VCAA Puts the “Con” into Consultation

As we have written, the Victorian Curriculum and Assessment Authority is “reviewing” Victoria’s senior secondary maths, which amounts to the VCAA attempting to ram through a vague and tendentious computer-based curriculum, presented with no evidence of its benefit apart from change for the sake of change. Readers can and should respond to the VCAA’s manipulative questionnaire before May 10. In this post we shall point out the farcical nature of VCAA’s “consultation”, as evidenced by VCAA’s overview and questionnaire.

The overview begins by framing VCAA’s review with the following question:

What could a senior secondary mathematics curriculum for a liberal democratic society in a developed country for 2020–2030 look like?

This is peculiar framing, since it is difficult to imagine how a society being “liberal” or “democratic” or otherwise has any bearing on the suitability of a mathematics curriculum. Why would a good curriculum for China not also be good for Victoria?

One could easily write off this framing as just jingoistic puffery; neither word reappears in VCAA’s overview. It is, however, more insidious than that. The framing is, except for the odd omission of the word “suitable”, identical to the title of the Wolfram-CBM paper promoting “computer-based mathematics” in general and Wolfram-CBM in particular. This paper is the heavy propaganda gun VCAA has procured in furtherance of its struggle to liberate us all from the horrors of mathematical calculation. Though the Wolfram-CBM paper never states it explicitly, this makes clear the purpose of the framing:

“[L]iberal” and “democratic” and “developed” amounts to “rich enough to assume, demand and forever more have us beholden to the omnipresence of computers”.

The VCAA overview continues by noting the VCAA’s previous review in 2013-2014 and then notes the preliminary work undertaken in 2018 as part of the current review:

… the VCAA convened an expert panel to make recommendations in preparation for broad consultation in 2019.

Really? On whose authority does this anonymous panel consist of experts? Expert in what? How was this “expert panel” chosen, and by whom? Were there any potential or actual conflicts of interest on the “expert panel” that were or should have been disclosed? How or how not was this “expert panel” directed to conduct its review? Were there any dissenters on this “expert panel”?

The only thing clear in all this is the opacity.

The overview provides no evidence that VCAA’s “expert panel” consists of appropriately qualified or sufficiently varied or sufficiently independent persons, nor that these persons were selected in an objective manner, nor that these persons were able to and encouraged to conduct the VCAA review in an objective manner. 

Indeed, any claim to breadth, independence or expertise is undermined by the constrained formulation of the questionnaire, the poverty of and the bias in the proposed curriculum structures and the overt slanting of the overview towards one particular structure. Which brings us to the issue of consultation:

There is no value in “broad consultation” if discussion has already been constrained to the consideration of three extremely poor options.

But, “consult” the VCAA will:

The VCAA will consult with key stakeholders and interested parties to ensure that feedback is gained from organisations, groups and individuals.

Well, great. The writer of this blog is a keenly interested stakeholder, and an individual well known to the VCAA. Should we be waiting by the phone? Probably not, but it hardly matters:

The VCAA has provided no indication that the consultation with “key stakeholders” and “interested parties” will be conducted in a manner to encourage full and proper critique. There is very good reason to doubt that any feedback thus gained will be evaluated in a fair or objective manner.

The overview then outlines three “key background papers” (links here). Then:

… stakeholders are invited to consider and respond to the consultation questionnaire for each structure.

Simply, this is false. Question 1 of VCAA’s questionnaire asks

Which of the proposed structures would you prefer to be implemented for VCE Mathematics?

Questions 2-8 then refer to, and only to, “this structure”. It is only in the final, catch-all Question 9 that a respondent is requested to provide “additional comments or feedback with respect to these structures”. Nowhere is it possible to record in a proper, voting, manner that one wishes to rank the Wolfram-CBM Structure C last, and preferably lower. Nowhere is there a dedicated question to indicate what is bad about a bad structure.

The VCAA questionnaire explicitly funnels respondents away from stating which structures the respondents believe are inferior, and why.

The good news is that the manipulativeness of the questionnaire probably doesn’t matter, since the responses will be presumably just be considered by another VCAA “expert panel”.

The VCAA overview gives no indication how the responses to the questionnaire will be considered and provides no commitment that the responses will be made public.

