This is not one we’ve had time to look at but it seems important. We don’t intend to comment but we’re providing this post as a forum for discussion.

In November last year, VCAA released its draft of the new mathematics study design, to begin in 2023. The draft is no longer linked on VCAA’s website, but we wrote about the draft here, here and here. The current study design, ostensibly in operation until the end of 2022, is here.

Given Covid, and anyway, more than a few teachers have expressed concern at the timing and the speed of the implementation of the new study design. In particular, it seems that many teachers consider the simultaneous implementation of the new Year 11 and Year 12 syllabi to be unnecessary and unwise. In early August, a network of Heads of maths submitted a joint letter to the VCAA expressing such concerns. VCAA responded to that letter a couple weeks later. At the time, we publicly stated our view of VCAA’s response, but we’ll hold off for now. Both letters are embedded below.

It has now been brought to our attention that, as flagged in the VCAA response to the Heads, VCAA has issued “advice” on the implementation of changes for Year 11 in 2022, in preparation for the not-yet-existent 2023 study design. That advice can be viewed here (Word) on this page, and the advice is embedded below.

That’s it. We’ll be interested to read what people think. Standard rules apply: play the ball, not the man.

**VCAA’s Implementation Advice for 2022 (original here)**

**Letter From Heads of Maths Network to VCAA (early August)**

**UPDATE (23/11/21) Angela Kotsiras, who coordinates the HoMN, has requested I take down this letter. She gave no reason for wanting the letter to be removed, simply noting that I had not been “given approval to do this”. This makes absolutely no sense to me, on any level, but I have obliged.**

**Reply From VCAA to Heads of Maths Network (late August)**

**UPDATE (06/01/22)**

On another post, John Friend has commented on VCAA’s “Advice” in the light of Cambridge’s Specialist 12 text. In the current study design, which *officially* applies to 2022, the Specialist 12 topics *Logic and algebra* and *Graph theory* are optional (pp 44-46). Presumably on the basis of that optionalness, and the strategic preference of most teachers to skip these topics, Cambridge made the decision to *not* include these topics in the print edition. As far as we are aware, Cambridge’s *Logic* chapter is currently *only* available through the online platform Cambridge Go, and the graph theory material is seemingly unavailable anywhere, although we understand the material exists. (**06/01/22 **– see the further update, below.) In any case, for various reasons many teachers and students will not have access to Cambridge Go, and thus will not have access to Cambridge material on either topic.

That is a big problem.

Through VCAA’s ineptness and pigheadedness, there is absolutely no sense in which *Logic and algebra* and *Graph theory* are optional for Specialist 12 in 2022. But, *many* teachers and students will not have access to the corresponding chapters of the vastly most popular textbook.* One can argue who is responsible for this screw up, but it is unarguably a screw up.

Of course if Cambridge gave a stuff about their customers they would now make their material on the “optional” topics freely available; we’ll see. And, of course, VCAA doesn’t give a stuff about anyone. Meanwhile, everyone can wait for the Heads of Mathematics Network to spring into inaction.

*) And deservedly most popular, since the Cambridge text is second rate, while the alternatives are fifth rate.

**UPDATE (06/01/22)**

According to John Friend, the graph theory chapter* is* available on Cambridge Go, although this is not indicated on the textbook website. Also, John indicates that the all of the alternative, fifth rate texts include chapters on the optional content.

**UPDATE (13/01/22)**

In a comment below, Red Five has attached his *Boolean Logic Summary ***(****15/01/22 – corrected version). **And, in another comment, John Friend has provided his pretty detailed thoughts about Specialist 12 in the light of VCAA’s new and not-yet-existent study design. (Idiots …)

We’re more than happy to highlight and attach other notes and thoughts, from anyone who wishes to share.

Let me see if I’ve got this right.

Teachers at the coalface: “students have had lengthy and severe disruptions to their learning, and are not nearly as prepared as they normally would be for VCE maths, and it is not feasible to catch them up in one year. This creates additional pressure / burdens on teachers to support these students, and it’s not feasible for teachers to do this in addition to doing the curriculum and professional development required to running the new courses effectively.”

VCAA: “Nah she’ll be right. PS here’s three sentences on how you can adjust the current study design to prepare for the new one”.

I just had a very superficial skim, and I might be reading this wrong, but (in addition to what SRK’s objected to) are they cutting out differentiation from first principles in Methods???

And restricting differentiation to just polynomials in Methods 1&2??

That is my reading of the “advice to teachers”.

Whether that is 2022-specific advice is not something we can know for sure.

I wonder if they will next declare we don’t need to teach the concept of a limit… if so, can they test “smooth join” of hybrid functions, as has been quite commonplace…?

Time, one hopes, will tell.

“And restricting differentiation to just polynomials in Methods 1&2??”

I believe this is how most schools already teach, as the Cambridge textbook only has calculus on polynomials in methods 1 & 2.

Ah ok! I must’ve been misremembering from my own experience, or maybe my teacher introduced more functions earlier.

From a student’s perspective I just think it’s better to introduce some more elementary function’s derivatives earlier on so students have more familiarity come 3&4.

Interesting…

I wonder if the use of matrices for transformations will be ommited for the entirety of the Mathematical Methods course, or just unit 1?

Hopefully. At this point having matrices in Mathematical Methods is pretty useless, as they’ve gotten rid of stochastic matrices and the only matrices used for transformations are “translation matrices” (basically equivalent to the adding of a vector, not the actual matrix used for translation), and dilation matrices, which don’t serve any real purpose in the course other than as an extra meaningless trick.

True.

What’s more interesting is the decision to omit first principles but add numerical approximations? 😅

I don’t understand why they would remove the concept that kinda serves the best way to introduce calculus to students.

Agreed! Learning about limits and continuity and understanding differentiation from first principles was a highlight of learning calculus for me.

