The current VCE Mathematics Study Design is, of course, appalling. This is not up for debate. I have spent the last few days, however, trying to figure why the SD is appalling. How did it get to be this bad? I am still climbing out of rabbit holes, and falling into new ones, and I hope to write on it all soon. But there appears to be a short answer that explains a lot: it was always appalling.
The thing appears to have been born crippled, the inevitably deformed offspring of a gargoyle VCE. Yes, it has all gotten way worse, thanks in no small measure to the yeoman’s work of David and Kaye. But it was always going to be bad, and it always was. The pits of Hell origins of the Study Design, however, is a topic for the future post. The topic of this post is just a simple question: What is a study design?
I have always been puzzled by the term “Study Design”. I had always figured it to be a synonym for “curriculum”, but why not then say “curriculum”? At least in nutso theory, however, there appears to be a distinction. The guiding dimwit light of VCE was school and teacher autonomy, including flexibility in senior subjects and their delivery. A “study design”, then, was supposed to reflect and respect and encourage this freedom, as opposed to a more prescriptive and rigid “curriculum”. Supposed to.
Whatever once was, and whatever is going in other subjects, there is not a hell of a lot of freedom now in VCE mathematics. Yeah you got the SACs, God bless ’em, and you’re free to do what you want there. Give or take the little Hitler rules, enforced by the little Hitlers. But there are exams at the end. And so, except for deciding whether the kids will “investigate” Absurd Model A or Absurd Model B, it is all very much constrained.
So, how, now, is the VCE “study design” different from a “curriculum”? It’s not like the thing is short, or that a curriculum need be particularly long; with the proper established and shared culture, a written curriculum can be very outline-ish and still work very well, and indeed much better than the unreadable tomes favoured by Australia’s educrats. True, the current Study Design has glaring gaps. This, however, appears to be not from a commitment to flexibility but rather from a commitment to incompetence.
At this stage, and whatever the original intent, I cannot see that there is any difference between a “mathematics study design” and a “mathematic curriculum”. If that is true then it is an important truth.
Fundamental to repairing VCE mathematics is repairing the study design, and this will be extraordinarily difficult. Yes, there is the obvious first step, to pack off to Siberia the techno-fetishists and the “modelling” fetishists who have screwed it all up; that is easy, if VCAA has the sense and the mind to do it. The much harder part is to then reinstitute and to reestablish something sane.
The culture of Victorian mathematics education has been so degraded for so long, there is almost no sense left of real mathematics. The majority of current teachers were taught by teachers who themselves are a product of this degraded culture. If the teachers’ teachers knew solid mathematics and its worth it was only through their own hard work or the dumb luck of having an older, teachers’ teachers’ teacher. For current teachers, it is an extra loop, an order of magnitude less likely. The majority of current mathematics teachers can have no sense of what a deep and coherent mathematics curriculum might be. Which means it is no gimme to now sell them one.
How to bring teachers back into the fold of sanity? I don’t know, although “at the point of a gun” springs to mind. Decisions about a mathematics curriculum, or “study design” or whatever you want to call it, must be made with the solid input of strong mathematicians, of those who know what mathematics is and how it all fits together. That has not been the case for, at least, forty years.
The main battle to be won is cultural, but the battle is much harder if there are administrative and bureaucratic barricades that first need to be torn down. Is the “VCE study design” such a barricade? In the manner of assessment presumably so. One simple, sane and sanity-preserving change would be to return to 100% on final exams for serious mathematics subjects. (For less serious subjects, do what you please. I don’t care.) Ironically, this change would also make the teaching and the learning much more flexible, and much more human, than it is now. Presumably such a change would be impossible, however, without deep-sixing some idiotic study design regulation.
Nonetheless, at least in terms of the determination of mathematical content and its presentation, a “study design” for VCE mathematics appears to be nothing more than a curriculum. Which means it can be done right. And obviously, desperately, should be.
Almost 250 years ago Australia was on par with Siberia, happy to receive ‘fetishists’ of all sorts. They were sent mostly from England, official records say about 160,000 ‘fetishists’ were sent to the continent under. However, it looks like the tables turned, well not for Siberia.
The second-biggest problem with the study design is that it is vague and incomprehensible.
It’s a weird mix. The Study Design is very detailed in places and, in sum, is interminable and unreadable. But it also has glaring gaps and confusions.
But this is really the point I’m trying to make in this post (not very well). I think the Study Design being a “study design” is in part used as an excuse for the vagueness and the gaps. It is an absurd excuse.
