A few days ago we received an email from “Concerned Student”, someone we don’t know, requesting advice on how to approach VCE mathematics. We have thoughts on this and intend to reply, but the email also seemed generally relevant and of likely interest. The email also raises interesting questions for teachers, and for the writer of this blog. With Concerned Student’s permission, we’ve reproduced their email below. We’ll hold off commenting until others, who actually know what they’re talking about, have had a go. Here is CS’s email:

*It seems clear from reading this blog that a significant proportion of the VCE Methods & Specialist curricula are in direct conflict with good mathematical education. As someone entering these subjects next year, what’s the recommended approach to make it through all the content of the study design while also *learning maths*? Should I largely ignore the (… Cambridge) textbook and overall course and focus on self-teaching content along the same lines from better sources, stopping only to learn specifically from the curriculum whatever button mashing is necessary for an exam; or should I instead focus on fighting through the curriculum, and learn some proper maths on the side – I guess the productive question there is “is it easy enough to apply properly learnt maths to the arcane rituals found in VCE course assessments?”*

*It’s probably worth noting that, as far as I’m aware, the Methods & Specialist teachers at my school are known for being quite good, but they’re obviously still bound by the curriculum they teach.*

Marty, students such as “Concerned Student” are few and far between and are in the vast minority.

Most students these days are simply interested in “learning” only what’s “on the test” and are, for the most part, agnostic to what’s “going on behind the scenes” (that is, the actual mathematics). Whilst this is true in Methods & Specialist to a small degree, it is utterly and gargantuanily pronounced in Further Maths (just know how to press buttons to get the answer, write the number and move on, you get ostracised for wanting to know more).

I’d find it quite difficult to teach “proper” mathematics due to time constraints – it takes the better part of 3 terms to go through the curriculum and term 4 is meant for exam revision etc.

Throw in the fact that the “SACs and exams” are devoid for the most part of proper mathematics (of course exceptions do exist), leads to a system in which good and proper mathematics is neither encouraged nor looked favourably upon.

A real disgrace for those students who seek true mathematical knowledge.

I’ve always thought one of the worst parts of SACs were the ‘application’ VCAA requirements. They were so contrived and fake it was pathetic. I think that with the level of maths taught at VCE level it would be hard to come up with compelling, interesting and (at least somewhat) realistic application SAC question.

I think a far more appropriate usage for application-style questions would be in a dedicated data analysis or applied modelling/simulation class – of course no such thing really exists at VCE level, and the IT subjects that did (still do?) exist are a joke (… so is Algorithmics too, unfortunately). It’s a shame though because, at least from my student perspective, such a class implemented well could be really engaging and useful…

Edit: @Marty, I can’t seem to get WordPress to remember me (Tau)

Thanks, Tau. I’ve put in your name on that comment. Others may know why or why not WordPress remembers names. It may be a matter of having a WordPress account.

As for “applications”, it’s not just the SACs. The applications idiocy is everywhere in VCE, and it’s just a manifestation of the numeracy poison, which begins destroying things in Prep and never stops. The rank stupidity of numeracy is symbolic of and central to the total perversion of education.

Hi, Steve. I think you are probably correct, that CS is in the very small minority. I think, however, there is a sizeable minority of VCE students who are aware or strongly suspect that Methods/Specialist are fundamentally nonsense, but shrug “Such is VCE” and get on with it. I’m not one bit critical of such students. The cultural damage, however, is probably worst for these students; they are smart enough to smell what is or is not intrinsically worthwhile, but they’ll then channel that smartness into some rewarding, non-maths activity. It is not impossible that they’ll think of maths as worthwhile in the future, but the odds are significantly lowered.

As for teachers not having the time to make up for the pathetic curriculum, that is of course a huge and hugely frustrating problem. I think there are richer and less rich ways of teaching the VCE curriculum, as commenters on this blog often suggest. But, fundamentally, you teacher guys are screwed.