I struggle to see how you could possibly motivate an actual understanding of differentiation without utilising limits and first principles. Otherwise it just becomes (even more so than currently) a bunch of meaningless rules and algebra.

I mean, you’d think the name “First principles” would’ve, you know, been suggestive of something…

If anybody is curious, I found the VCE 2023 draft study design (saved it to my laptop before it was removed by VCAA website)

2023VCEMathematicsStudyDesignConsultationDraft (1)

Here’s how I see it:

1) VCAA has pig-headedly refused to say that implementing the new Stupid Design for all four units in the same year is a bad decision.

2) Not withstanding 1), VCAA DOES know that common sense demands a formal staged implementation. But it refuses to admit it. Instead, it IS implementing the new Stupid Design in stages BY STEALTH AND DECEIT. The advice VCAA has given is advice on implementing Units 1 – 2 in 2022.

3) The new Stupid Design IS being implemented in stages, by stealth and deceit.

AND without the benefit of teachers actually seeing the new Stupid Design. Teachers must take VCAA’s word on what changes to make to Units 1-2 in 2022. Teachers would be idiots to believe what VCAA says. The things that VCAA is telling schools to omit are things that will probably be in Units 3-4. Does anyone believe, for example, that, under the new Stupid Design, the following will NOT be in the Units 3-4 Maths Methods sillibus:

a) Using matrices for transformations.

b) Differentiation from first principles.

Does anyone want to teach these things FOR THE FIRST TIME in Units 3-4 Methods?

Take a leap of faith with VCAA? I don’t think so.

VCAA has been dishonest, deceitful, hard-headed and incompetent. It is more interested in saving face by sticking with a poor plan than doing the right thing. It is treating teachers with contempt. It has treated the Head of Maths Network (HoMN) with total contempt (unfortunately the obsequious tone of the HoMN letter all but ensured this). The Maths Mangler is dead, long live the Maths Mangler.

I don’t know what can be done. Maybe an open letter calling out VCAA on its reprehensible attitude. A bit of media attention won’t hurt either. The MAV should be a focal point for all maths teachers and condemn the current implementation plan. It should strongly support the HoMN letter. But this won’t happen because the MAV is a lapdog for the VCAA. Maybe the HoMN can put on its bovver boy boots (if they fit) and be a lightening rod for all VCE teachers.

The only reasonable action VCAA can take is to admit that its current implementation plan of the new Stupid Design is NOT in the best interests of students and teachers, and to change it to a staged implementation: Units 1-2 in 2023 and Units 3-4 in 2024. This can easily be done without losing face, and in fact, I think VCAA would gain a lot of respect from teachers for doing this.

PS – I found the VCAA’s response to the letter from the HoMN patronising, arrogant and contemptible. The statement

“Stakeholders have been consulted extensively throughout the process and have provided overwhelmingly positive feedback through the public consultation process for its 2023 implementation.”

is laughable. VCAA is clearly either deluding itself or is trying to stooge teachers into thinking that support for the new Foundation Maths subject means support for all of the Stupid Design. And as for the statement

“Figures for Mathematics studies in 2021, including the ‘more demanding’ studies, do not support the thinking that ‘a higher proportion of students are opting out of the more challenging Maths studies’.

Perhaps VCAA can release the enrolment figures over the last 15 years for Specialist Maths and Maths Methods to prove how woefully wrong we all are in thinking otherwise. Here is some recent enrolment data (courtesy of VCAA) for enrolments in Specialist Mathematics:

2022: ?

2021: ?

2020: 4,128

2019: 4,232

2018: 4, 389

2017: 4, 532

I asked them if, out of curiousity, is the content omited from unit 1 and 2 omited from methods or just rearranged and he replied:

My apologies, but any other specific information linked to Unit 3 and 4 must wait until the Study design is published in early 2022.

Is it really that confidential and hard to release the unit 3 and 4 study design, they had ages to publish it. they want to publish it in late feb.

Who was “them”?

Kevin, the curriculum manager guy

Of course. The Acting Mathematics Mangler.

The position of Mathematics Mangler is being RE-advertised:

https://careers.vic.gov.au/job/mathematics-manager-570165

RE-advertised … Either no-one competent and honest was interested first time around (and why would they), or such people DID apply but VCAA does not want people with such attributes.

Interestingly, it includes the following statement:

“The Ongoing Mathematics Curriculum Manager role provides the incumbent with exciting opportunities to proactively provide support to teachers across the three schooling sectors and to stakeholders on a statewide basis.”

More VCAA lies. Because I would have thought an answer to Allan’s question was of vital importance in supporting teachers.

It was approved by the VRQA at least 3 weeks ago (from 16/11/2021). So I don’t see any impediment to it being published now. It’s just another power trip by VCAA.

Very good point/question.

The number of students enrolled in SM4 is decreasing; the number of students enrolled in MM4 appears to be on a downward trend since 2018; the number of students enrolled in FM4 is increasing steadily, as is the number of students enrolled in FDN2.

What’s your point?

Just adding some information about enrolments because both letters raised this matter, although I thought that they could have been more specific.

Additional data:

2006: 5300

2000: 5856

Enrolments in Specialist Mathematics over the last 20 years have steadily declined from 5,856 in 2000 to to 4,128 in 2020. A 30% decrease by my calculations. But according to VCAA

“Figures for Mathematics studies in 2021, including the ‘more demanding’ studies, do not support the thinking that ‘a higher proportion of students are opting out of the more challenging Maths studies’.

Liar! Liar! Pants on fire!

And if VCAA lies about things that are very easily checked, I can only imagine the lies it’s told and telling about things that are less easily checked.

To be fair, this trend is likely because universities stopped requiring specialist maths as a prerequisite for engineering and other courses. The 2010 figures are not too dissimilar to the 2019 figures.

I expect that the trends will be exacerbated by some universities no longer requiring Methods for engineering; e.g. “Units 3 and 4: a study score of at least 20 in any Mathematics”.

