Vanessa’s Appt Concerns

Today, the Australian government released COVIDSafe, the Government’s coronavirus tracking app, based on Singapore’s TraceTogether version. The release comes complete with the Government’s predictable reassuring and cajoling and guilt-tripping. Should Australians trust them and use the app? Really? For us, there is a very simple answer: when and only when Vanessa Teague gives the all clear.

Vanessa is an expert on cryptography and, as it happens, is an ex-student and a good friend. She is very smart and is as principled a person as we have ever met. Along with many of her colleagues, Vanessa has been critical of the Government’s needless (and entirely predictable) secrecy over COVIDSafe. She has written a series of blogposts about their underlying concerns, and in particular the Government’s failure to follow up on promises and release COVIDSafe’s source code. This is Vanessa’s current stance on using the app (as of 23/04):

“In its TraceTogether form, I would be happy to run it on the train but refuse to run it in my home or office. I need to see the details of Australia’s version before I decide.”  

And, if that’s what Vanessa suggests then that’s what we’ll do, right up until Vanessa and her colleagues suggest otherwise. We’ll regularly be checking on Vanessa’s blog and twitter account.

 

Postscript: We had planned on writing about Vanessa a month or so ago, when she made the news. That story is highly relevant, since it involves privacy concerns, government screw-up, an arrogant and inept minister, a limp lettuce watchdog, a thuggish department secretary being matey matey with a vice chancellor, and a spineless university. Yep, same old, same old. But, given the speed of the times, we’ll probably have to leave that story be.

 

UPDATE (27/4)

The Minister for Health has today made an undertaking to release the source code “within two weeks”. We’ll see. (The formal agency response on privacy (26/4) states that such release will be “subject to consultation with the Australian Signals Directorate’s Australian Cyber Security Centre”.)

Vanessa and her colleagues have a new blog post (27/4). The post has been written “on a best-effort basis using decompiled code from the app, without access to server-side code or technical documentation.” Their conclusion:

Like TraceTogether, there are still serious privacy problems if we consider the central authority to be an adversary. That authority, whether Amazon, the Australian government or whoever accesses the server, can

    • recognise all your encryptedIDs if they are heard on Bluetooth devices as you go,
    • recognise them on your phone if it acquires it, and
    • learn your contacts if you test positive.

UPDATE (01/05)

We’re not going to bother with the nasty guilt-tripping on the COVIDSafe app, including from numerous media nitwits who should know better. This from Bernard Keane suffices.

Vanessa now has a very good twitter thread on the seemingly contradictory safe/not-safe messages from IT folk.

UPDATE (11/5) Vanessa has a twitter thread (08/05) on ScoMoFo’s latest round of silly buggers.

UPDATE (13/5) This will come as a great surprise, but it turns out that Greg Hunt is a dishonest piece of shit.

UPDATE (15/5) Vanessa and her colleagues have a new blog post (14/5): The missing server code, and why it matters.

UPDATE (20/5) Vanessa and her colleague Chris Culnane have a new blog post (19/5), on flaws in and corrections to the UK covid app (and why this was possible). Vanessa also has an accompanying twitter thread.

WitCH 36: Sub Standard

This WitCH is a companion to our previous, MitPY post, and is a little different from most of our WitCHes. Typically in a WitCH the sin is unarguable, and it is only the egregiousness of the sin that is up for debate. In this case, however, there is room for disagreement, along with some blatant sinning. It comes, predictably, from Cambridge’s Specialist Mathematics 3 & 4 (2020).

MitPY 6: Integration by Substitution

From frequent commenter, SRK:

A question for commenters: how to explain / teach integration by substitution? To organise discussion, consider the simple case

    \[\boldsymbol{ \int \frac{2x}{1+x^2}dx \,.}\]

Here are some options.

1) Let u = 1 + x^2. This gives \frac{du}{dx} = 2x, hence dx = \frac{du}{2x}. So our integral becomes \int \frac{2x}{u}\times \frac{du}{2x} = \int \frac{1}{u}du. Benefits: the abuse of notation here helps students get their integral in the correct form. Worry: I am uncomfortable with this because students generally just look at this and think “ok, so dy/dx is a fraction cancel top and bottom hey ho away we go”. I’m also unclear on whether, or the extent to which, I should penalise students for using this method in their work.