The VCAA overview goes on to provides outlines of the three structures being considered, which we’ll write upon in future posts. We’ll just comment here that, whereas Structures A and (to a lesser extent) B are laid out in some reasonable detail, Structure C looks to be the work of Chauncey Gardiner:

What is written about Structure C in the VCAA overview could mean anything and thus means nothing. 

True, for a “detailed overview” the reader is directed to the Wolfram-CBM paper. That, however, only makes matters worse:

A 28-page sales pitch that promotes particular software and particular commercial links is much more and much less than a clear, factual and dispassionate curriculum structure, and such a pitch has absolutely no place in what VCAA describes as a “blue-sky” review. By giving prominence to such material, the VCAA fails to treat the three proposed structures in anything close to a comparable or fair manner. 

If there were any doubt, the overview ends with the overt promotion of Structure C:

The distinctive proposal … contain[s] aspects which the Expert Panel found valuable … There was support for these aspects, indeed, many of the invited paper respondents [to the 2018 paper] independently included elements of them in their considerations, within more familiar structures and models.

Nothing like putting your thumb on the scales.

It is entirely inappropriate for a VCAA overview purportedly encouraging consultation to campaign for a particular structure. A respondent having “included elements” of an extreme proposal is a country mile short of supporting that proposal lock, stock and barrel. In any case, the cherry-picked opinions of unknown respondents selected in an unknown manner have zero value. 

Though woefully short of good administrative practice, we still might let some of the above slide if we had trust in the VCAA. But, we do not. Nothing in VCAA’s recent history or current process gives us any reason to do so. We can also see no reason why trust should be required. We can see no reason why the process lacks the fundamental transparency essential for such a radical review.

In summary, the VCAA review is unprofessional and the consultation process a sham. The review should be discarded. Plans can then be made for a new review, to be conducted in the professional and transparent manner that Victoria has every right to expect.

The Moon Landing Hoax Hoax

July 20th was the 50th anniversary of Neil Armstrong’s walking on the moon. Well, maybe.

I still have vivid-grainy memories of watching Armstrong’s first steps. A random few students from each class in Macleod State School were selected to go to the library to watch the event on the school’s one TV. I was not one of the lucky few. But Mr. Macrae, our wonderful Grade 4 teacher, just declared “Bugger it!”, determined which student in our class lived closest to the school, and sent out a posse to haul back the kid’s 2-ton TV. We then all watched the moon landing, enthralled and eternally grateful to Mr. Macrae.

But did it really happen?

There have been plenty of questions and questioners, suggesting that the moon landings were faked. How, for example, is the flag in the above photo flapping, given there is no atmosphere to flap it? Then, there is the fake photo of astronauts playing golf on the moon. And the lack of stars in moon photos. And the killer radiation that didn’t kill. And the strange links to Stanley Kubrick. And on and on.

Can all this evidence of doctoring be discounted? Did Man really walk on the moon?

The answers, of course, are Yes and Yes.

The idea that the moon landing was faked is completely ridiculous, and it takes a wilful stupidity to believe it. Which includes about 5% of Americans, and 10% of millenials. (The funniest take is that Kubrick did indeed stage the moon landings, but he was such a perfectionist that he went to the moon to do it.)

There is more to this story, however, than a bunch of conspiracy clowns and gullible slobs. As the brilliant Matt Taibbi writes, there is, indeed, plenty of sleight of hand going on.

The important question is why so many people are willing to believe something so patently false? The answer must be some combination of an inability to discern truth with a lack of concern for truth. And why might that be? Well, just perhaps one factor is an extended history of media and government authorities willing to misdirect and to obfuscate and to flat out lie about everything else. Just perhaps people don’t trust authorities because authorities have abused people’s trust for too long. As Taibbi writes:

“… the flowering of conspiracy theories has an obvious correlation, to a collapse of trust in institutions like the news media and the presidency. … It’s simple math. You can only ask the public to swallow so many fictions before they start to invent their own. The moon story is a great illustration.”

Which is a huge problem. It doesn’t matter a damn if people believe moon landing conspiracy crap. But if they believe that crap then they’ll also believe, more easily, climate change conspiracy crap. And then, an authority that has lost authority is powerless to convince them otherwise. And then, we’re doomed.

But at least we can laugh at the dumb slobs while the Earth goes down in flames.

WitCH 18: Making Serena Pointless

We have lots of catching up to do, WitCHes to burn and whatnot. However, we’ll first try to get in a few quick topical posts (give or take a couple weeks …). This first one is half-post, half-WitCH. We had planned it as a post, but it then seemed worth letting readers have a first whack at it; as always, readers are welcome and encouraged to comment below.