I don’t know if you’re being serious or not with that remark.

So, I will pretend you are.

Universities will not accept a student into Engineering with a study score of 20 in Foundation Mathematics.

They may well accept them into a bridging course during which they teach some rigorous applied Mathematics and decide for themselves if a student can progress to an Engineering degree, but beyond that…

The scores they allow for entry into teaching degrees (undergraduate, not postgraduate) are perhaps more telling. You want students to graduate primary school knowing times-tables? Make sure the teachers leaving university as primary teachers know them first.

Foundation Mathematics is not a Unit 3 or 4 subject – yet. The quote – and it is a quote from a university website – “Units 3 and 4: a study score of at least 20 in any Mathematics” is referring to SM, MM, and FM. It will be interesting to see what happens when Foundation Mathematics 3 and 4 come on board in 2022.

The position gets more confusing as the University of Melbourne seems to offer engineering only as a post-graduate degree.

As for u/g teaching degrees, one university website describes the prerequisites as “Units 1 and 2: satisfactory completion in one of Maths: General Mathematics, Maths: Mathematical Methods or Maths: Specialist Mathematics or Units 3 and 4: any Mathematics” – and we all know what “satisfactory completion” means.

I think it’s serious. I think they are pre-requisites for engineering at RMIT. But it looks like it depends on the type of engineering.

I can see that the Bachelor of Science (Applied Mathematics and Statistics) at RMIT requires a study score of at least 20 in one of Maths: Mathematical Methods or Maths: Specialist Mathematics.

It’s hard to see for sure, but it seems genuine. Maybe Terry can post a link.

However, although I usually like a rambling blog that goes where the wind blows, I think what this blog has alerted us to is too important to get distracted by side issues like university entry requirements. What the universities have done with regards to entry requirements – in the pursuit of money – is a disgrace and worthy of its own separate blog.

Perhaps it is relevant, perhaps it isn’t, but I’ve been busy lately looking at UK A-Level Mathematics exams from the various examination boards as well as different states here in Oz.

Whilst the top level Mathematics subject seems to have a lot of common areas, the way in which things are examined is really, really different.

I wonder if the decline in enrolments is Australia-wide, or perhaps VCE and its way of examining is part of the issue.

For a national perspective, see

I don’t know what happened to the link, so I will try a different approach:

Wienk, M., & O’Connor, M. (2020). Year 12 participation in intermediate and higher mathematics remains stubbornly low. AMSI

I have worked in statistical forecasting for many years, and it is pretty clear which way the wind is blowing. There are issues with comparing states. We can’t even agree on the railway gauge.

Huh … The same Michael O’Connor as the President of the MAV.

Anyway, I find it the height of either arrogance, stupidity or both that VCAA’s response to the HoMN letter would contain such an obvious falsehood.

As I wondered earlier, I wonder how many falsehoods VCAA say.

In addition to John’s valuable opinions, a small summary pdf with some data (most should be accurate) for readers to ponder.

Data_Analysis_Specmath_VCE_enrol_trend

And here is a pdf version.

Data_Analysis_Specmath_VCE_enrol_trend

I’m curious about the ‘Stakeholders have been consulted extensively throughout the process and have provided overwhelmingly positive feedback’. Where is this positive feedback coming from? In the MAV session I went to Specialist Maths teachers were universally opposed to the changes to the study design with the removal of dynamics and introduction of proof. I’m genuinely curious – is this a change endorsed by the tertiary sector? industry? Where is the push for change coming from and why? I love dynamics – the way it brings together vectors, kinematics and calculus so that’s just personal preference.

I was temporarily happy that matrices had gone from Methods until I realised they’ve moved to Specialist 1/2. I’m really apprehensive about the Proof in Units 3/4 since apparently students can be asked for proof across any topic from Units 1-4 – so Combinatorics, Sequences and Series, Networks, Matrices etc – none of this is in Unit 3/4 so we wont have time to teach it but students need to remember if from Yr 11 to the extent that they can complete proofs in these areas. I think that’s a pretty big ask.

They also have not fixed the perennial problem that if you teach 3/4 Specialist in a school that does not have the timetable structure to offer advanced Methods, all our students are doing 3/4 Methods and Specialist in the same year and we need our students to have working knowledge of Methods calculus before they get to it in Methods. We have always done a calculus unit in 1/2 Spec even though it is not in the study design because we can’t function without it. I don’t understand why the Unit 1/2 preparation for what is (or was) largely a calculus course contains no calculus.

From what I understand, Specialist 1&2 is a subject struggling for identity. I love to teach it because of the flexibility, but in a number of schools it is (again, to my knowledge) often combined either with Year 11 Further (General) Mathematics (in which calculus is just not going to happen) or (much, much worse in my opinion) Specialist 3&4 in which case calculus will be taught whether it is in the course or not.

I’ve always put a calculus topic in Specialist 1&2 for what it is worth.

I will admit that I like Boolean algebra as a topic for students to explore, perhaps in an investigation task. To make it an examinable topic though…? Similar feelings about examining proof. I can’t see it being done on Paper 2 exams which means it will either be trivial or rushed.

Your last comment is key. It simply doesn’t matter what the new study design if the consequent exams are implemented in the same incompetent and anti-mathematical manner that is currently practised. As they will be.

Nothing matters until the culture and the (lack of) competence of VCAA changes. That will not happen until sufficiently many knowledgable and intelligent teachers complain sufficiently loudly. And that will happen never. Teachers either do not know about or do not care about the current awfulness. Mostly both. Teachers are the victims but they are also the insurmountable problem.

Wild guess: how many is “sufficiently many”?

I sense that after the most recent exam period, the ground may be fertile for recruiting to your cause.

Your sense is wrong. (Which doesn’t mean I don’t think any and all teachers should be complaining, high up, at the top of their voices.)

