An Educational Qandary

We see that Monday’s episode of Q & A has an education theme. The panel features Tanya and Adrian and, of course, Eddie the Great. (There’s also a token principal and a token student, who one hopes have the foresight and the intelligence and the courage to be troublesome tokens.)

We won’t watch. We can’t watch. We do, however, have a question about how the show might go:

How long into the show might it be before we have the first dumb question on PISA, and how long until the first dumber answer?

We’ll guess 2 minutes into the show for the question, and 2:30 for the answer.

UPDATE (11/02/20) We had to look up the commenters’ reference to “Jurgen Klopp reply”, but we’re glad we did. It should be watched by everybody with a platform in the media and, in particular, by everyone who appears on Q and Fucking A:

The Last Picture Show

The AustMS Education Afternoon is done and dusted. Thanks to our fellow speakers, and in particular to David Treeby, who bucked the trend and offered something of genuine value. And, thanks to all those who turned up. It was great to see some old faces, and to meet some new ones. One should also acknowledge AAMT and AMSI and MAV. The effort these institutions made to promote the event is noted and is reassuring.

The plan is to write some posts based on our presentation, in the near future. That’s perhaps not as entertaining as a live delivery from a vodka-infused Marty, but we’ll do what we can.

As for future presentations, we very much doubt it. In all likelihood, that was the last picture show.

AMSI’s Brain Teaser

Last week, AMSI released yet another paper on the issue of school mathematics being taught by “out of discipline” teachers. It will come as no surprise to readers of this blog that we have many issues with AMSI’s paper. Here, we’ll focus on just one aspect.

The Sydney Morning Herald’s report on AMSI’s paper begins:

Fewer than one in four Australian high school students have a qualified maths teacher …

That statement is, of course, utter nonsense. By any reasonable definition, a much higher percentage of secondary students are taught by formally “qualified” teachers. It is concerning that an “education reporter” would lead with such an implausible claim, but SMH was not alone. The report was titled:

Only 1 in 4 high-schoolers are being taught maths by qualified teachers

The Australian’s barely comprehensible sentence, courtesy of another education reporter, appeared to suggest that matters are even worse:

Fewer than one in four students are taught by a qualified maths teacher — one with at least a university minor in the subject — at some stage between Years 7 to 10.

So, what is the source of all these inflated declarations of educational doom? It would appear to be on page 2 of AMSI’s paper. In the first of the paper’s eye-catching Key Points, the authors write:

The extent of the problem [with the supply of qualified teachers] is illustrated by the estimated amount of out‐of‐field teaching occurring with less than one in four students having a qualified mathematics teacher in each of Years 7 to 10.

That reminds us: we must buy AMSI a box of commas for Christmas.

The above sentence, which turned out to be the grabber of AMSI’s paper, is like an optical illusion: you think you’ve got the meaning, and then it slips around to mean something entirely different. It is no wonder if reporters misinterpreted.

What did the AMSI authors intend to convey, and on what basis? It is difficult to tell. A linked endnote in AMSI’s paper refers to a 2017 AMSI publication. The page reference to this second document is clearly incorrect, but it appears that the intention is to refer to page 4, which has its own list of key points, including:

At least 26% of Years 7–10 maths teachers are not fully qualified.

This is an admirably clear statement and, if true, one may (or may not) regard it as a relatively major problem. The statement, however, is not remotely supportive of the educational catastrophe that AMSI’s garbled 2019 statement led gullible reporters to declare.

Also puzzling, it is not clear how AMSI’s 2017 statement, or any other AMSI declaration that we could find, leads reasonably to any natural interpretation of AMSI’s 2019 statement. This is the case even if one ignores that “not fully qualified” does not clearly equate to “not qualified”, and that 26% of teachers does not equate to 26% of classes, nor to 26% of students. Even with the most liberal assumptions and generous interpretations, we still cannot determine the basis, any basis, for the 2019 statement. The reader is invited to give it a go.

There are plenty more serious issues with AMSI’s paper which, though raising some very important issues and suggestions, also connects some distant and very disputable dots. It probably doesn’t matter, however. We worked hard to read AMSI’s clumsily written paper. It seems unlikely that many others will do likewise.

Numberphile and the Cult of Collegiality

Mathologer recently posted a long video addressing the “proof” by Numberphile of the “astounding result” that 1 + 2 + 3 + … = -1/12. As well as carefully explaining the underlying mathematical truth, Mathologer tore into Numberphile for their video. Mathologer’s video has been very popular (17K thumbs up), and very unpopular (1K thumbs down).

