Note that our question is not whether smart Victorian students *should *avoid Methods. Given that Methods is the ugliest, stupidest, most aimless, digitally perverted, anally retentive, error-strewn, little Hitler managed, God forsaken heap of anti-mathematical garbage ever conceived, or even conceivable, of course *all* students should avoid Methods* if* they possibly can. The question is, *can* they?

The obvious way to avoid Methods is to avoid VCE in its loathsome entirety, by taking the International Baccalaureate instead. That is not necessarily easy, however; in particular, it requires avoiding second rate schools, such as Scotch College. Still, IB is clearly the best option for those students who want to learn something and for whom IB is available. But perhaps VCE students can also get away with simply not doing Methods.

The idea of just ducking Methods has at times crossed our mind, but we’ve never pursued the thought. The possibility is explicitly raised, however, in VCAA’s Specialist Webinar, explaining their new, You Didn’t Think We Could Make It Even Stupider Did You Mathematics Study Design. Quoting VCAA Curriculum Manager, Michael MacNeill,

*“A perennial question which crops up at least once a year I’m sure, can students study units three and four Specialist Maths without previously or concurrently studying units three and four Maths Methods? The answer is that it is technically permitted. However, please apply the lens of common sense should any students ask around that sort of a question.”*

So, Methods is not “technically” a prerequisite or corequisite for Specialist. Which means that a Specialist student could conceivably take instead a more palatable subject, such as Techniques in Manure Shovelling, or Advanced Toenail Extraction. But what is implied by (ugh!) “the lens of common sense”? Does taking Methods help enough for Specialist to outweigh the transcendental relief of not doing Methods? Does it make any difference for university applications?

We don’t know the answers. We are curious what the smart and experienced teachers who read this blog think about it all.

(For context for other commentors, I currently teach undergraduate maths at UniMelb)

I guess ‘the lens of common sense’ for me would be that if person asking is an average student who showed no sign of significant mathematical prowess (and noting that at the undergraduate level I only notice 1-2 such students every year across the ~200 or so students I teach every year) then the answer would be a firm no. If, however, they were clearly enthusiastic or already ahead of the curve then it’d be something I’d reasonably consider.

Can’t speak for university applications in a general sense, but in terms of pre-reqs for 1st-year maths subjects, I just had a look at UniMelb’s handbook:

Introduction to Mathematics requires completion of Methods 1/2, so is effectively UniMelb’s Methods 3/4 equivalent.

Calculus 1 requires >25 in Maths Methods, no mention of Specialist: https://handbook.unimelb.edu.au/2022/subjects/mast10005/eligibility-and-requirements

Calculus 2 requires >29 in Specialist Maths, but no mention of Methods: https://handbook.unimelb.edu.au/2022/subjects/mast10006/eligibility-and-requirements

So I guess I’d conclude that doing Specialist without Methods, so long as it’s done well enough, could be viable, but would still require noticable exceptional ability/enthusiasm for me to even reasonably recommend it to anyone.

Melbourne also doesn’t allow entry into the BSc without Methods.

Thanks, Ryan. Do you have a link?

Huh, my mistake, they take Spec or Methods.

Perhaps Methods 3/4 can just be avoided at all costs. Wish I’d have known that.

Thanks, Matt. Note that I qualified with “smart” in the title. But I’m not sure why you’re putting the bar as high as “noticeable exceptional ability/enthusiasm” to recommend ducking Methods.

Perhaps just feeling a little too jaded after having taught thousands of university students (and not just at UniMelb). I have mildly wondered if I should change careers before the jadedness gets worse 🤔😬

Burkard manages not being jaded. But he’s nuts.

VCE study design (from VCAA website), Page 109:

“Specialist Mathematics Units 3 and 4 assumes familiarity with the key knowledge and key skills from Mathematical Methods Units 1 and 2; the key knowledge and key skills from Specialist Mathematics Units 1 and 2; and concurrent study or previous completion of Mathematical Methods Units 3 and 4. ”

So, technically a student is permitted to not study Methods, but it is assumed that they are/have…

WOW.

But what are the assumptions in practice? I’m asking the practical question of whether Specialist can be done without Methods, not whether the Left Hand of VCAA is aware of the Right Hand.