VCAA’s letter to the heads was perhaps a bit of a dampener on the enthusiasm of many to complain. It took a fair bit of negotiating and agreeing on wording (from what I am told) and for it all to be so casually brushed aside is…

…disheartening?

…unnerving?

…soul crushing?

(This isn’t multiple choice)

I have never needed a group with which to complain, and I have never paid attention to being brushed off. But of course, I’m Marty. I can do these things because … why, exactly? Why is it any different for me?

Every teacher has every right to yell at McMenamin and/or Chandler and/or their superiors. If they do not, that is their choice, but they then have no right to whine.

If I had to guess, group 1 would be the majority.

Group 2 is an interesting one. Scared of whom? Sometimes it is their HoD, sometimes it is school management and, often enough (I have limited experience, but more than zero) the fear is warranted. Teacher makes noise, teacher loses Year 12 class mid-way through the year.

Group 3 can deal with themselves.

I know that VCAA dislikes teachers who rock the boat. I know of teachers that have complained to VCAA and where VCAA has subsequently sent a letter to that teachers Principal, objecting to the complaints.

So it’s a legitimate fear. Even when your Principal is a good guy who supports you and will stand up for what’s right. And certainly when you know your Principal won’t support you. It will be a sufficient deterrent to most young teachers. And teachers who are on fixed term contracts. VCAA counts on this. Like any dictator, VCAA is a bully that’s long overdue for getting a (metaphoric) blood nose.

One can complain to VCAA in a manner that is polite but still firm. (So I’ve heard.)

I’ve heard the same. But I’ve also heard that it doesn’t always work. For example, the previous Mathematics Mangler always turned a deaf ear, pretended to misunderstand the complaint, treated the complainent like a fool.

I’ve heard that complaints made higher up the food chain often work. But I get the feeling – from what I’ve heard – that VCAA unofficially gives each teacher a quota (Q) of complaints. Once Q is exceeded, things become a bit … testy. Frosty. Which is a problem, because VCAA make a huge number of mistakes (X) and there are only a small number of teachers (Y) who are willing to complain about those mistakes. And X/Y >> Q.

I’m sure maths teachers can figure out what needs to happen. (IF they want a positive change in the culture at VCAA).

RF, I think you are correct, and I think it is why, in the right hands, S12 has been a (uniquely) good subject. Teachers with the mathematical sense to do the topics well, and the courage to ignore the nonsense of S34 to come, can do great stuff there. The VCAA changes will kill that.

Maybe not. Unless VCAA starts actively auditing unit 1&2 studies the way they do Unit 3&4 SACs, there will hopefully remain enough wriggle room for careful and forward-thinking teachers to make the following argument within their own schools:

1. Find what is essential for Units 3&4 and plan that into our Units 1&2 course.

2. Ignore for now everything else in the Units 1&2 course description.

3. Find ideas from around the world that fit nicely enough into part (1) to make a decent course in Mathematics: reasoning, abstraction, generalisation (proof, of course).

4. Repeat as steps 1 – 3 if and when anything significant changes at Units 3&4 level.

It wouldn’t surprise me if VCAA did to audit Units 1 – 2 studies. Under the euphemism of ‘providing support to teachers’.

My interpretation of the vague threat that any topic from Unit 1&2 can turn up on the 3&4 exam under the topic of proof is that that is the stick to make us actually follow the Unit 1&2 study design….

Hi Amber.

Re: “‘Stakeholders have been consulted extensively throughout the process and have provided overwhelmingly positive feedback’. Where is this positive feedback coming from?”

It has come from nowhere because it is a LIE.

VCAA’s response to the HoMN letter contains many lies and empty rhetoric. The response is dishonest and patronising. It treats us all like idiots. It is a total disgrace. As Marty said below:

“Nothing matters until the culture and the (lack of) competence of VCAA changes. That will not happen until sufficiently many knowledgable and intelligent teachers complain sufficiently loudly.”

What is needed is for teachers to deluge VCAA with emails and phone calls of complaint.

The killing of dynamics is educational vandalism. Anybody who signed off on this is a bona fide idiot.

I couldn’t have said this better myself.

Why, oh why, do they have to butcher Specialist Maths this way?

I’m sure there’s some apt Chinese proverb, about a mathematician carrying a scorpion across the river, or something like that.

Marty, you might be thinking of this:

https://en.wikipedia.org/wiki/The_Scorpion_and_the_Frog

Then again … Man who pushes piano down mineshaft get tone of A flat miner.

At least it seems to be getting some media attention:

https://www.theage.com.au/national/victoria/top-teachers-alarmed-by-drop-in-secondary-students-maths-skills-20211122-p59axo.html

Well done to the Head of Maths Network for trying to get some media attention on this issue. Now put on the other boot and start rattling the cage.

Interesting. Adam Carey is not a lightweight. I’m not sure how much faith I’d be putting in The Age’s Education wing.

Faith is not required. Media attention is.

What I found most interesting were the responses from the MAV and the Govt spokesperson. Both used strawman ‘arguments’ against the Heads of Maths network. Who would you believe: 260 Heads of Departments plus hundreds of teachers or the MAV and the VCAA trying to suggest otherwise.

Yes, it was reassuring to see Peter Saffin support teachers to the extent that he did.

Yes, you can depend on the MAV, under its current leadership, to be a VCAA mouthpiece.

Perish the thought that it would provide unequivocal support for 260 Heads of Mathematics plus hundreds of classroom teachers. It’s a shame that comments on the article are not enabled – I’m sure the comments from the MAV and the Govt spokesperson would soon be exposed as spurious.

Sarcasm?

Maybe recall the meaning of “reassure”.

At the request of the HoMN coordinator, I have removed the letter from HoMN to the VCAA. As I wrote in the update, nothing about this makes any sense to me whatsoever.