Dear ‘CS’,

I was in a similar position to you last year. I can’t say there’s necessarily a ‘recommended approach’, but I chose the latter approach you suggested. I learned the curriculum, memorised all the CAS button-pushings, looped through the practice/past papers and clenched my teeth at the VCAA absurdities. But I never let that prevent me from pursuing maths outside of school passionately; in other words my maxim (throughout school) was “never let school interfere with my education” (Twain?).

Also, to keep me sane during VCE, I completed UMEP Maths last year, which was an amazing experience (and free!). I’d highly recommend you look at it for next year (being mindful of application dates). You also get credit for first-year university level maths (be prepared to fight the red-tape when it comes to trickier things though … 😀). I think it’s a good way to ‘learn some (actual) maths’ whilst going through the motions of what VCAA thinks is maths.

Hopefully if you go on to pursue maths at uni then those misconceptions and rubbish taught will be corrected, and you’ll learn new and exciting things, but I can definitely appreciate your position.

Feel free to reach out to me if you’d like to have a chat about anything!

Thanks, Tau. I’m not suggesting this applies to CS, but what would you recommend for a less-strong VCE student? There has to be some trade-off between doing genuine maths and focussing upon VCE. Also, as it happens, I don’t think UMEP is all that great, but it’s a million times better than VCE swill.

Hmm, I’m not entirely sure, perhaps other commenters might have some ideas. The fault really lies with the VCE system. I suppose I’d recommend to simply try and educate oneself outside of class as much as possible (which I believe should go for all subjects, not just maths), and to seek help from those (teachers, peers, forums ….) who are willing and capable.

Out of curiosity, what were some of the things that stood out about UMEP that you didn’t think were great?

Hi, Tau. No question the VCE system is the awfulness with which one must cope. But it’s just not obvious to me how. I admire any student, such as yourself, who continues to value education while in school. (It appears that very apt saying is due to an author called Grant Allen.) But Year 12 VCE is a very, very important year.

Briefly on UMEP, it is in effect first year pass-level Unimelb maths, which has been roughly the same since 1953, and was probably ready for an overhaul in 1954. It’s a solid enough for a cookbook pass level 1st year uni subject, topic by topic it is ok, and it is unpolluted by calculators and exam cheat sheets. But it is pretty uninspiring, bitsy and without a coherent theme. It also has no pretensions to rigour, but it also has no rigour.

“Better sources” …. A wretched indictment on Australian textbooks (and teachers) when a student has to try and decide what’s a better source than their textbook (or classroom notes?) for a particular topic.

I hope that Concerned Student gets a teacher that does NOT ‘teach from the textbook’, rather uses the textbook as a source of (carefully curated) questions to set for students, and actually teaches using their own notes and examples in class.

In other words, I hope CS gets an excellent teacher and not an average teacher.

Re: Cambridge. I hope that CS has not formed the view that Cambridge is hopeless and should be ignored. That would be a big mistake in my opinion. Cambridge certainly has its faults, but on the whole it’s not a bad textbook. I certainly wouldn’t be ignoring it wholesale to try and find ‘better sources’. I would use it, ask questions about it, and supplement it with additional sources as required. Most of Cambridge’s faults have been extensively discussed in Marty’s blogs – this provides a good starting point for most of the things in which ‘better sources’ are required.

As for the SACs of shit, a good student will always do ‘well’ in them despite his/her worries.

JF, I disagree: Cambridge

isa bad textbook(s). And I haven’t discussed all its/their faults by a longshot. If you pick a page at random, the odds are that it’ll contain something annoying, or worse. But, yes, for VCE, Cambridge’s exercises are probably as good as you can do.Fair enough. But if you pick a car on the road at random, the odds are that it’ll be unroadworthy. Nevertheless, the odds are that it will still get you safely from A to B. But if you spend all your time trying to find a car that is

completelyroadworthy, you’ll never get from A to B.My concern is that CS will be so busy trying to find reliable sources for everything (plus having to try and decide, without knowing the stuff

a priori, whether that ‘better source’ismore reliable) that s/he will never get from A to B.My point is that Cambridge is not bad as at least a first approximation for trying to learn the stuff. And with a good teacher CS can easily get to a second-order approximation from Cambridge.