Serena Williams was back at Wimbledon this year, for the ninety-fifth time, almost grabbing her eighth title. This phenomenal athlete was also the subject of some media fluff, of the type that always accompanies these events. It was reported, pretty much everywhere, that

“One in eight men think that they could score a point off Serena Williams”.

Oh, those silly, silly men.

Twitter, of course, lit up over these “delusional” men and the media gleefully reported the ridicule, and more often than not piled on. A rare few articles gave tepid consideration to the idea that the men weren’t delusional, and none more than that.

The Serena fluff came courtesy of British polling firm YouGov, popular with those comforted by the illusion that someone cares what they think. Specifically, YouGov asked:

“Do you think if you were playing your very best tennis, you could win a point off Serena Williams?”

YouGov announced the result of the poll on Twitter, with catchy headline and accompanying graph:

“One in eight men (12%) say they could win a point in a game of tennis against 23 time grand slam winner Serena Williams”

Note that 3% of women also answered that they could win a point; we could see nothing in the media reports questioning, much less ridiculing, this percentage. (The missing percentages correspond to people who answered “don’t know”.)

On the YouGov website, the poll is also broken down by age and so on, but there is little information on the nature of the polling. All we are told is:

“1732 [Great Britain] adults were questioned on 13 Jul 2019. Results are weighted to be representative of the GB population.”

OK, so now the WitCH aspect. What is wrong with the poll? What is wrong with the reaction to it and the reporting of it? As always, feel free to respond in the comments. (You might try to keep your answers brief, but it won’t be easy.)

Finally, to state explicitly what should be obvious, we are not in any way having a go at Serena Williams. She is a great athlete, and throughout her career she’s had to put up with all manner of sexist and racist garbage. We just don’t believe the YouGov poll is such an example, or at least so clearly so.

Tootering Your Own Horn

Eddie Woo is reportedly concerned about private tutoring. His warning comes courtesy of SMH‘s education editor, Jordan Baker, in an article entitled ‘Be very, very careful’: Experts raise warning on private tutoring. The article begins,

Maths teachers including high-profile mathematician Eddie Woo have sounded an alarm on private tutoring, warning that bad tutors could be “fatal” to students’ future in the subject.

Eddie said it, so it must be true. And, Baker quotes another expert, the chief executive of the Australian Tutoring Association, Mohan Dhall:

I am absolutely dismayed at the lack of creativity and lack of real-world applicability most tutors bring to maths …The main problem stems from this idea that they focus on the outcome – ‘this is what students need to know’, rather than ‘this is what kids need to learn to be interested and engage’.

Finally, Baker quotes expert Katherin Cartwright, a lecturer in mathematics education at The University of Sydney. Cartwright, according to Baker, is concerned that poor tutoring could lead to a lack of confidence:

If it becomes about skill and drill and speed, and it becomes an anxious, emotional issue for students, then they are not going to like it, and they will not want to take it further.

Yep, of course. The most important consideration when framing an education is to be sure to never make a student anxious or emotional. Poor, fragile little petals that they are.

Baker’s fear-mongering is nonsense. Almost every line of her article is contentious and a number contain flat out falsehoods. Beginning with the title. Woo and Dhall and Cartwright are “experts” on the issues of tutoring? According to whom? Based on what? Perhaps they are experts, but Baker provides no evidence.

OK, we could concede Baker’s point that Eddie is a mathematician. Except that he isn’t and we don’t. Not that it matters here, since most mathematicians are unlikely to know much about the role of tutoring in Australian education. But the false and pointless puffery exemplifies Baker’s unjustified appeals to authority.

What of the declared concerns of Baker’s “experts”? Cartwright is supposedly worried about “skill and drill and speed”. This in contrast to school, according to Baker:

Most schools no longer emphasise speed and rote learning when teaching maths, and now focus on students’ understanding of key concepts as part of a concerted effort to improve engagement in maths across the system.

This hilarious half-truth undercuts the whole thrust of Baker’s article. It is true that many schools, particularly primary schools, have drunk the educational Kool-Aid and have turned their maths lessons into constructivist swamplands. But that just means the main and massive job of competent Year 7 maths teachers is to undo the damage inflicted by snake-oilers, and to instil in their students, much too late, an appreciation of the importance of memory and skill and efficient technique. Such technique is critical for formal success in school mathematics and, which is sadly different, for the learning of mathematics. Baker seems entirely unaware, for example, that, for better or worse, Year 12 mathematics is first and foremost a speed test, a succession of sprints.