By my estimation, all 260 Heads of Maths will/should have a copy of that letter. And most Heads of Maths will have consulted with the VCE teachers of their department. And many Heads will have made the letter available to those teachers for comment etc. So I’d estimate that thousands of teachers have a copy of this letter. I’m not aware of any particular secrecy or confidentiality surrounding the letter. It may as well be an open letter to VCAA. So any efforts to keep the letter secret, or to claim retrospectively that the letter was secret, should be greeted with an eye roll and a snort of derision.

Question: What’s the best way of ensuring that something is made public.

Answer: Publicly attempt to prevent it being made public.

This letter is everywhere!

On another note, people wonder how and why VCAA gets away with all its mistakes … Look inwards, folks.

And for the record … I retract my congratulations Re:

“Well done to the Head of Maths Network for trying to get some media attention on this issue. Now put on the other boot and start rattling the cage.”

I thought it seemed strangely out of character that the HoMN would take some initiative and make the issue known to the wider community. But the issue was important … Sadly, no boots after all, just soft fluffy slippers.

Fetch the comfy chair!

(With half-hearted apologies to anyone who is not a fan of Monty Python)

Fetch the comfy chair!

(With half-hearted apologies to anyone who is not a fan of Monty Python)

Marty, thanks for this second update! I think it’s a very important update. It alerts us to a big problem that is an unexpected consequence of VCAA’s pig-headedness in the face of stupidity.

It’s likely to be one several unanticipated negative consequences that will only manifest once teachers return and the reality of preparing and teaching Units 1&2 with an eye on what’s required for Units 3&4 in 2023 starts to bite. (Of course, VCAA doesn’t give a flying Philadelphian apt about the problems and difficulties its stupidity and pig-headness will cause teachers).

And it’s a blind eye. For an indeterminant amount of time. Because VCAA in it’s wisdom has chosen to NOT disclose the new (and approved by the VRQA) Stupid Design for the time being. When it finally disclosed, teachers will by then be time-poor once more (unlike during the Term 4 break) and will potentially also be contending with other problems (including the fallout of the last two years).

A couple of updates to your update:

1) Apparently some schools specifically booklist Cambridge Go ($20) (with a footnote). I think this is done in order for students to access the extra ‘resources’ rather than access otherwise unavailable chapters needed to actually form a complete textbook that is fit for purpose.

2) I’ve been told by a reliable source that the Graph Theory topic actually IS available on Cambridge Go. But this is NOT apparent from the Contents tab at the Cambridge website: https://www.cambridge.edu.au/education/titles/Specialist-Mathematics-VCE-Units-12-print-and-interactive-textbook-powered-by-HOTmaths%3ACambridge-Senior-Mathematics-Australian-Curriculum-VCE/#.YdY-PGhBw2w

3) All the alternatives to the Cambridge textbook have chapters for ALL topics and are therefore a complete textbook. But you’re right, these textbooks are no real competition to Cambridge. Which is very unfortunate.

I’d strongly urge all users of the Cambridge textbook to contact Cambridge and strongly request access to the chapters currently be kept behind a pay-wall. The Cambridge textbook is otherwise NOT fit for purpose in 2022.

Hi John / Marty,

I’m wondering if other Specialist teachers on this blog might be happy to share their course outlines for next year? We tend to be fairly isolated in schools. I’m quite stressed about the new study design – I teach Yr 12 and I’ve met with the Yr 11 teacher and Head of Maths at our school to discuss. We’re struggling to keep in what we think we need, add in what we might need, and not make Spec 1/2 the grueling slog that Methods 1/2 is. We are making a series of judgement calls that may not pay off (eg dropping an algebra topic to free up space meaning I’ll have to teach partial fractions in Yr 12 for the first time). We’ve still got a calculus chapter in (product rule, chain rule, e^x, trig etc) that isn’t and still wont be in the course. We’ve planned Unit 1 and there’s nothing in there that can go, so we’re hoping for more info before Unit 2.

So Unit 1 next year we’re doing Sequences and Series, the Number and Proof chapter from Cambridge, lots of trig (we start with some methods trig to revisit symmetry and introduce radians, then applications of trig sin rule etc, then double and compound angle formulas), and Graphing techniques (ellipses, hyperbolas, reciprocal graphing, modulus function, parametric equations).

We may need to rejig things completely to free up space by following the methods trig chapter but currently we do that second last in the year so at the moment it’s not possible.

So for unit 2 there’s vectors and complex numbers, unfortunately we can drop statics, and up for consideration is calculus, statistics and prob, networks, matrices(???), all the geometry and proof stuff, boolean algebra etc etc. It doesn’t feel like we have enough time to do all that and it’s not clear how much will be required for Yr 12. I know Yr 11 is not just prep for Yr 12 but that’s a lot of new content for Yr 11 students that wont be revisited in Yr 12 at the expense of having them well prepared for the Yr 12 content they will need to learn (calculus! partial fractions!).

I would love to know how other teachers are approaching this is anyone is happy to share.

Thanks,

Amber

Hi, Amber. You mean sharing actual files? I’m more than happy to set up a post for file sharing, both for SM12 and in general, if you think teachers would find benefitt from it.

I don’t need actual files unless that’s easier – just the list of topics that are being included and what schools have decided to leave out.

OK, sure. Then obviously easiest for just any teacher willing to indicate their plans to do in a comment.

FWIW, my thinking is that it’s better to make sure students are well practiced in skills / knowledge that will definitely be required in Units 3&4 (ie. algebra + calculus) rather than trying to rush through everything just to squeeze in a few things that may turn out to be unnecessary (ie. networks, boolean algebra, matrices).

But I think it’d be wise to explain this to your students and also provide them with resources they could use to learn the topics over which you are skipping, if they have that completionist itch.

But like you Amber, I’m also curious how teachers will deal with this, in the absence of any clear and practical guidance from VCAA.

Hi Amber. You’re not alone. We’re all sailing on the VCAA Titanic! And the iceberg is straight ahead.