Many who objected to Mathologer’s video were Numberphile fans or semi-literate physicists who were incapable of contemplating the idea that Numberphile could have gotten it wrong. Many others, however, while begrudgingly accepting there were issues with the Numberphile video, strongly objected to the tone of Mathologer’s critique. And it’s true, Mathologer’s video might have been improved without the snarky jokes from that annoying cameraman. (Although, awarding Numberfile a score of -1/12 for their video is pretty funny.) But whining about Mathologer’s tone was mostly a cheap distraction from the main point. Fundamentally, the objections were to Mathologer’s engaging in strong and public criticism, to his lack of collegiality, and these objections were ridiculous. Mathologer had every right to hammer Numberphile hard.

Numberphile’s video is mathematical crap and it continues to do great damage. The video has been viewed over six million times, with the vast majority of viewers having absolutely no clue that they’ve been sold mathematical snake oil. Numberphile made a bad mistake in posting that video, and they’re making a much worse mistake in not admitting it, apologising for it and taking it down.

The underlying issue, a misguided concern for collegiality, extends far beyond one stupid video. There is so much godawful crap around and there are plenty of people who know it, but not nearly enough people willing to say it.

Which brings us to Australian mathematics education.

There is no shortage of people happy to acknowledge privately their frustration with or contempt for the Australian Curriculum, NAPLAN, VCE, AMSI, AAMT, MAV, teacher training, textbooks, and on and on. Rarely are these people willing to formally or publicly express any such opinions, even if they have a natural platform for doing so. Why?

Many feel that any objection is pointless, that there is no hope that they will be listened to. That may well be true, though it may also be self-fulfilling prophecy. If all those who were pissed off spoke up it would be pretty noisy and pretty difficult to ignore.

More than a few teachers have indicated to us that they are fearful of speaking out. They do not trust the VCAA, for example, to not be vindictive. To us, this seems far-fetched. The VCAA has always struck us as petty and inept and devoid of empathy and plain dumb, but not vengeful. The fear, however, is clearly genuine. Such fear is an argument, though not a clinching argument, for remaining silent.

It is also clear, however, that many teachers and academics believe that complaining, either formally or publicly, is simply not nice, not collegial. This is ridiculous. Collegiality is valuable, and it is obviously rude, pointless and damaging to nitpick over every minor disagreement. But collegiality should be a principle, not a fetish.

At a time when educational authorities and prominent “experts” are arrogantly and systemically screwing things up there is a professional obligation for those with a voice to use it. There is an obligation for professional organisations to encourage dissenting voices, and of course it is reprehensible for such organisations to attempt to diminish or outright censor such voices. (Yes, MAV, we’re talking about you, and not only you.)

If there is ever a time to be quietly respectful of educational authority, it is not now.

Smoke Gets in Your IQs

There’s not much more revolting than the tobacco industry. Well, OK, there’s racist scum like Trump and Turnbull. And there’s greasy media apologists. And Bill Gates. And Mia Farrow.*

Alright, the world is full of awful people. But you get the point: it is difficult to be on the side of smoking and tobacco-pushing sociopaths.

Difficult, but not impossible.

Recently, the media was full of shock and horror at a new study on smoking. It was widely reported that 2/3 of people who try one cigarette end up as “daily smokers”. This was the conclusion of a meta-analysis, covering over 200,000 respondents from eight surveys. Professor Peter Hajek, one of the study’s authors, noted the meta-analysis constituted documentation of the “remarkable hold that cigarettes can establish after a single experience.”

Which is crap, and obvious crap. The implied suggestion that a single cigarette can turn a person into a helpless addict is nothing but Reefer Madness madness.

How can a respected and sophisticated academic study come to such a conclusion? Well, it doesn’t.

Anyone who has read the great debunking by Susan Traynor‘s son knows to never take a statistical study, much less a one sentence summary of a study, at face value. In this case, and as the authors of the study properly and cautiously note, that “2/3 of people” hides a wide variance in survey quality, response rates and response types.

More fundamentally, and astonishingly, the study (paywalled) never attempts to clarify, much less define, the term “daily smoker”. How many days does that require? The appendix to the study suggests that only three of the eight surveys included in the meta-analysis asked about “daily” smoking with specific reference to a minimal time period, the periods being 30 days, “nearly every day” for two months, and six months.