ThenCS is in a better position to supplement with ‘more reliable sources’ and get to a third-order approximation.The other viable alternative is that s/he gets someone completely reliable as a tutor to safely drive him/her from A to B for a few hours each week (you can’t expect his/her teacher to do this, otherwise every other student deserves the same offer …)

CS needs to focus on the class half-full, not the glass half-empty. And then start filling up the glass.

I agree CS shouldn’t hunt further. Cambridge is probably as good as they can do.

Busy as you are, maybe you could look at collaborating with a few like-minded others, get a publisher on board, and write the textbook students and teachers deserve to have.

(It would be a labour of love, not a labour of financial reward).

Yes, well that’s a funny story.

This is a suboptimal solution for many reasons, but I find that the Cambridge texts for HSC Extension 1 and 2, where the topics coincide with Specialist Mathematics, have a superior set of exercises. So if you can get your hands on those texts, then curating a set of questions from them might be an improvement…

SRK, are you referring to NSW texts? Who are the writers? Are the exercises superior as practice for VCE, or are they intrinsically, mathematically superior? I can imagine the latter, but the former would surprise me.

Here are the texts from Cambridge’s site. Extension 1: https://www.cambridge.edu.au/education/titles/CambridgeMATHS-Stage-6-Mathematics-Extension-1-Year-12-print-and-interactive-textbook-powered-by-Cambridge-HOTmaths/

Extension 2: https://www.cambridge.edu.au/education/titles/CambridgeMATHS-Stage-6-Mathematics-Extension-2-Year-12-print-and-interactive-textbook-powered-by-Cambridge-HOTmaths/

Mostly I think the latter. The best practice questions for VCE exams are past VCE exam questions. A combination of the two seems like a good compromise.

CS,

Not knowing your background and interests it is difficult to give specific advice

as there are many ways to complete the VCE courses and every student learns differently.

The mere fact you believe you have “good” teacher’s and have asked the question of Marti is an encouraging sign though and you could do worse than consider some of the following as time permits:-

view a few of the WITCHES and links on this site that interest you ignoring the occasional expletive.

follow the advise of Tau on UMEP.

learn how to program ideally in any “open source” or” academically free” language.

learn how to think first and then use your CAS calculator effectively.

know its limitations and build your own or copy functions,programs,shortcuts etc to enhance the standard build

(there are some examples on this site and you could ask MK,RF, PN or others about Mathematica for further options alternatively if you are using a TI nSpire CX Sean Turkington has been “pushing the envelope” for over 10 years here https://www.youtube.com/user/turksvids )

Enter some mathematical competitions and talent quests where the idea is to make you think. One long running example for Madison Wisc US high school students is https://www.math.wisc.edu/talent/?q=50-anniversary

I you can get hold of a copy of ” a mathematical bridge ” by S Hewson it offers a reasonable introduction to the different fields of mathematics and theoretical physics at undergraduate level and has some challenging questions for the reader in the appendix a few sample pages are here

https://books.google.com.au/books?hl=en&lr=&id=08w7DQAAQBAJ&oi=fnd&pg=PR7&dq=a+mathematical+bridge&ots=E6NHRg7oBW&sig=Vj9lycQrU3ntUIVS2efpgTdv7Ik&redir_esc=y#v=onepage&q=a%20mathematical%20bridge&f=false

Regards

Steve R

BTW In my descendant cohort’s case luckily they could “game the system” by avoiding VCE altogether and complete the IB Diploma instead. The STEM investigation you can undertake in year 11 gives you an opportunity to explore a subject of interest over a 4 week period. Unfortunately not every one has that opportunity in Victoria.

Thanks, Steve. Intrinsically, they are all very good suggestions (except for ignoring the expletives: they have meaning, too, and they’re there for a reason). I totally agree that the best approach to VCE is to avoid it: IB is so vastly superior. It’s a shame that more students don’t have that choice, but any student with the choice should take it.

