A few years back, I was pondering how to bring about the desperately needed reform of Victorian mathematics education and, in particular, of VCE. I had been sermonising on the awfulness of VCE, and everything, for a good ten years, and blogging for five, and it all made zero difference. Not because anyone argued, or could have argued, against anything I said or wrote: my criticisms were obviously valid and obviously important. It made zero difference, however, because the arrogantly clueless VCAA, backed by His-Master’s-Voice MAV puppy, could simply ignore me. They did not give a damn about my opinion or about anybody else’s. But I wanted to do more than simply yell at the clouds. I came up with a plan.
The problem wasn’t that VCAA were ignoring me; the problem was that VCAA had no serious association with properly strong mathematicians and had had none for decades. This is the fundamental category error about which I have written, which has led to decades of VCAA screw-ups, as well as screw-ups in Tasmania and Queensland and Western Australia and South Australia and New Zealand and, well, pretty much everywhere. Mathematics teachers, even when they are not third-rate VCAA mates, are simply not sufficiently knowledgeable or sufficiently attentive to detail to be in charge of a school curriculum or of senior mathematics exams. Mathematics education clowns are, of course, even worse. A man’s gotta know his limitations; the majority of teachers and education academics, and certainly those employed and engaged by VCAA to do the proper job of mathematicians, do not.
What to do? I thought about it this way:
• VCE is the focal point of Victorian education;
• The exams are the focal point of VCE;
• Exam errors are thus VCAA’s weak spot, where pressure could be applied.
Backed by Burkard as my professorial muscle, in mid-2022 I decided to confront VCAA with their past exam errors, reasoning that, when directly confronted, VCAA could not deny the prevalence and importance of these errors, and that this would be a compelling argument for the need for proper mathematical expertise. That turned out to be far from an automatic truth, and there are still cretins within and associated with VCAA who are in denial, but it turned out, at least eventually, to be true enough. The Bennett report, as implemented in letter and spirit by the irreplaceable Kylie White, ensured that the Monash mathematicians were signed on. The battle was won. Soon after, the war was lost.
Dealing with the exam errors was never my central goal. Sure, it was an important goal in itself and that the exams no longer contain the absolute howlers of past years is a very big win. But the exams are still appalling, inevitably crippled by incompetent writers and an abysmal curriculum and VCAA’s insane CAS fetishism. The grading is still appalling, overseen by prissy assholes with no proper sense of mathematical argument. Beyond the exams, the SACs are still a maddening disaster, policed by little hitlers. And on and on. VCE mathematics generally, and Victorian mathematics education more generally, is still an unmitigated disaster.
None of this can be fixed without the systemic employment of proper mathematical expertise. One cannot possibly have coherent goals for mathematical education without a deep and clear-headed sense of mathematics, what it means and the way it works. Teachers must be part of this but they cannot lead this; they are simply not qualified to do so. Mathematics education must, always, be led my mathematicians. Yes, mathematicians, when left to their own devices, can also screw it up. But, mathematics education not led by solid mathematicians is absolutely guaranteed to be screwed up. Which it is, and which it will remain so.
Kylie White had genuine appreciation and respect for the mathematician help that she received (and the appreciation and respect was very strongly reciprocated). There was every chance that Kylie would have reformed VCE mathematics, and mathematics education more generally, in a strong and properly informed and intelligent manner. Now, thanks to a flunky mistake, and a cowardly Minister and a Liberal nitwit and a Murdoch thug, Kylie White is gone. Gone with Kylie is any hope of the desperately needed reform.
At VCAA now, there is zero appreciation for the mathematicians and less than zero understanding of what else the mathematicians might have to offer. New VCAA CEO, Andrew Smith, is making the same old category error. Smith has backed the status quo of mediocrities and half-wits, and he is treating the mathematicians with contempt, as nothing more than the hired help; the mathematicians are tolerated, barely, and nothing more. Smith is useless and thus worse than useless.
Ironically, the current presence of the Monash mathematicians, which VCAA only grudgingly accepts, pretty much ensures that no greater presence can occur. Smith and his nitwit “mathematics team” can take the mathematicians for granted but if the mathematics exams stay off the front page news it is only because the mathematicians are catching the howlers before the exams go to press. And, with the howlers off the front pages, there is no further public pressure for the reform of mathematics education, and thus no general call for mathematical expertise. The exams are still appalling but it is more subtle than the presence of blatant howlers; the media does not have the skills or the sense to understand or to explain this more general depravity. VCAA is thus now safe to continue with its long and proud tradition of arrogant incompetence.
