AMSI to the Rescue

The Australian Mathematical Sciences Institute has just released its Report on Australian Year 12 students’ participation in mathematics from 2008 to 2017. The Report indicates, of course, that the percentage of girls doing a “higher level” maths subject is lower than the percentage of boys. (One headline trumpets that “Less girls are studying maths than boys”, proving only that fewer journalists are studying grammar.) More generally, the overall participation in higher level maths is reportedly the lowest for 20 years.

Gee.

Who would have thought that a boring and aimless curriculum, and lousy texts, and the crappy training of teachers by clowns who have in turn had crappy training, and the belittling of Mathematics by the S and the T and the E of STEM, and the faddish genuflection to technical gods, and decades of just plain dumbing down would have pissed off so many students?

AMSI’s Report of the bleeding obvious doesn’t consider the causes of the decline in participation. Fair enough. The Report is seriously flawed, however, in failing to note that the meaning of “higher level mathematics” is not a constant. The “higher level mathematics” of 2017 is significantly lower than that of 1997, which is lower again than that of 1977. The problem is much, much worse than AMSI’s Report suggests.

AMSI is not just reporting on the decline in participation, they are supposedly working to fix it. AMSI’s new director, Tim Brown, has been out and about, discussing the Report. Professor Brown is reported as saying that the reasons for the decline are “varied”, but of these varied reasons, he appears to have indicated just two to the media; first, “a shortage in qualified maths teachers”; second, “teaching from the textbook” rather than “active learning”.

Really? With all those plump targets, AMSI chooses these two? Yes, the lack of qualified teachers is a problem, and a problem AMSI apparently enjoys talking about. And yes, the current textbooks are appalling. But such low-fruit targets are not the substantive problem, and false fixes of second order issues will do little or nothing to improve matters. The real issue is one of systemic cultural decline.

We believe Professor Brown knows this. The question is, will Professor Brown drag AMSI, finally, into waging the genuine, important fights that need to be fought?

NAPLAN’s Latest Last Legs

The news is that NAPLAN is on its way out. An article from SMH Education Editor Jordan Baker quotes Boston College’s Andy Hargreaves claiming tests such as NAPLAN are on their “last legs”. This has the ring of truth, since Professor Hargreaves is … who knows? We’re not told anything about who Hargreaves is, or why we should bother listening to him.

Perhaps Professor Hargreaves is correct, but we have reason to doubt it. And, Jordan Baker has been administering NAPLAN’s last rites for a while now. Last year, Baker wrote another article, on NAPLAN’s “death knell”.

Regular readers of this blog would be aware that this writer would love nothing more than to see ACARA sink into the sea, taking its idiotic tests and clueless curriculum with it. But it’s important to understand why, and why the argument for getting rid of NAPLAN is no gimme. It is here that we disagree with Hargreaves and (we suspect) Baker.

Baker quotes Hargreaves on national testing such as NAPLAN and its “unintended impact of students’ well-being and learning”:

[They include] students’ anxiety, teaching for the test, narrowing of the curriculum and teachers avoiding innovation in the years when the tests were conducted.

Let’s consider Hargreaves’ points in reverse order.

  • Innovation. Yes, a focus on NAPLAN would discourage innovation. Which would be a bad thing if the innovation wasn’t poisonous, techno-fetishistic nonsense. Hargreaves, someone, has to give a convincing argument that current educational innovation is generally positive. We’ll wait. We won’t hold our breath.    
  • Narrowing of the curriculum? We can only wish. The Australian Curriculum is a blivit, a bloated mass of pointlessness.
  • Teaching to the test is of course a bad thing. Except if it isn’t. If you have a good test then teaching to the test is a great thing.
  • Finally, we have to deal with students’ anxiety, a concern for which has turned into an academic industry. All those poor little petals having their egos bruised. Heaven forbid that we require students to struggle with the hard business of learning.

There is plenty to worry about with any national testing scheme: the age of the students, the frequency of the tests, the reporting and use of test results, and the ability to have an informed public discussion of all of this. But all of this is secondary.

The problem with the NAPLAN tests isn’t their “intended consequences”. The problem with the NAPLAN tests is the tests. They’re shithouse.

 

PoSWW 5: Intelligence is not a Factor

The following PoSWW comes courtesy of Franz, who states that “when it comes to ‘stupid curricula, stupid texts and really monumentally stupid exams’ no Western country, with the possible exception of the US, is worse than Germany.” We take that as a challenge, and we’re waiting for Franz to back up his crazy-brave claim.

Franz’s PoSWW, however, has nothing to do with Germany. This PoSSW follows on from two of our previous posts, on idiotic questions appearing in New Zealand exams. Franz wrote to us, noting that the same style of question appears in the Oxford Year 8 text My Maths. Indeed, a number of versions of this ludicrous question appear in My Maths, all inventively awful in their own way. The two examples below are enough to give the flavour:

PoSWW 4: Overly Complex

This PoSWW comes courtesy of a smart Year 11 VCE student who, it appears, may be a rich source of such nonsense. It’s an exercise in the Jacaranda text MathsQuest 11, Specialist Mathematics (2019).

To be honest, we’re not sure the exercise below is a PoSWW. It may simply be a minor error, the likes of which are inevitable in any text, and of which it is uninteresting and unfair to nitpick. But, for the life of us, we have no idea what the authors might have intended to ask. Make of it what you will:

UPDATE: For those hoping that context will help make sense of the exercise, the section of the text is an introduction to factoring over complex numbers. And, the text’s answer to the above exercise is A = 2, B = 5, C = -1, D = 2.