2)  Let u = 1 + x^2. This gives \frac{du}{dx} = 2x. So our integral becomes \int \frac{1}{u}\times \frac{du}{dx}dx = \int \frac{1}{u}du. Benefit. This last equality can be justified using chain rule. Worry: students find it more difficult to get their integral in the correct form.

3) \frac{2x}{1+x^2} has the form f'(g(x))g'(x) where g(x)=1+x^2 and f'(x) = \frac{1}{x}. Hence, the antiderivative is f(g(x)) = \log (1+x^2). This is just the antidifferentiation version of chain rule.  Benefit. I find this method crystal clear, and – at least conceptually – so do the students. Worry. Students often aren’t able to recognise the correct structure of the functions to make this work.

So I’m curious how other commenters approach this, what they’ve found has been effective / successful, and what other pros / cons there are with various methods.

UPDATE (21/04)

Following on from David’s comment below, and at the risk of splitting the discussion in two, we’ve posted a companion WitCH.

An Educational Conjecture

OK, time for a competition (And, no, we haven’t forgotten our previous competition, which we shall revive at some stage.)

Here is a conjecture:

Every new idea in modern mathematics education is either trivial or false.

Can we prove this conjecture? Of course not. Not, at least, without reading thousands of pages of educational gobbledegook. (Which. We. Will. Not. Do.) Is the conjecture true? We don’t know. But we are not aware of any counterexample.

The competition, then, is to attempt to prove the conjecture false. The winner is the commenter(s) who comes up with and argues most persuasively for a counterexample: the new idea in modern mathematics education that is true and the least trivial. The winner(s) will receive a signed copy of the number one best seller,* A Dingo Ate My Math Book.

Just a few notes on the parameters:

  • By “idea”, we mean any claim about or approach to teaching or learning mathematics.
  • By “new” we mean something other than dressing up a traditional idea in new clothing.
  • By “modern”, we mean from the last fifty years or so, back to about 1970.
  • By ”least trivial”, we mean something of genuine value, least trivial to mathematics education. So, deep ideas in neuroscience, for example, will score little if the subsequent application to mathematics education is trivial.
  • By “true” we mean true.
  • Suggestions, which can be made in the comments below, need not be long, specific or heavily documented. We will reply politely to any suggestion (and other are welcome to reply), querying and critiquing. Further argument and evidence can then be provided.
  • Will we be fair? Probably not. But, we’ll honestly try.
  • Multiple entries are permitted, and there may be multiple winners.

Go for it. We’re genuinely curious about what the responses may be.

*) In Polster and Ross households.

UPDATE (17/4)

Just a few (?) words about this competition, and this blog.

The competition is, of course, a challenge: put up or shut up. If a reader cannot propose and defend one single idea of modern mathematics education then that reader should perhaps stop imagining that any such idea exists. And, if such an idea does not appear to exist, the reader should consider what that suggests about the mountains of Wow produced by the maths education industry, and what it suggests of the shovelers creating these mountains.

Now, what could or should one expect the response to be to such a challenge on an aggressively antiestablishment blog such as this? This blog has a decently large (but not huge) readership, although we can only determine the nature of the readership from the minority who comment, which is obviously a very biased sample. Still, it is probably reasonable to place readers of this blog into three camps:

  1. There are the fellow travellers: like thinkers and “Marty fans”.
  2. There are puzzled and/or annoyed teachers, who smell that there is something wrong with their teaching world, while still maintaining some faith in the orthodoxy. They may appreciate some of the specific critiques on this blog, while not buying the overall message of contempt.
  3. There are the Marty haters, people who are convinced that Marty is an asshole or a nutcase,** who loathe this “nasty” blog, but who visit occasionally in order to feel superior.

This competition is primarily directed at members of Group 3, those who create and promote and value modern maths education. Again, it is a challenge: put up or shut up. If such a person cannot defend such ideas outside of the comfort of their cult, then there is no reason for anyone else to take them seriously.