Here are my thoughts:

1) I strongly agree with most of what SRK says, particularly “that it’s better to make sure students are well practiced in skills / knowledge that will definitely be required in Units 3&4”.

But …

a) I don’t think calculus should be a big deal (more to say below). It gets taught in MM2 and many schools teach the product, quotient and chain rules and their applications in end-of-year ‘Headstart’ programs for MM34. A lot of schools teach the chain rule in MM2. Focus on the algebra, do NOT drop partial fractions. See 3) for my further thoughts on calculus.

b) I think matrices should be taught. There’s a fair bit in SM34 in 2023 (based on the Daft Stupid Design) that uses matrices. You don’t want to be teaching matrices from scratch in 2023. I think the matrices topic lends itself to a bit of classwork and then a structured take-home assignment with references from the textbook.

I’d try to teach matrices vectors, to exploit using the dot product in the definition of matrix multiplication (introducing the representation of vectors as column and row matrices).

c) I think ‘Logic’ and ‘Graph Theory’ should be taught. In class. And then give students a structured take-home assignment.

2) Principles of counting is implied in SM34 (in the context of proof) but is NOT mentioned in the VCAA implementation advice. I’d be looking to add to what gets done in MM12 (so it needs to follow from this) or at least provide ‘extension work’ for students to work on outside of class – another structured take-home assignment with references from the textbook.

3) Calculus … I notice that VCAA do not mention ‘Kinematics’ in its Blunt Implementation. I think that kinematics MUST be taught in SM2. This is where you can BUILD on the calculus done in MM2. Do everything using calculus and the interpretation of x-t and v-t graphs. Forget about the straight-line motion formula for uniform acceleration.

NB: 2) and 3) greatly depend on SM12 sequencing ‘in harmony’ with MM12. It’s crazy teaching things that you ‘need’ in SM12 that get taught later in MM12. This is redundancy that wastes valuable time.

4) Statistics in SM12 is a joke. It is total rubbish. Mickey Mouse.

My advice – DON’T TEACH STATISTICS IN SM12.

All of the SM34 statistics can be taught in 2 weeks without the SM12 crap, PROVIDED that the co-requisite probability and statistics has already been taught in MM4. This is a tricky thing to juggle – another problem we can thank VCAA for (note that none of these VCAA idiots have to actually teach what they dump on us).

Not teaching statistics will free up valuable time for teaching kinematics.

Finally, here’s the hard part – I strongly urge all VCE teachers to maintain regular correspondence with VCAA via telephone and email. Give VCAA plenty of feedback on a regular basis. Let it know how swimmingly well things are going with teaching what it has dumped on us. Make sure you cc the Executive Director of Curriculum and the Mathematics Mangler (assuming an appointment is made and VCAA don’t have to re-re-advertise …) Suggest to your students that they also give feedback.

John,

You are definitely heroic and a legend – singlehandedly saving so many teachers who will be doing the hard yards in SM12 this year (and SM34 too!)

Thanks John! That’s great information and give me lots to think about.

I have suggested before (maybe in a submission or this blog) that statistics could be removed from the Year 11-12 mathematics curriculum entirely and offered as a separate sequence of four subjects. Instead of Foundation Mathematics 1-4 we could have Statistics 1-4. This would make more time available for the remaining material in the mathematics subjects. There are plenty of textbooks, that are quite well written, on areas such as business statistics that could be suitable for the 4 units. Statistics 1-4 might prove to be popular.

It is a no-brainer to remove the statistics from VCE mathematics. Unfortunately, our Glorious Leaders have fewer than no brains.

Our Inglorious Leaders have SFB.

Thanks JF, a couple of follow-up thoughts (it has taken me a while – busy with MM34 stuff):

1. Matrices vectors? Could you not teach matrices first and then vectors as a special case? I like to teach the cross product at SM1&2 which means 3×3 matrix determinants.

2. Agree that logic lends itself nicely to a self-paced investigation of sorts. So does graph theory (networks) and, at a stretch, counting techniques.

3. Could not agree more about the algebra and “harmony with Methods”. Really shouldn’t be that way, but…

4. Yes, yes, yes to kinematics with constant acceleration, SUVAT equations and all that jazz, MUST include a lesson on graphs and ideally, the derivation of the SUVAT equations.

5. Still puzzled as to what (apart from statistics) can be really left out to make room for the new rubbish (ahem, I mean… highly considered and totally worthwhile quality mathematics…) One of the best things about SM1&2 is that you had TIME to explore ideas IN DEPTH as opposed to Methods which is “got it? OK, new idea” type learning.

Hi RF.

1) My main reason for teaching matrices vectors is that it makes matrix multiplication a lot easier to teach and understand (and provides a certain rationale for the rule). So I’d be teaching the cross-product of vectors as an application of the determinant of a matrix. But of course:

a) Using the determinant is simply an efficient heuristic for calculating the cross product, and

b) The cross-product can and should be taught in vectors by defining it and then using , and for calculations (until the heuristic can be taught).

2) Yes, a couple of lessons and a self-paced investigation with appropriate topics (like Logic, Graph Theory, and Counting Methods) ticks a lot of boxes!

4) Are you saying that the ‘SUVAT’ equations should be taught? I’ll show how they arise as special cases of simple DE’s and v-t graphs when the acceleration is constant, but I will not teach them as such. Otherwise:

a) You use time (at least two hours) that could be spent on better things (and time is going to be in very short supply), and

b) Students will want to use them in SM34, which I strongly discourage since they’re not on the course and can only lead to trouble (particularly with weak students).

5) Statistics is the only rubbish I can see in SM12 (and SM34, but that’s another story). The problem is that the rest of the content is good and interesting BUT there’s too bloody much of it!! So it IS going to be a sprint from one idea to the next – just like bloody MM12 – and no time to ENJOY what’s being taught. Not a great way of increasing Specialist Maths enrolments, let alone even maintaining current numbers.