The VCAA Dies Another Death

A while back we pointed out two issues with the 2018 Specialist Mathematics Exams. The Exam Reports (though, strangely, not Exam 1) are now online (here and here). (Update 27/02/19: Exam 1 is now also online.) Ignoring some fresh Hell suggested by the Exam 2 Report (B2(b), B3(c)(i), B6(e)), how did the VCAA address these issues?

Question 3(f) on Section B of Exam 2 was a clumsy and eccentrically worded question that covered material outside the curriculum. Unsurprisingly the Report made no mention of these issues. But, what about a blatant error by the Examiners? Would they remain silent in the face of such an error? Again?

Question 6 on Exam 1 (not online) required students to find the “change in momentum” of an accelerating particle. Unfortunately, the students were required to express this change in kg m s-2. The Exam had included the wrong units, just a careless typo, but a blatant error. The Report addressed this blatant error with the following:

Students who interpreted this question as asking for the average rate of change of momentum to be dimensionally consistent with the units and did this correctly were awarded marks accordingly.

That’s it. Not an honest word of having stuffed up. Not a hint of regret or apology. Just some weasely no-harm-no-foul bullshit.

 

 

WitCH 9: A Distant Hope

This WitCH (as is the accompanying PoSWW) is an exercise and solution from Cambridge’s Mathematical Methods Units 1 and 2, and is courtesy of the Evil Mathologer. (A reminder that WitCH 2, WitCH3, Witch 7 and WitCH 8 are still open for business.)

Update

As Number 8 and Potii pointed out, notation of the form AB is amtriguous, referring in turn to the line through A and B, the segment from A to B and the distance from A to B. (This lazy lack of definition appears to be systemic in the textbook.) And, as Potii pointed out, there’s nothing stopping A being the same point as C.

And, the typesetting sucks.

And, “therefore” dots suck.

PoSWW 3: Not the Right Angle

This PoSWW (as is the accompanying WitCH) is from Cambridge’s Mathematical Methods Units 1 and 2. and is courtesy of the Evil Mathologer. (A reminder, we continue to post on Cambridge not because their texts are worse than others, but simply because their badness is what we get to see. We welcome all emails with any suggestions for PoSWWs or WitCHes.)

We will update this PoSWW, below, after people have had a chance to comment.

Update

Similar to Witch 6, the above proof is self-indulgent crap, and obviously so. It is obviously not intended to be read by anyone.

One can argue how much detail should be given in such a proof, particularly in a subject and for a curriculum that systemically trashes the concept of proof. But it is difficult to see why the diagram below, coupled with the obvious equations and an easy word, wouldn’t suffice.

 

WitCH 8: Oblique Reasoning

A reminder, WitCH 2, WitCH 3 and WitCH 7 are also open for business. Our new WitCH comes courtesy of John the Merciless. Once again, it is from Cambridge’s text Specialist Mathematics VCE Units 3 & 4 (2019). The text provides a general definition and some instruction, followed by a number of examples, one of which we have included below. Have fun.

Update

With John the Impatient’s permission, I’ve removed John’s comments for now, to create a clean slate. It’s up for other readers to do the work here, and (the royal) we are prepared to wait (as is the continuing case for WitCh 2 and Witch 3).

This WitCH is probably difficult for a Specialist teacher (and much more so for other teachers). But it is also important: the instruction and the example, and the subsequent exercises, are deeply flawed. (If anybody can confirm that  exercise 6G 17(f) exists in a current electronic or hard copy version, please indicate so in the comments.)

WitCH 7: North by Southwest

Our new WitCH, below, comes courtesy of Charlie the Enforcer. Once again, this WitCH is from the 2018 SCSA Mathematical Methods Exam (here and here): it’s the gift that keeps on giving. (And a reminder, WitCH 2 and WitCH 3 still require attention are still unresolved.)

Question 11 and the solution in SCSA’s marking key are below. Happy hunting.

Update

John has pretty much caught it all. The killer issue is the use of the term “deceleration” in part (c) which, the solution implies, refers to the drone speeding up in the southerly direction. This is arguably permissible, since deceleration can be (though is far from universally) defined as a negative acceleration, and since way back in part (a) it was implied that North coincides with the positive x direction.

Permissible acts, however, can nonetheless be idiotic: voting Liberal or Republican, for example. And, to use “deceleration” on a high stakes exam to refer implicitly to increasing speed is idiotic. Moreover, to use “deceleration” in this manner immediately after explicitly indicating the “due south” direction of motion is truly ruly idiotic. Still not as idiotic as voting Liberal or Republican, but genuinely special-effort idiotic.

That’s enough to condemn the question, even by SCSA standards. But, the question is also awful in many other ways:

  • The question is boring and butt ugly.
  • No indication is given whether exact or numerical solutions are permitted or required.
  • Having a drone an arbitrary 5m up in the sky for a 1D problem is asking for trouble. For example:
  • The “displacement” of x(0) = 0 for a drone 5m up is pretty stupid.
  • “Where is the drone in relation to the [mysterious] pilot?” Um, kind of uppish?
  • “How far has the drone travelled …” is needlessly wordy and ambiguous. If you want a distance, for God’s sake say “distance”.
  • Given the position function x(t) is at hand, part (c) can easily and naturally be solved by hand. But of course why think about things when you can do mindless calculator crap?