I do have some reservations about most of your suggestions, and the suggestions of others here. I’ll make it a separate comment.

Thanks to everyone who has commented above. There’s a lot of smartness there. I wonder, however, if the suggestions, smart as they are, might be insufficiently cynical. I’m yet to be convinced that the best advice for a VCE maths student isn’t to write off Year 12 as a period of Alice-in-Wonderland weirdness, to just get through it and wait to get on with reality once out of the rabbit hole.

I am also curious of what this predicament means for VCE teachers. How much do you, or should you, or can you work to give a properly mathematical treatment of the curriculum, and/or to add reasonable depth to the paper-thin, hole-full topics? Do you have the time, either to prepare or deliver such material? Can the educational benefits for your students, even your better students, outweigh the loss of mega-precious time playing the VCE game? On top of that, or anyway, how honest should teachers be on the third-rate nature of the curriculum, and the SACs, and the exams? Of course all of this also relates in a non-trivial way to the Mathematic Oath (which is exactly why I chose to post the Oath at this time).

That last question also applies very much to this blog. Whatever the value of the blog as a source of information and mathematical sense, is it outweighed by the blog’s demoralising negativity? I’m not looking at all for reassurance here; I’m perfectly comfortable with what I’m doing. But I’m curious about what others might think.

Marty, we’ve all met

thatstudent who gets 90% on his/her test but only dwells on the negative. You’d think they’d got 30%, listening to their lamentations …. And then they come and ask how can they improve. They just cannot see the positive, and they judge themselves against impossible standards. I know students who are disappointed getting 84 in UMEP maths, because they know people who got 99 and 100 …. They cannot take pride and celebrate their own amazing and wonderful achievement. (Jeez, I wish I could have gotten 84’s in my uni subjects).I think it’s important that the negativity (and yes, there’s plenty to be negative about) does not demoralise a student from the positive. The fact is that plenty of students can and do learn plenty of good maths in VCE and then go on to greater things. If CS is cynical now, wait until s/he gets to universtity ….. (Spoiler to CS: You’re going to continue being disappointed, so make the best of it).

In the case of CS, I think s/he has a bad case of pessimism. There’s plenty to be optimistic about, particularly if they have ‘good teachers’. We are world weary and cynical and often see the glass as almost empty. Year after year we see the same crap, get the same dishonesty from VCAA etc. and it all adds up. But students only see VCE for 2 years. Our job is to help the student see at least a glass half full during that time and then do our best to keep filling the glass up.

Regarding VCE, Cambridge etc. – You can’t shine shit, but you

canmold it and shape it.Actually, Mythbusters showed some years ago that you can “polish a poo”.

So I’ve taken to an alternative saying: “it doesn’t matter how much sugar you put on a turd, it will never be a doughnut.”

OK, fair point, RF. But “You can’t sweeten a turd” doesn’t sound nearly as good as “You can’t shine shit” ….

…just because you

canpolish a poo doesn’t mean youshould.Like teaching a pig to sing – it is a waste of time and tends to annoy the pig.

JF, I don’t interpret CS’s letter as either pessimistic or cynical, just thoughtful. But maybe I’m wrong and, in any case, it is quite possible that plenty of other students are pessimistic and cynical, and that my blog encourages those feelings.

Such is life. My aim is not to make students, and teachers, cynical but to make them critical. That is, I am pushing people to be analytical, to question authority, to be thoughtful and concerned citizens in exactly the way official bodies pretend but then demand the very opposite. If a good teacher, and I know there are many and that they are the beacon of hope, needs to narrow the focus for VCE students, or whomever, then fine, I understand. But that is not my focus or my self-determined job. The glass is not near half full and I won’t pretend it is.

I see posts like this often on Reddit or the like. My advice to the kid is to follow the standard curriculum. There are vast tranches of new content that you are learning. Even if it is slightly suboptimal, you’ll still learn a ton.

If you want to go back through Spivak later, fine. But if the class is using Stewart, follow that and learn it perfectly. Don’t get derailed. Also, it can be a lot easier to embrace rigor in retrospect than at first.