Fair point.

Calculus and Probability/Statistics would be the places to look for evidence one way or the other. I’m 90% confident that the authors of Specialist exams assume those sitting the paper have completed Methods as well.

Is it possible to skip Methods? Without any evidence it is difficult to say.

The Specialist 1&2 teachers I know (yes, your question is more about 3&4 and it is difficult to extrapolate) often find themselves waiting until the Methods 1&2 class has covered certain topics before teaching topics such as Trigonometry, Transformations, Complex Numbers. If more time was available, the Specialist teacher would more often than not do a better job of teaching the whole lot.

RF, truer words (your last paragraph) never spoken. This is what happens when any provider has a monopoly. Lack of genuine competition breeds contempt. If the IB was available to any student who wanted it, the VCE would be dead in the water in its current form (oh happy day).

The non-alignment between Maths Methods and Specialist Maths is farcical. Some obvious examples:

1) It’s difficult to delay teaching trigonometry in Specialist 1&2 in order for it to have been covered in Maths Methods Unit 2. And it would be crazy to teach complex numbers before trigonometry (although I’m aware of some schools that do).

2) It’s almost impossible to teach statistics in Specialist Unit 4 concurrently or behind the normal distribution being taught in Methods Unit 4.

3) It’s difficult to try and align kinematics in Specialist Unit 2 with calculus in Methods Unit 2. (Yes, I know what MacNeill said some dumbass comment about teaching kinematics as part of vectors. Screw that).

4) It’s difficult to teach integration in Specialist Unit 3 concurrently or behind the integration being taught in Methods Unit 4.

In other words, it’s difficult to impossible for the Maths Methods content to align with the Specialist Maths content. All too often, Specialist teachers have to teach the bare minimum from Methods in order to progress. Neither VCAA nor it’s stooges will acknowledge what is common knowledge among teachers of Specialist Maths. Requiring Specialist Maths SAC 3 to focus solely on statistics magnifies this problem.

And under the new Study Design the farce continues and there will be even less time to cover things properly in Specialist Units 1&2.

On a related note, I have often mused that it should be possible in some schools to teach Specialist Maths 3&4 and Maths Methods 3&4 as a single ‘super subject’ with double the time (maybe somewhere it is …??) Imagine the possibilities. You could perfectly align the content from each subject, no teaching time would be wasted with doubling up of content and there would be a significant amount of time to fill in the gaps in the Study Design for both Methods and Specialist.

On an unrelated note, I found out the other day that there are schools in Victoria who offer the NHT VCE. That is, there are students in Victoria who sit midyear VCE exams. I had always assumed it was only taught in the Northern hemisphere.

Thanks, JF. May I ask directly? Can a student reasonably (and sensibly) do Specialist without also doing Methods?

Marty, do you mean not doing Methods 1&2 as well as not doing Methods 3&4.

It’s impossible to give a definite answer. The student may well be smart, but their background knowledge is also an important factor. There is prerequisite knowledge that any student needs. That knowledge gets consolidated and extended in Specialist Maths. At a minimum the smart student would need to be fluent with:

Exponentials and Logarithms.

Polynomial equations.

Trigonometric equations.

Continuous random variables including normal distribution.

If the smart student has a decent background in the above (eg. from natural curiosity and independent learning), then I do not think they need to suffer through Methods 3&4 in order to successfully do Specialist 3&4.

You don’t ask whether the student can avoid doing Methods 1&2. If we agree that doing Methods 1&2 is required, then I think a smart student can definitely avoid doing Methods 3&4, although they would need to self-learn the required probability and statistics needed in Specialist.

It’s conceivable that a Specialist 1&2 student could learn all of the prerequisite Methods stuff, but they would need to have been taught thoroughly and well. It’s also conceivable that a thorough and well-taught Yr 10 mathematics subject could equip the student with all they needed and they could avoid Methods altogether.

Thanks, John. I don’t really know what I’m asking. I’m just responding to MacNeill’s comment, and on the basis of my loathing of Methods.