A curriculum need not spell out every detail, and probably should not, at least for senior mathematics. If there is a shared understanding reinforced by clear examples, references to solid texts and a bank of previous, well-written exams then the curriculum can get away with broad statements, and it is better to. This works much, much better than having a legalistic document, which then has people arguing over whether Question 3(a)(ii) is covered by Content Descriptor 17, dot point 3. That is all madness.
But this proper approach to a curriculum is exactly dependent upon the kind of mathematical educational culture that has been lost and has been almost totally forgotten.
On the other hand, VCE is regarded as a high-stakes examination. Teachers and students want as much information as possible. The more detailed curriculum the better, as far as they are concerned.
Teachers and students may want it but that doesn’t mean they know what’s good for them, and they do not.
I suppose that the study design is a stepping stone between the curriculum and the text book.
You mean a stepping stone between the non-existent curriculum and the appalling and stupid textbook that tries as hard as possible to follow the study design? Yep, that makes sense, and is working wonderfully.
I’m not sure it answers the question (or if it does, possibly raises a few more…) but in 1858 the University of Melbourne published (in their manual for students) the following half-page regarding the annual Algebra examination:
– Explanation of the meaning of algebraical symbols, and the method of using them, especially the bracket.
– Addition subtraction multiplication and division of algebraical expressions of an integral and fractional form.
– Explanation of the meaning of an index, with the proof of the equation
– Reduction of expressions to their simplest form.
– The solution of equations.
– Colenso’s Algebra Part I will be used as a textbook for the examination.
The 1858 Algebra exam itself, amongst other questions then asked:
If
, show that 
.
Well, obviously in 1858 they were a little short on details. But “Colenso’s Algebra Part 1” then pretty much said what you needed to know. Of course “Nelson’s SM 34 will be used” doesn’t quite work the same way.
Was there a curriculum when I did HSC in 1977? Undoubtedly, but I have no memory of it, let alone a memory of pawing over it to determine what was examinable, and I very much doubt that it mattered much. There were solid, great, textbooks, with many excellent problems, and there was a good decade of past exams, which were hard and which did not contain errors. That was the curriculum. Yes, the “curriculum” was either evolving or had surgery performed on it: we knew that older exams were less reliable and some topics were becoming less emphasised. But in practice that was a very minor detail.
Thanks for the reference to Colenso. I just bought it!
My copy of Colenso, J. W. (1867) “The elements of algebra designed for the use in schools”, Longmans arrived today. 4.5 cm x 6.75 cm. 168 pp. + 25 pages of 400 miscellaneous problems and answers to all the exercises in the book. No photographs and no diagrams.
What I fail to understand is the stupidity behind the areas of non-relatedness of Unit 1/2 with Unit 3/4 for a subject like General Mathematics. Unit 1/2 lists concepts that are non-assessable in Unit 3/4 and yet, VCAA has an expectation that we would teach it in the era of ATAR and 40+ study scores. For example, why would I teach about space and measurement in Year 11 GM when it is not even assessable in Year 12 GM? In an ideal world, I see why students should know these concepts but as far as the current system goes, it’s useless.
So why not simply not teach it? Who the hell cares what VCAA expects in Year 11?
In Victoria, government schools are expected to teach according the the Victorian curriculum.
Yeah, yeah. Heaven forbid a teacher bend the stupid rules in order to benefit her students.
The stuff that is in year 11 GM but not year 12 is basically mensuration and trigonometry. This takes kids up to the sine and cosine rules that are not seen in non-advanced year 10 classes. It’s kind of nice to teach that down-to-earth maths content and would be a shame for the students to miss out – even if it does not directly help them on their exam 1 year later.
The other topic that does not *explicitly* carry though is “variation” which is useful for building student algebra skills used for transforming and fitting bivariate data in year 12.
I do not think VCE is the right time for idealism.
I wouldn’t be a teacher if I couldn’t hold onto a bit of idealism – irrespective of curriculum bodies. And the y11 GM curriculum is pretty light on – you have time to teach it. [Admittedly, I’ve only taught each GM unit one time…]
Yeah, ok, let me walk it back a bit. Y12 VCE is certainly no time for idealism, but Y11 VCE is a judgment call.
I don’t know the situation now, but certainly there used to be a two-take issue with SM Y11. Some teachers went to town with the good topics and taught a strong course. Others essentially ignored the good stuff and gave a warm-up version of SM Y12.
I can see the argument for SM students. I think the argument is significantly weaker for GM students.
I have to confess that even in the best of modern documents, the Singapore curriculums, I still jump straight to the table section that lists what is covered in plain language and avoid all the extra guff beforehand. I think the brevity is a necessary but not sufficient condition for a good document. Sadly, the modern world seems to think the other way around.
JJ: Where do I find the Singapore curriculum? Terry
On my blog, of course.
Look at the links here and here.