Of these three studies, the 2013 US NSDUH survey, which used the 30-day period, had around 55,000 respondents and the highest response rate, of around 72%. Amongst those respondents, about 50% of those who had ever smoked had at some time been “daily smokers” (i.e. for 30 days). Hardly insignificant, nor an insignificant time period, but a significant step down from “2/3 daily smokers”. (For some reason, the figures quoted in the meta-analysis, though close, are not identical to the figures in the NSDUH survey; specifically the number of people answering “YES” to the questions “CIGEVER” and “CIGDLYMO” differ.)

Even accepting the meta-analysis as sufficiently accurate, so what? What does it actually indicate? Reasonably enough, the authors suggest that their study has implications for efforts to stop people becoming regular smokers. The authors are tentative, however, rightly leaving the policy analysis for another forum. In particular, in the study the authors never make any claim of the “remarkable hold” that a single cigarette can have, nor do they make any remotely similar claim.

The “remarkable hold” line, which was repeated verbatim in almost every news report, originates from a media release from Hajek’s university. Of course barely any media organisations bothered to look beyond the media release, or to think for half a second before copying and pasting.

There is indeed a remarkable hold here. It is the remarkable hold university media units have on news organisations, which don’t have the time or experience or basic nous to be properly skeptical of the over-egged omelettes routinely handed to them on a platter.

Update: Just a quick addition, for those might doubt that Turnbull is racist scum.

* Yeah, yeah, no one knows, except Mia and Woody. But I believe Moses.

Wenn Will We Ever Learn?

Another day, another person banging the STEM drum.

Today we’re supposedly learning about The case for making maths mandatory in high school.

Except we’re learning nothing of the sort.

What we are learning is that the author is incapable of composing a paragraph containing more than one sentence.

This is very annoying.

We are also learning nothing about mathematics education.

This is also very annoying.

We are learning, however, that a sequence of tendentious and unsupported and unconnected dot points makes for a boring and pointless newspaper column.

We are learning all this from Kim Wenn, the retiring CIO of Tabcorp.

This is perfect.

The “Marriage Theorem” Theorem

The Marriage Theorem is a beautiful piece of mathematics, proved in the 1930s by mathematician Philip Hall. Suppose we have a number of men and the same number of women. Each man is happy to marry some (but perhaps not all) of the women, and similarly for each woman. The question is, can we pair up all the men and women so that everyone is happily married?

Obviously this will be impossible if too many people are too fussy. We’ll definitely require, for example, each woman to be happy to marry at least one man. Similarly, if we take any pair of women then there’s no hope if those two women are both just keen on the one and same man. More generally, we can take any collection W the women, and then we can consider the collection M of men who are acceptable to at least one of those women. The marriage condition states that, no matter the collection W, the corresponding collection M is at least as large as W.

If the marriage condition is not satisfied then there’s definitely no hope of happily marrying everyone off. (If the condition fails for some W then there simply aren’t enough acceptable men for all the women in W.) The Marriage Theorem is the surprising result that the marriage condition is all we need to check; if the marriage condition is satisfied then everyone can be happily married.

That’s all well and good. It’s a beautiful theorem, and you can check out a very nice proof at (no pun intended) cut-the-knot. This, however, is a blog about mathematical crap. So, where’s the crap? For that, we head off to Sydney’s University of New South Wales.

It appears that a lecturer at UNSW who has been teaching the Marriage Theorem has requested that students not refer to the theorem by that name, because of the “homophobic implications”; use of the term in student work was apparently marked as “offensive”. How do we know this? Because one of the affected students went on Sky News to tell the story.

And there’s your crap.

But, at least we have a new theorem:

The “Marriage Theorem” Theorem

a) Any mathematician who whines to her students about the title “Marriage Theorem” is a trouble-making clown with way too much time on her hands.

b) Any student who whines about the mathematician in (a) to a poisonously unprincipled pseudonews network is a troublemaking clown with way too much time on his hands.

Proofs: Trivial.

The Marriage Equality Theorem

Theorem: Let V be the set of valid arguments against marriage equality. Then is empty.

Proof: Let P be a valid argument. Then, by now, someone would have argued P. This has not occurred. (Proof: by exhaustion.) By contradiction, it follows that P does not exist, and thus V is empty. QED.

An alternative, direct proof of the theorem was provided by the California Supreme Court; their proof applied the definition of equality.

Consideration of the many straight-forward corollaries of this theorem are left to the reader.