I don’t think MacNeill has thought through the implications and consequences of many of his comments. (Or comments-for-money made by VCAA stooges, but that’s another story). He’s inherited a minefield of bullshit. All the more reason for him to think his comments through carefully before making them.

I’m still willing to give MacNeill some time and space, but he’s sounding more and more like a Company Man.

Of course he’s a Company Man! What other person would VCAA employ!? I’d loved to have been a fly on the wall at the interviews (if only to see who was on the interview panel). I know people who were thinking of applying for the position but decided against it because they realised that their decency, honesty and transparency would be incompatible with what the position required and they would hate themselves for what they would be forced to do and say. (One might argue that the position could corrupt those ideals over time).

As long as VCAA continues to ignore it’s shortcomings, it will continue to employ Company Men (and Women) and corrupt or push out those few it employs who aren’t.

I contend that VCAA hires from a small and skewed pool of applicants.

JF – I know of such a school in Melbourne (won’t name them, but they are a BIG school) that offers NHT VCE.

If students do well enough, they are done with Methods and focus on their other subjects.

If they don’t do as well as they want, they can sit the November exams.

Not entirely sure this is within the spirit of the game, so to speak, but it must be within the rules if it is happening.

That’s quite interesting. That would mean you could do Methods at a time in between accelerating it a whole year early and doing it concurrently with the rest of your subjects. The extra semester lead time would help add probably enough buffer to the topics that need it for Specialist U2-4 but still gives a semester for looking at a number of topics at a year 10 level in preparation for it.

The point RF makes about having essentially two attempts in close succession with attempting the exams does sound a bit suspect though, where under normal circumstances you’d be repeating the whole subject a year after and needing to complete all of the course work and assessments again (I assume).

JF’s idea of a super subject also sounds interesting as you can then intersperse a lot of the more interesting ideas and applications from Specialist to make the Methods course a lot more palatable on top of the benefits of ordering the courses in a sensible manner. Biggest issue I can think of would be timetabling that in around students’ subject choices.

Yes RF, I too heard of a school very recently. It’s also big, with strong ties to China. Maybe we’re thinking of the same school.

Schools are experts at subverting the rules with little regard or care to the of those rules (look at what many schools do with Further Maths). It might be legal but often it’s completely immoral (in my view, anyway). This is another reason I despise VCAA, VCAA allows it to happen.

But the whole game has already been gamed, with essentially trivial 34 subjects being completed in Year 11.

Correct.

When brainiac Yr 10’s and 11’s are allowed to do Further Maths, what hope of success do genuine Further Maths students have in a ranking system? (This comment applies more forcefully to the pre-2016 VCE era when Further Maths genuinely catered for students who wanted/needed maths but had no hope of success in Methods).

VCAA should be totally ashamed of itself for allowing this subversion to occur (in fact, VCAA changed the rules to specifically allow it to happen!!) You have to have rules and regulations that assume that schools have no morality or ethics. Because schools don’t when it comes to dressing up their results.

I was thinking of Methods34 in Year 11. But yes, Further as well.

Once upon a time (as all fairy tales begin), acceleration in any subject was reserved for the best students. Not slightly above average. The best. Out of 200 Yr 11 students, you might have 10-15 at most that did Methods 3&4 in Yr 11. I was OK with that.

But then schools decided to use acceleration as a marketing tool. So you had 40 – 50 Yr 11 students doing Methods 3&4 in Yr 11. At least 2/3 of these students would have been much better off doing Methods 3&4 in Yr 12.

An accelerated student who does not get a 37 – 50 raw study score should never have been accelerated. And yet in my experience, roughly 2/3 of accelerated students achieve below this threshold.

Marketing gimmicks and timetabling have been the main factors determining acceleration for at least the past 15 years.

That’s the school… so it is something of an open secret, perhaps?

Further was once something resembling a decent subject before the mass enrolment of Methods students – a call I have no doubt was made by a principal somewhere and not a Mathematics teacher.

Becoming an open secret (I didn’t know until a few days ago. But I guess the secret will spread quicker now …)

On the other hand, could a student do all 8 units of VCE mathematics subjects?

I meant at Year 12 level; SM, MM, Further, Foundation

Terry,

Technically no, because of timetabling issues.