You make a convincing argument…

I suspect a lot of it comes down to what type of student you typically have studying the course.

I’ve never had an issue getting through the SM1&2 curriculum, MM1&2 has been a constant nightmare though.

Mostly due to algebra skills.

Maybe your students haven’t used enough CAS in earlier years. I hear that’s great for skills.

I think most of us have had no trouble getting through the SM12 course – in the past. However, that was then and this is now. Now there’s more content and it’s ALL pre-requisite for SM34. That’s a game changer (for the worse).

Plus:

1) The lack of clarity in the Stupid Design leaves everyone guessing the finer details of the content, so a lot of teachers will probably teach more than is required in the new compulsory topics such as Logic and Graph Theory.

2) Now that Proof is an explicit part of SM34, proof in SM12 will be taught more thoroughly and therefore take longer to teach.

3) How many teachers explicitly taught Counting Methods? I’m guessing not a lot. How many teachers taught over and above what was required for Complex Numbers, Vectors, Trigonometry etc because these topics were explicitly part of the SM34 course? I’m guessing most teachers, and that won’t change.

My gut tells me that teaching SM12 is going to be a sprint from now on.

If I may suggest to make explicit what I think has been implicit in a few comments thus far:

1. Specialist tends to be taught by teachers who have an idea about what they are doing and in many schools, they can be the only Specialist teacher, so to an extent have been allowed to do their own thing, successfully.

2. School leaders who have never taught the subject cannot possibly comprehend just how big the changes are and if a Specialist teacher suddenly appears unable to get through the course it is on the teacher.

3. Specialist 1&2 WAS an amazing subject because the teacher had CHOICES and TIME to make it that way. The course guide did not ensure this, the experience and long preparation hours of the teacher did.

4. Any and all mistakes made by VCAA will be, most likely, assumed by school leaders to be the fault of the teacher and not of the study design/exam setting panel.

5. It is going to be very easy to say “oh, that is because it is a new course, give yourself another year or 2 of it and things should get better…” didn’t happen in 2016, so why should this time be any different?

End Rant.

High five, RF! You’re summary hits the nail on the head. But I’ll make one subpoint:

The conjunction “Specialist tends to be taught by teachers who have an idea about what they are doing and in many schools, they can be the only Specialist teacher”

is not a tautology.

I think there is a significant minority of Specialist teachers who only have a rote-learnt idea of what they’re doing, and most of those only because of diligent preparation (because they are conscious of their short-comings. And there are some in this category who don’t have such self-awareness).

This is particularly true of those who are the only Specialist Maths teacher in their school.

My guess is that many Specialist teachers will essentially be teaching out-of-field with the new content. Many will read the textbook, stay one section ahead of the students and breath a sigh of relief when the topic is finished. Many will attend PD that will create the illusion of understanding. (It’s a dream come true for the snake-oil sellers). Very few will feel comfortable fielding questions from students.

And all this will be happening in a year where teachers will once again be challenged by circumstances and the legacy of 2020 – 2021.

So my guess is that Logic, Graph Theory, Proof etc. will get taught quickly and superficially. They will be taught ‘straight from the textbook’, including the examples. Whether the Stupid Design supports such a treatment is unclear due to its lack of clarifying detail. The best students will develop an understanding of these topics better than their teacher, which will probably create a peer-teaching environment in many classrooms (fostered by the teacher out of the necessity for sheer survival during the topics).

Teachers should be given the time and support to enrol in an on-line micro-course. For example, something from https://www.edx.org/course/subject/math

Melb Uni was running professional development: https://happeningnext.com/event/vce-teacher-pd-day-logic-and-proof-eid4sntk7fc0f1

(closed now but it will probably get repeated). I wonder how much insight Melb Uni has into what VCAA expects?

When I first read the draft, I started trying to re-learn Graph Theory and Boolean algebra/logic.

I will openly admit feeling much more confident with the latter and not because I found it easier. My concerns with introducing a topic at Specialist that has been a favorite in Further is that the examiners will PROBABLY go to great lengths to make the examination questions VERY DIFFERENT.

School leaders (and perhaps some department heads) will just see the two topic names and assume they are the same. The consequences of this could be quite problematic for the Specialist teacher…

For Boolean logic, there is quite a lot of good (and free!) material online from (mostly US) university 1st year courses. AMSI has some graph theory notes which are pretty good as a starting point, but again, UNTIL WE HAVE A CLUE AS TO HOW VCAA PLANS TO ASSESS THIS CONTENT WE ARE ALL GUESSING.

It would appear that the VCAA are now too much for even the mild-mannered RF.

Mild mannered? I have rarely been paid such a complement, so thanks Marty.

Unfortunately, it is not just VCAA, but school leaders who have un-learned the art of staying out of certain teachers’ way and trusting that they will get the job done.

Lockdown actually made things better, temporarily. A lot of the lessons that could have been learned by a lot of people were not and…

…another time, perhaps.

Who said it was a compliment? In any case, I’ve linked the corrected version of your notes in the post update.

Marty, RF said it was a complment …

(Perhaps he meant the negation of what you said …)

(At least one reader got your pun, RF).

Hi RF.

Yes, the AMSI notes are interesting. They were written in 2015 as a “Guide for teachers – Years 11 and 12” in response to the Daft National Curriculum (which seems to have fled during the darkness of night, never to be spoken of again). The notes are copyright “VCAA and University of Melbourne on behalf of AMSI 2015”.

I downloaded the Logic and the Graph Theory notes a few years ago as part of collecting resources to prepare my teaching notes for when the time came (the time never came until now). Both sets of notes had “DRAFT” stamped on the front. The current notes still have “DRAFT” stamped on the front – there’s been no effort made (yet) to edit them into ‘Final draft’ form. The link to these notes is here: https://www.amsi.org.au/ESA_Senior_Years/SeniorTopic7/7_md/SeniorTopic7.html

I found the the Logic notes to be very … ordinary – mainly because of the numerous typographical errors and a lack of real substance and relevance. But I found the Graph Theory notes to be pretty good. Both sets of notes have some really good questions – but the solutions are often … ‘brief’ and you’ll need to write out your own detailed solutions. I’d also suggest scaffolding some of the more interesting (but abstract) Logic questions with some concrete questions.