As for Dhall, does he really expects tutors to be more offering of “creativity” and “real-world applicability”? Dhall seems blissfully unaware that most “real-world” applications that students must suffer through are pedagogically worthless, and are either trivial or infinitely tedious. Dhall seems unaware that some subjects have warped “applicability” into a surrealist nightmare.

And Eddie? What worries Eddie? Not much, as it happens, but too much. Eddie’s quoted comments come from a NSW podcast, which appears to have been the genesis of Baker’s piece; stenographic fluffing is of course the standard for modern reportage, the cheap and easy alternative to proper investigation and considered reflection.

Eddie’s podcast is a happy public chat about teaching mathematics. Eddie is demonstrably a great teacher and he is very engaging. He says a number of smart things, the half-hour podcast only being offensive for its inoffensiveness; Eddie, or his interviewer, was seemingly too scared to venture into a deep public discussion of mathematics and the sense of it. The result is that, except for the occasional genuflection to “pattern”, Eddie may as well have been talking about turtle farming as teaching mathematics.

Eddie’s comments on tutoring are a very minor part of the podcast, a response in the final question time. This is Eddie’s response in full:

When I think about external tuition – again just like before this is a really complex question – there is tuition and then there is ‘tuition’. There is some which is enormously helpful to individual students to come in at a point of need and say “you have got gaps in your knowledge, I can identify that and then help you with those and then you can get back on the horse and off you go, fantastic”. There are other kinds of tuition which are frankly just pumping out an industrial model of education which parents who are very well intentioned and feel like they cannot do anything else, it is like “at least I can throw money at the problem and at least they are spending more time on maths hopefully that will help”. Maybe it does and maybe it is making your child hate maths because they are doing it until 9pm at night after a whole day? That to me is heartbreaking.

I think that students need to be very, very careful and parents need to be very, very careful about how they experience mathematics. Because yes the time is a worthwhile investment, it is a practical subject, but if you are just churning through, often tragically learning things which actually are just machine processes. I have students come to me and they say “I can differentiate, I am really good at that, I am only fifteen years old”. You don’t need to know what differentiation is, but they come to me with this ability to turn a handle on this algorithm this set of steps. Just like me; I don’t know how to bake, but I can follow a recipe. I have no idea what baking powder does or why 180 degrees Celsius is important but I can follow steps. That is okay for a cake because you can still eat it at the end, but that is fatal for mathematics because you don’t know why you are doing any of the things that you are doing. If that is what you are, you are not a mathematician, you are a machine and that is not what we want our children to become. We have to be careful.

Eddie says plenty right here, touching on various forms of and issues with tutoring, and school teaching. The issues do not get fleshed out, but that is the nature of Q & A.

Eddie also gets things smugly wrong. Sure, some tutoring might be characterised as “industrial”. But more so than schools? How can mass education not be industrial? This isn’t necessarily bad: mostly, it just is. Unless, of course, little Tarquin’s parents have the time and the money to arrange for individual or small-group lessons with an, um, tutor.

All the concerns Baker and her experts raise about tutoring apply as much or more so to school education and, as a matter of business necessity, are largely a reflection of school education. And, how do tutors and tutoring companies deal with this? Some well, some poorly. But mostly with industry, which is not a dirty word, and with good and honest intent.

Baker notes the underlying issue, seemingly without even realising it:

However, Australian students’ performance in maths has either stalled or declined on all major indicators over that period, and academics have raised concerns about students arriving at university without the maths skills they need.

Why do parents employ tutors? Having enjoyed and suffered forty years of tutoring, in pretty much all its forms, we can give the obvious answer: there’s a zillion different, individual reasons. Some, as Eddie suggests, are looking for a little damage control, the filling of gaps and a little polishing. Some, as Eddie suggests, think of mathematics, falsely, as a syntactic game, and are looking for lessons in playing that dangerously meaningless game. Some believe, correctly or otherwise, that their teacher/school is responsible for little Johnny’s struggling. Some are trying to get darling Diana into law school. Some are hothousing precious little Perry so he/she can get a scholarship into Polo Grammar or Mildred’s College for Christian Ladies.