6 units of maths – possible, at certain schools with large cohort and many classes only.

Based on previous experiences- SM, FM and MM can be taken by students concurrently…

I know of many schools that don’t allow students to take three maths subjects.

The reasons will vary, mostly between equity issues and timetable clashes.

Thanks

I personally know one student that did Further, Methods, Specialist and Uni maths over a two year period. Totally legal, but allowing that student to do Further Maths was totally immoral of the school, in my view. (Then again, what can you do when it’s all done within the VCAA ‘rules’ and a school can’t stop the student doing it).

I think adding Foundation to Further, Methods and Specialist would be a bridge too far. I don’t have the inclination to check, but I would sincerely hope that VCAA have enough morality to regulate against this happening. Because I guarantee there would be schools that would attempt to exploit it (enrolling their bright Yr 8’s in Foundation Maths, then Further Maths in Yr 9 and then Methods and Specialist) all in order to inflate their ‘scores of 40 and above’. Some schools have the morality and ethics of Attila the Hun.

Funny story, I know a guy in uni who did further and specialist, but not methods. The school apparently didn’t verify details? I’m not sure what the heck happened. He’s studying engineering/computer science at Monash, and had no issues with ENG1005 enrolment (MTH1030 equivalent) and MAT1830 (which states either spesh or methods). I think the general rule of thumb is to just look at completion of the previous math unit, i.e MTH1020/ENG1090/Specialist mathematics. The university equivalent subjects enforce the requirements, so it is a bit confusing as to why it’s not enforced in high school. Also, goes without saying, he is very smart. As a student, I never really thought about the weird misalignment between Methods and Specialist content, since I opted to learn it on my own, but it does seem to be unproductive? It’s confusing, in retrospect.

There was a story told to me about a student doing law at Monash – decades ago; he was doing OK but not brilliantly until the final year where the wheels seemed to fall off; he was asked to show cause as to why he should be allowed to continue; at the interview he admitted that he had been doing medicine at Melbourne and law at Monash simultaneously, but he got into trouble in his last year of law because he was based in hospitals full-time for his course in medicine; the university allowed him to continue with his study of law.

Almost certainly an urban myth, Terry. (Then again, maybe the student wanted to save money by being able to defend against malpractice suits).

@JF: Perhaps … although…

John von Neumann (1903-1957) studied chemistry at university in Berlin and Zurich while he was enrolled in mathematics at university in Budapest. He did well in both courses.

Johnny was one of the smartest people on the planet (arguably the smartest). I doubt the character in your story came anywhere even remotely close to his level.

“Does taking Methods help enough for Specialist to outweigh the transcendental relief of not doing Methods?”

Not really, MM is pretty much a subset of SM. My experience was that everything taught in MM was taught in SM anyways, just at a faster pace. Instead of spending a month or so in MM1/2 learning differentiation of polynomials, we spent a week in SM1/2. However the process of convincing schools to let you do SM without MM is probably more painful than doing MM itself.

“Does it make any difference for university applications?”

Anyone who takes SM and understands it can do MM easily and get good marks. The main skill that MM tests (use of the CAS) is also a skill tested by SM, so a student who wants to maximise their results, should probably take MM.

Also, for entry into UMEP, students apparently must do MM. This requirement might be able to be ignored, but knowing the University of Melbourne, probably not.

Thanks, Anon. I appreciate the argument (which JF also made), that one may as well take MM as well. As for UoM demanding MM for UMEP, that would be monumentally stupid, and thus would be entirely consistent with UoM practice.

Given that Semester 1 of UMEP Mathematics is Linear Algebra, the only background a student would need is Matrices and Vectors. Both are taught in Specialist Maths Unit 1 (the previous year). So Maths Methods is not essential in Semester 1.

In Semester 2 UMEP Mathematics is Calculus. By this stage the required calculus has been taught in Specialist Maths. So Maths Methods is not essential in Semester 2.

So yes, if UoM turned down the application of a smart VCE student (with mathematical maturity) who had not done Maths Methods, that would be dumb. The moral of the story is that one size does not fit all – some cases require individual attention. A student who had not done Maths Methods but wanted to do UMEP Mathematics would be such a case.