We have lost. I have lost. VCAA no longer need listen to me or to mathematicians. I will still yell at VCAA, of course. I will still call out VCAA nastiness and idiocy when it occurs and, hopefully, I will create some headaches for Smith and his team of arrogant mediocrities. But we have lost.
I’m sorry. I tried.
I thought that the Monash guys were going to be involved in writing the exams this year, after only being there to check for mistakes, or something, last year, or was this all scrapped when Kylie White was kicked out?
And what sort of reasoning or excuse does Smith have to not use the mathematicians? Would love to hear it.
The forces of mediocrity within VCAA are very strong. Smith won’t explain anything to anyone.
It seems to be generally agreed that no school today (and that includes the ones charging parents $50K per year) is as good as an ordinary high school of 40 years ago.
The public service is a shadow of its former self, as are universities. It (and many schools and unis) are staffed by executives who often have no experience of the coalface, no respect for front-line staff and no care about what is actually going on there. Their salaries are many multiples of the coalface workers.
Thank you for continuing the fight – all we can do is our best against the general enshittification of society. The situation is hopeless – we must take the next step…..
Your first sentence is all that needs to be said. Everything else is depressing detail.
Looking at this from my own little corner (Ontario), seventy years ago when I was going through high school and university, teaching high school was a main occupational goal for many students who got an honours degree in mathematics and physics (which were more closely linked then than they are today). In the 1960s, there were many more opportunities for math grads opening up, not just with computers and also in sciences that were developing a more theoretical side). The pool of teachers depended to a greater extent on students who had more general degrees with less advanced mathematics.
Until the 1960s, there was one provincial examination at Grade 13 which was set by a committee of university mathematics professors and teachers. These were marked during the summer by teams of high school teachers supervised by mathematics professors and a report was issued by the province (this was true for every subject) on how the questions were answered. Thus, teachers had the ability, either through the marking or the report, of what constituted a correct answer and the standards that applied. This knowledge was fed back to the schools, who during the whole of the five years of high schools, gave students end of term examinations under formal conditions, so that by the time the kids got to grade 13, they were prepared for it.
When the syllabus was reformed around 1960, it was by a committee of professors and seasoned teachers, so that while not completely, we managed to avoid most of the madness of the New Mathematics. Sorry to go on so long, but i think there may be something to learn from us old fogeys. There is a long tale on how things slowly went downhill from there.
Thanks, Ed. I’ve read about the Australian version of that long, sad tale, and summarised it the final part of my Arena article.
The academisation and bureaucratisation of mathematics education, and of all education, has been a disaster.
Marty: I just read your Arena article, and I think it is one of your finest essays. A couple more points: in the 1950s, most universities in Ontario (if any) did not have a faculty of education. Teacher training was through one normal school year for elementary teachers or one year at the Ontario College of Education for secondary teachers. The instructors of the latter were beforehand practising teachers and the cadet teachers could practise on students in a secondary school attached to the University of Toronto, where admission was by examination, set up for that purpose in 1912 (it was intended to be two schools, one for boys and one for girls; the girls school never opened and eventually in 1973 the boys school became coed). In the 1960s, the Ontario government set up the Ontario institute for Studies in Education, which was at the beginning a very interesting mixture of faculty of all sorts of background, but over the years morphed into the sort of ideological academicese many of us now decry.
Rote learning has a bad rap. I expect that in the days of the dinosaurs, a lot of the mathematics was taught by rote and it largely worked bacause it was taught in the context of useful mathematics, students had to identify the input, use and check the output. In this sense, it has been replaced by pocket calculators. But the more important aspect that is not replaced by technology is its role in revealing to students the structure of mathematics and its orderly interlocking of facts and techniques. It also provides a foundation for adaptations and generalizations to other mathematical situations.
It is analogous to technical exercises for one learning a musical instrument, exercises that reflect the structure of musical composition and solve ahead of time some of the technical challenges encountered later in pieces.
Thanks, Ed, for the comments and the kind comments. I’m proud of that essay.
I don’t know a lot about teacher training in Australia before the academisation and bureaucratisation of education. I suspect that it was similar to what you describe in Ontario, that it was largely in the hands of teacher types, and it was all more akin to apprenticeship rather than emphasis on (bad) theory.
In the early 90s, Melbourne University had a school of education with mathematics education lecturers. So, to-be teachers could do an undergraduate degree in teaching there. The mathematics part of that was somehow then folded in with the mathematics department at unimelb, with the education lecturers then teaching and/or tutoring regular mathematics and engineering maths classes. I co-taught with some of those guys and I liked them. They were not by any stretch mathematicians, and Unimelb’s snotty mathematicians tended to look down on them, but they were solid in the mathematics they taught and they saw their job and their vocation to teach mathematics. Whatever else was going in the undergraduate education degrees up to the 90s, clearly some reasonable mathematics was being taught.
