room to “supervise” during my spare time is apparently a really good use of resources…) and the more I read it the more I come to the same conclusions:

1. There is actually some good Mathematics in this study design.

2. That doesn’t matter because the curriculum is more crowded than ever, very few current teachers of the subjects will be able to transition straight to this new curriculum without a lot of work (networks, Boolean logic, statistics) and will probably learn to survive as best they can, however that works.

3. Why the hell are internal assessments still a thing???

4. And now at Year 11 as well!?!

5. Seriously… introducing Units 1 to 4 in the same year… did they not learn from the monumental train-wreck that was 2016?

RF, your assessment of the Stupid Design is perfect. Regarding 5 and “did they not learn”: Even if VCAA *did* learn (and it probably did), it does not care. Until the consequences of VCAA’s decisions directly hurts VCAA, VCAA will continue to not care.

There are some ideas in this proposed curriculum for Victoria that are related to the recent more general proposal for NSW:

https://research.acer.edu.au/cgi/viewcontent.cgi?article=1005&context=nswcurriculumreview

Is there any reason why NSW, or anyone, should be listening to ACER clowns?

And as a final twist in the tail… if Boolean algebra is introduced into SM34 and IF SM34 students who used Mathematica for their Methods exams are allowed to use it for SM34, then there is a major issue with what I assume will be a common multiple choice type question (simplifying expressions) as Mathematica has the in-built (no need for special code to be written) command BooleanMinimize amongst others.

I haven’t got a Casio or HP to check if they have something similar (but somehow I doubt it).

Reading back over those “discussion papers” Marty posted a while ago from VCAA and Wolfram, it just feels like thumbs are being put on the scales like never before!

RF, you are quite right. But no-one at VCAA has the brains or the inclination to be concerned about “thumbs are being put on the scales like never before!” It is also more likely than not that Mathematica will now continue indefinitely in schools that already support it – so this issue is not going away any time soon. (For those who came in late: Mathematica is being rolled back and the licensing agreement expires on Dec 31 of this year. Mathematica will only be used in schools that are currently using it)

On another note, as some of you will have seen, NESA has recently released its marking guidelines for all NSW 2020 mathematics exams. I know it keeps being said, but it can never be said too often:

It is a total disgrace that:

1) VCAA don’t publish its marking guidelines.

2) VCAA don’t publish its examination reports until many teachers have died of old age.

There will be a reckoning one day … Here’s hoping a new broom starts sweeping in 2021.

You forgot point (3): the examination reports are regularly flawed, giving no indication about how critical questions were marked, nor what was done with questions that clearly contained (one or more) errors.

The critic in me says that the reports are bad and released late so that a particular organization can make money selling worked solutions and tickets to “meet the assessors”. All of which are less useful than a bucket of warm piss.

RF, don’t look for conspiracy when incompetence is sufficient explanation.

RF, you’re right again on all counts – except on how useless meet the stooges is. Even a bucket of warm piss can be useful (don’t ask!) Try less useful than a paper-mâché bomb shelter or an inflatable dartboard …

Indeed, 3) is a big problem. The issue of questions clearly containing errors is directly related to 1):

a) VCAA has *never* directly admitted its mistakes – the evidence clearly shows that VCAA resorts to half-truths and gobbledygook at best and lies at worst in its attempts to keep its mistakes covered up.

b) How critical questions get marked probably changes from year to year, so VCAA doesn’t want to set any inconvenient precedents (which would provide a degree of certainty to students and teachers). This would also explain VCAA’s steadfast refusal over the years to include *detail* in its Mathematics Study Designs (the current draft continues this trend).

All of which means that VCAA will never willingly publish its marking guidelines ( we have to rely on what blows into a face on a windy day) or publish an honest examination report.

Meeting the VCAA stooges is a very big money earner (the biggest in fact, from what I hear) for a particular organisation. So given the cosy relationship VCAA has with a particular organisation, it is *very* likely that the Report gets delayed for exactly that reason.

In the Department, people don’t get sacked for incompetence. They get put in a ‘black taxi’ and transferred to where they can cause even more damage. So things could be worse. We could all be History teachers …

It’s a great pity that VCAA is not required to hold an AGM of the shareholders (teachers) each year where the VCAA subject managers face the shareholders (teachers) and explain themselves. Then we’d see a huge improvement in governance.

It was once remarked that a US presidential candidate’s choice of running mate mattered about as much as a bucket of warm piss – I liked the phrase and so have borrowed it.

And yes, Marty, incompetence is an excellent explanation in that it explains almost all the observable phenomena, but (without a hint of conspiracy, so ignoring the money-trail for now) I somehow suspect there is a bit more to it.

But I may be looking for the proverbial black cat in a dark room again.

RF, I’m with you. I am certain there’s more to it than simple incompetence. I’m sure laziness plays a big part. And I’m certain the cosy relationship with VCAA plays a big part – it’s not a black cat in a dark room, it’s a pink elephant in a well lit room.

PS: I believe it was John Nance Garner that said this soon after he accepted the 1932 vice presidential nomination. And there’s some confusion about whether he said “piss” or “spit”. (If the latter, I’ll most certainly agree with you on that too).

It may well have been spit or even swill. In this context I think piss is a much better noun.

Well, I wasn’t playing fair. VCAA and MAV are “conspiratorial” in the exact same manner as the Liberals and Murdoch’s propaganda merchants. It’s not conspiracy if it’s open and admitted. But, I don’t think the blatant VCAA-MAV incestuousness is needed to explain the farcical delay in receiving the the VCAA examination reports. The ineptness and arrogance and dishonesty, on the other hand …

An ex-colleague of mine who used to work for the ABC showed me a fun game to play with the Murdoch or Murdoch-sympathizing newspapers:

Read any political article out loud, but whenever the article mentions “The Economy”, instead you say “Rich People’s Yacht Money”.

I wonder what similar games we could play with VCAA draft study designs… (genuinely think this could provide some moments of fun in what is otherwise a very depressing document)