Do we expect responses from members of Group 3? No, of course not. They regard debating on a blog such as this as beneath them. But the challenge is there, and it will remain there.

What about Group 2? Here, we’re guessing there are some thoughts of possibly defensible ideas, but there is probably some nervousness in proposing them. Such ideas will of course be critiqued (that’s the whole point), and strongly. So, we totally understand any such trepidation, although it is misguided. This blog is scathing of bad ideas, but it is respectful to all good faith commenters, which has been pretty much everyone.

Group 1 can take care of itself, of course, although its members could be more actively critical of this blog …

**) Both are true.

UPDATE (12/05)

OK, it seems like a good time to begin rounding this off. So, who is the winner? We’re not convinced anybody “won” in the sense that anyone has suggested a significant counterexample to our conjecture. None of the suggestions compares, for example, to the elephant truth that mathematics teachers need to understand mathematics a hell of a lot better than they do. None of the suggestions deals with the fundamental flaws of modern education, with, in particular, the deification of technology and the demonisation of discipline. We’re convinced as much as ever that modern educational “research” is fundamentally useless, when it is not actively destructive.

Still, if the suggestions below are minor in effect, some are good and sensible. We have thoughts on a winner, but we thought to let readers have a shot at it first. So, if you have an opinion on the best response to our challenge, please indicate below. We’ll consider, and we’ll announce our winner later in the week.

The Methods Intelligence Test

Psychologist Daniel Kahneman dedicates his book Thinking Fast and Slow  to the memory of Amos Tversky, his long-time collaborator. Tversky was considered so brilliant by his colleagues that they came up with the Tversky Intelligence Test:

The faster you realise that Amos Tversky is smarter than you, the smarter you are.

It has occurred to us that there is a similar Methods Intelligence Test:

The slower you realise that Methods is stupider than you, the stupider you are.

DIY Teaching Degrees

Dan Tehan, the Federal minister for screwing up education, has announced a rescue package for Australia’s universities. This was clearly necessary, since the universities are no longer in a position to fleece international students. The package guarantees funding for the universities, and introduces a range of cheap six-month courses in “areas considered national priorities”.

The government’s package is “unashamedly focused on domestic students”. That was inevitable since:

a) the government, and Tehan in particular, doesn’t give a stuff about international students;*

b) Tehan is a born to rule asshole, entirely unfamiliar with the notion of shame.

And, what of these “priority” courses? According to the ABC,

The Government said prices would be slashed for six-month, remotely delivered diplomas and graduate certificates in nursing, teaching, health, IT and science provided by universities and private tertiary educators.

OK, so ignoring all the other nonsense, we have a few questions about those six-month online teaching diplomas:

  • Will such a diploma entitle the bearer to teach?
  • If not, then what is it good for?
  • If so, then what is a school to do with the mix of 6-month diploma-qualified applicants and the standard 24-month Masters-qualified applicants?
  • And, if so, what does that tell us of the intrinsic worth of those standard 24-month Masters?

To be clear, we have no doubt that six months is plenty sufficient for the initial training of a teacher, and indeed is at least five months too many. We also have no doubt that a diploma-trained teacher has the same chance to be a good teacher as someone who has suffered a Masters. They have a better chance, in fact, since there will have been less time to pervert natural instincts and feelings and techniques with poisonous edu-babble.

But, good or bad, who is going to give these diploma teachers a shot? Then, if the teachers should be and are given a shot, who is going to address the contradiction, the expensive and idiotic orthodoxy of demanding two year post-grad teaching degrees?

 

*) Or anyone, but international students are near the bottom.

MitPY 4: Motivating Vector Products

A question from frequent commenter, Steve R:

Hi, interested to know how other teachers/tutors/academics …give their students a feel for what the scalar and vector products represent in the physical world of \boldsymbol{R^2} and \boldsymbol{R^3} respectively. One attempt explaining the difference between them is given here. The Australian curriculum gives a couple of geometric examples of the use of scalar product in a plane, around quadrilaterals, parallelograms and their diagonals .

Regards, Steve R