It’s unclear to me how much of these notes are relevant to the Stupid Design, but that’s the fault of the Stupid Design. Having said this, the Stupid Design has a lot more detail for SM34 Graph Theory than it does for SM12 Logic.

I’m betting that VCAA will superficially re-brand these notes as teacher resources to support the new Stupid Design (box ticked) and expect all us dumb rubes to coo how wonderful VCAA is and how hard it’s worked to help us.

I’m not teaching Specialist this year (was, but got moved late in the piece…) but I am willing to share the planning I got through thus far which includes a fair whack of the Logic topic (since I was going to do this quite early).

If Marty is happy to act as a go-between that might be the best option for now (I like to maintain a small degree of anonymity here as I know some of my colleagues read this blog but don’t know that I also read and comment…)

Aha. I thought you seemed smarter than the average bear with the logic stuff … I’m sorry that you got moved. Screwed over again. Never let good decisions stand in the way of school politics or convenience. I assume you did a fair bit of preparation on your own time … I know this sounds selfish but I’d let the ‘replacement’ do their own prep, I wouldn’t be giving them a free pass with the work you’ve already done. Besides, it will be better for the replacement to do their own prep, they might actually learn something. The cynic in me wonders whether this was done deliberately – get RF to do the prep because he’s competent and reliable, and then hand it all over to some goofy. (Yes, I know. I make House look like a happy optimist).

I can see why the set theory stuff might have concerned you if you were planning teaching logic early. Most of the algebra of sets stuff won’t have been learnt by students. Personally, I plan to teach Logic later in the year, followed by Proof so that – hopefully – the students will have an appropriate understanding of sets by then from Methods. I can see some benefits in doing Logic early in the year, but I decided against this for the above reason.

A lot of the set stuff should get taught in year 10 rather than students spending three weeks playing cards and spinning roulette wheels in a dumb attempt to make learning ‘fun’ by letting students ‘discover’ probability. (I think it also gets back to another conversation we had about poor understanding of probability).

It actually bothers me that SM34 will be relying so heavily on many other teachers doing their job properly. There will be plenty of teachers that don’t understand how what they’re meant to be teaching links to SM34. (Circle geometry and trig of non-right triangles should be getting taught in Yr 10 and reviewed in SM12 but it doesn’t seem to happen. I actually don’t know what they get taught in Yr 10, given what they don’t know coming into SM12 and MM12).

My idea with Specialist 1&2 planning is to try to start with something students are not likely to have seen before.

In some years I’ve started with Matrices, followed by a general Proof topic then Sequences and Series (basically treading water until Methods 1&2 has covered transformations…)

Thought about starting with a multi-part Geometry topic (Circle Theorems, Non Right-angled Triangles etc) but thought it better later in Semester 1.

Semester 2 I like to start with Complex Numbers or Vectors and finish with Mechanics then (wherever possible) a bit of Calculus.

Counting Techniques can pretty much go anywhere there is time (2 weeks is normally more than enough to do it well).

My interest in Logic actually pre-dates the VCAA study design change – I’ve just been generally interested in it all (everyone needs a hobby!) and I think that IF you prepare well and IGNORE THE TEXTBOOK, it is possible to start SM1&2 with Logic. My idea for structuring the topic would be three “lessons” (with each being more than 1 timetabled lesson in length):

1. Introduction, axioms, truth tables, conjunction, disjunction, negation.

2. Binary arithmetic (defining basic operations, re-writing truth tables, simplifying expressions with and without using Lesson 1 axioms), logical equivalence.

3. More complex operations (logical equality, exclusive disjunction, Sheffer stroke, material implication).

And then when I see how (if?) VCAA examines the material, make large-scale changes as appropriate.

Thanks, RF. I’ve had one email from an SM12 teacher, who would be interested in having a look at others’ materials, or having their outlined critiqued or something. I’m more than happy to assist this.

BUT, please don’t attach willy nilly on random posts. That just creates a non-navigable swamp.If you have materials which you wish to share, such as the set stuff on the Fractions post, please let me me know in a comment or an email, and I’ll attach it as an update to the post, or maybe set up a dedicated post that and related material.

OK, here is one, fairly basic, student-in-mind offering.

Same as the file I posted on the Fractions post.

Boolean Logic Summary Sheet

Again, it’s preferable to flag with me first, and then I can update the actual post. Notes embedded in a thread of 100 comments aren’t gonna be found by many.

Thanks, John. I’ve further updated.

A further update:

Re: The Nelson SM12 textbook.

I’ve managed to looked at a copy – there is a (formerly) sealed Student Access Code Card that states on the back that “Four Access Codes have been provided to cover resale of the printed book”. This is three more than Cambridge gives.

The copy I looked at only had two Access Codes on the back (both expired, unfortunately but predictably). Nevertheless this is still one more than Cambridge …

Very poor show, Cambridge. Well done, Nelson.

But … the Nelson textbook comes across as very try-hard and gimmicky. I find it hilarious that it doesn’t have Exercises. Instead, it has gimmicky Exam Prep and Exam Practice … (Roses by any other name …) I’d expect no less – the point-of-difference it’s trying very hard to cultivate is “Where every question is exam practice”. (It also includes SM34 questions and relevant exam reports).

And, written by well-known VCAA examination assessors and CAS pushers (because of course none of the other textbooks are …), it even has a gimmicky ‘Exam hack’ that provides “insider advice to help students overcome common errors, achieve learning success and gain valuable marks”. Self-promotional try-hard sales gimmicks that make it read like one big glossy advertisement for your typical School Holiday Revision Program.