I don’t know how the current Melbourne Education faculty was born, and why it did not continue to include the mathsy types who ended up in the mathematics department. But, from around that time, or earlier, education degrees ceased to contain any meaningful mathematics, or meaningful anything. What is going on now is simply madness.
I’ll admit, I am puzzled by “rote learning”. I’m not exactly sure what it means, whether it refers to the methods, chanting and whatnot, or simply the desired result of such (or other) methods, of automatic recall. I’m an advocate of both, but one could conceivably be the advocate of the outcome but not the traditional techniques. The NCTM has an idiotic position statement against “rote learning”, and it’s on my long list to figure out what NCTM is against and to then hammer them.
if rote learning is to be effective, you have to contrast “automaticity” with “mindlessness”, and strive for the former rather than the latter. There are lots of practical things in life we learn by rote beginning with the alphabet and the counting numbers in order and continuing into such things as dressing and tool using; we might not understand what is going on under the hood, but we should be monitoring the situation making sure that what comes out in the end works and having the ability to check and adapt if something is going haywire. I think that this was an aspect of good “traditional” teaching, but somewhere along the way got lost by teachers who focussed more on the process rather then the situational understanding. Oddly enough, some of those who railed against traditional rote learning were guilty of their own debased version of it with the use of things like “keywords” in solving problems and canned methods and “shortcuts” in situations where students need to be discriminating and encouraged to figure things out. One of my favourite examples is the student who having to solve, say, (x-5)(x-7) = 0, multiplied it out and used the quadratic formula because that is the only way he was told how to solve quadratic equations. A close relative to this is the student who asked me whether his solution to an equation was correct and was surprised that he could discover this for himself by plugging it in and seeing if it worked.
In some areas, rote memorization is the only way to go. I presume your students have to learn the names of the states and their capitals, and I do not see any structural reasons that helps a student along in this task in the way that mathematics offers. (Although one might suppose that the capital of a state might be its largest city; this might work in Australia, but it sure does not in the US — cf. California, New York and Illinois, nor to a lesser extent in Canada.)
Thanks, Ed. I think mindlessness is underrated. The way to learn 7 x 7 = 49 is to learn 7 x 7 = 49. I think you would also be shocked at how little straight out information, about anything, students are now expected to learn. But I think you’ve said it all very well.
Your factorisation example is an excellent illustration of how perverted education has become. Most Australian students would not ever use the QF to solve (x – 5)(x – 7) = 0, because most Australian students do not learn the QF. But they do learn various techniques to solve quadratics (only), and they really really suck at them. All the propaganda is about “understanding” but it is all shit. The students absolutely suck at solving equations because they never get sufficiently hard or sufficiently varied equations to solve. It is all absolutely fake. And then they move on to CAS.
I hate ACARA. I hate VCAA. I hate MAV. I hate AAMT. I hate MERGA. I really hate them all. They are arrogant know-nothing monsters. And I hate AMSI and AustMS and the show-pony mathematicians sucking up at teacher conferences for the likes, for Pontiusing the whole thing, for not giving a flying fuck about what is actually happening.
Fuck them all.
My goodness — the pure passion in your reply is truly impressive! However, it is justified. The problem in education is that so many involved have their own little schtick and genuine debates are very rare. Genuine problems to be carefully unpacked.
Yes, I am passionate about it. I got an excellent PUBLIC education in Melbourne, and my Year 12 mathematics subjects were very very very good. These motherfuckers are making it impossible for the vast majority of today’s kids to get what I got for free, and the motherfuckers are so fucking proud of it.
And with a special shoutout to the University of Melbourne mathematics department. Useless fucks.
Hi Marty, 1980s mathematician here from Monash. Finally someone who knows the way to learn 7 x 7 = 49 is to learn 7 x 7 = 49. My kids have just finished in the school system and I’ve had many arguments in the past with blue rinse hair teachers who are more concerned with preaching the benefits of mathletics rather than why my kid doesn’t know 6 X 8 =48. It’s a seriously fucked up system. I think the powers at be in the vcaa and the education department can’t bring themselves to admit they fucked up education and education in the 80s and 90s and before was so much better.
Thank you, CT. The problem goes way, way beyond VCAA and the DoE, and they are not really the fundamental source. They implement the madness but the main instigators of the madness are education academics, their promotion of teachers as experts, and and their sidelining of “subject matter experts”: i.e., in this case, mathematicians.