But, underlying it all, there is one obvious, central reason why parents employ tutors: parents are unsatisfied with the education their child receives at school.

Why are parents unsatisfied? Are they right to be? Of course, it depends. But, whatever the individual analyses, the massive growth of the tutoring industry indicates a major disconnect, and either a major failing in schools’ performance or a major blindness in parents’ expectations, or both.

That would be a much more worthwhile issue for Baker, and everyone, to consider.

Laboring the Obvious

Following the lead of France and Ontario, the Victorian Labor government has decided to ban mobile phones in government classes. One stated reason is to combat cyberbullying, but they’re probably lying. The good and blatantly obvious reason is that smart phones destroy concentration.

Still, any change, no matter how compelling, will have its detractors. There is the idiotic argument that the ban is unenforceable; the claim is almost certainly false, but if true points to such a profound loss of authority that schools may as well just give up entirely. And, there is the argument – one in a stream of tendentious half-truths – that occasionally the internet is down, meaning a lesson can only continue aided by a mobile’s hotspot. The argument is based upon a falsehood but in any case is much worse than wrong; any teacher so addicted to the internet for their teaching may first wish to heal thyself. They may also wish to consider a new profession. Please.

And of course there is discussion of the suggested educational benefits of smart phones, proving only that there is no idea so idiotic that some educational hack cannot be found to support it.

Luckily, it would appear that the Labor government is holding firm, and students will be able to get back to the intended lessons. On their fucking iPads.

Wollongong the Craven

It would appear that the Ramsey Centre‘s Degree in Western Civilisation will now be a thing. This comes after the ANU rejected the idea out of concerns about Ramsey’s autocratic meddling. And, it comes after Sydney University shot itself in the foot by censoring its own academics. But, the University of Wollongong is hellbent on offering Ramsey’s Bachelor of Arts in Western Civilisation. This comes with the news that the University Council overruled Wollongong’s academic senate because, after all, what would those silly academics know about academic integrity?

Jillian Broadbent, UoW’s chancellor, claimed that the council had “full respect for the university’s academic process”. If only Broadbent had a modicum of respect for the meaning of English words.

Underlying all of this is the question of the meaning of “Western civilisation”. UoW advertises that in Ramsey’s degree a student will:

Learn how to think critically and creatively as you examine topics in ethics, aesthetics, epistemology, metaphysics, philosophy of religion and political philosophy.” 

The irony is palpable. But, at least it makes clear what is meant by “Western civilisation”. It means the power of a business-bloated gang to use Orwellian language while ramming through the selling out of a public institution to rich bigots.

We intend these words, of course, with the fullest of respect.

A Quick Word on Julian Assange

 

Either you are horrified by the persecution of Julian Assange or, like Lisa Millar and Patricia Karvelas and Peter Greste and Michael “Gold Star” Rowland, you support the fascistic, war-mongering motherfuckers out to get him. There is no middle ground.

Update (31/07/19)

ABC’S Four Corners has just aired a 2-part program on Julian Assange. It is well-made, interesting and, in keeping with modern journalistic style, entirely without self-awareness and entirely off the fucking point.

WitCH 16: The Root of Our Problem

This WitCH comes from one of our favourites, the Complex Numbers chapter from Cambridge’s Specialist Mathematics 3 & 4 (2019). It is not as deep or as beWitCHing as other aspects of the chapter. But, it’s still an impressive WitCH.

Update (11/08/19)

I guess if you’re gonna suggest a painful, ass-backwards method to solve a problem, you may as well fake the solution:

  • Checking directly that P(1 – i√2) = 0 involves expanding a cubic, and more, which the text does in one single magic line.
  • The painful multiplication of the products for part b is much more naturally and easily done as a difference of two squares: (z – 1 – i√2)(z – 1 + i√2) = (z – 1)2 + 2, etc.
  • After all that the third factor, z – 1, is determined “by inspection”? Inspection of what?

AS RF notes, it is much easier to spot that z = 1 solves the cubic. Then some easy factoring (without long division …) gives P = (z – 1)(z2 – 2z + 3). Completing the square then leads to the linear factors, answering both parts of the question in the reverse, and natural, order.

Alternatively, as John notes, the difference of two squares calculation shows that if z – 1 + i√2 is a factor of P then so is the quadratic z^2 – 2z + 3. That this is so can then be checked (without long division …), giving P = (z – 1)(z^2 – 2z + 3), and so on, as before.