They once turned down a student who hadn’t done Latin.

For Mathematics? Or just for some random subject (or degree like Law or medicine)? Purely on the principle of snobbery.

And you heard this from someone whose family handed the story down from generation to generation, starting with the great-great-great grandfather who was the one that got turned down in the early 1800’s?

I remembered wrong. The student’s lousy mark in Latin in Year 11 resulted in the student being rejected for UMEP.

Aha. Yes. I know a student who missed out because their poor result in Accounting dragged down their otherwise excellent average to slightly below the cut-off. No recourse. The one-size fits all mentality strikes again.

These days I advise students not to disclose a poor result in an unrelated subject (like Accounting) that will drag down an otherwise excellent average. Simply state the best five subjects (which will typically include a Unit 3&4 subject – usually Maths Methods).

There’s always a recourse.

Of course. If you want to paint a target on the student’s back. The student did appeal but there was persistent pushback due to the red-taped prerequisite minimum average. In the end the student decided it wasn’t worth pursuing. The mistake made by the student was including Accounting on the original application.

Someone can appeal for the student.

Indeed. But the student got cold feet and decided it wasn’t worth the hassle of pushing back harder etc. So the matter was dropped.

Sure, although it’s really frustrating when students acquiesce like that. I hate that kind of gaslighting (from UoM, not the teachers).

On matters MM, yesterday I was prepping a class for their 3/4 exam and not a single student was able to solve 2x = π/12 for x (by hand ie. no CAS). All insisted that x = π/6. Their regular teacher commented that it is not at all unusual. At my school, the best maths student is studying FM. She views MM as pointless.

Ugh. Obviously CAS and the curriculum(s) have destroyed fraction/algebra skills, but isn’t there still enough tested that such students will be massacred on Exam 1?

Carnage indeed: expected and largely unavoidable. What I’m wondering is how such students managed to get all the way to MM 3/4? I’m somewhat baffled (but I’m new at this). Amazing.

I explicitly go through a bunch of questions like that because it’s such an issue.

2×π/3 1/2×π/2 2×5π/6 π/4+π/3 2π/3+5π/6

2x=π/4 x/2=5π/4 (x+π)/3=π/3 x+π/4=4π/3

(too many students answer the first as 2π/6 the first time and the second last equation they don’t often spot x=0 until they go through the motions.

I think it’s a combination of years 9 and 10 not having enough fraction work / relying on integers for most topics because the fractions makes it “too hard”. As well as not enough work with algebraic fractions.

Aha ha. That’s very funny, Marty.

To get a C+ on Exam 1 you only have to get 15-18/40 (see attached. Note – the exam is marked twice so all scores are out of 80). And C+ has you on the way to a raw Study Score of around 30 (the set median score).

The only massacre in Exam 1 is the VCAA distribution of grades (forced upon it by a reality of its own making, I suppose).

vce_mathematical_methods_ga21

I see. Now, how do I unsee?

Once seen, it can’t be unseen.

Yes, this is a very common ‘careless mistake’. You should ask them to solve the following:

2x = π/12

x/2 = π/12

and see what happens.

And asking students to solve something as simple as x^2 = x is always entertaining. (Even more so when x gets replaced with sin(x) or ln(x) etc)

Is the “best maths student” studying Further AND Methods? Any reason they chose Further and not Specialist? (If this student was honest, you might discover she’s gaming the system by studying Further).

But it’s not just mathematical ability and the poison of CAS. I spend all year trying to get all students to understand and follow basic instructions that appear in the VCAA instruction box at the top of page 2 of the exams:

“In all questions where a numerical answer is required, an exact value must be given, unless otherwise specified.”

“In questions where more than one mark is available, appropriate working must be shown.”

And yet even by the end of the year I still have students who fail to follow these instructions.

On a different tack, it’s possible that many students will avoid all mathematics at VCE level simply by leaving school and getting a job. Employers appear to be desperate to hire more workers, and many students might seize the opportunity to leave school and enter the workforce. If so, this will have ramifications for schools, TAFE and universities. (Universities have already been affected by the state government offering free TAFE courses, and I understand that there are more to come.)

That sounds like a good thing.