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.)
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?
This one’s shooting a smelly fish in a barrel, almost a POSWW. Sometimes, however, it’s easier for a tired blogger to let the readers do the shooting. (For those interested in more substantial fish, WitCH 2, WitCH 3 and Tweel’s Mathematical Puzzle still require attention.)
Our latest WitCH comes courtesy of two nameless (but maybe not unknown) Western troublemakers. Earlier this year we got stuck into Western Australia’s 2017 Mathematics Applications exam. This year, it’s the SCSA‘s Mathematical Methods exam (not online. Update: now online here and here.) that wins the idiocy prize. The whole exam is predictably awful, but Question 15 is the real winner:
The population of mosquitos, P (in thousands), in an artificial lake in a housing estate is measured at the beginning of the year. The population after t months is given by the function,.
The rate of growth of the population is initially increasing. It then slows to be momentarily stationary in mid-winter (at t = 6), then continues to increase again in the last half of the year.
Determine the values of a and b.
Go to it.
As Number 8 and Steve R hinted at and as Damo nailed, the central idiocy concerns the expression “the rate of population growth”, which means P'(t) and which then makes the problem unsolvable as written. Specifically:
In the second paragraph, “it” has a stationary point of inflection when t = 6, which is impossible if “it” refers to the quadratic P'(t).
On the other hand, if “it” refers to P(t) then solving gives a < 0. That implies P”(0) = 2a < 0, which means “the rate of population growth” (i.e. P’) is initially decreasing, contradicting the first claim of the second paragraph.
The most generous interpretation is that the examiners intended for the population P, not the rate P’, to be initially increasing. Other interpretations are less generous.
No matter the intent, the question is inexcusable. It is also worth noting that even if corrected the question is awful, a trivial inflection problem dressed up with idiotic modelling:
Modelling population growth with a cubic is hilarious.
Months is a pretty stupid unit of time.
The rate of population growth initially increasing is irrelevant.
Why is the lake artificial? Who gives a shit?
Why is the lake in a housing estate? Who gives a shit?
Finally, it’s “latter half” or “second half”, not “last half”. Yes, with all else awful here, it hardly matters. But it’s wrong.
The marking schemes for the exam are now up, here and here. As was predicted, “the rate of growth of the population” was intended to mean “population”. As is predictable, the grading scheme gives no indication that the question is garbled garbage.
The gutless contempt with which certain educational authorities repeatedly treat students and teachers is a wonder to behold.
OK, after a long period of dealing with other stuff (shovelled on by the evil Mathologer), we’re back. There’s a big backlog, and in particular we’re working hard to find an ounce of sense in Gonski, Version N. But, first, there’s a competition to finalise, and an associated educational authority to whack.
It appears that no one pays any attention to Western Australian maths education. This, as we’ll see, is a good thing. (Alternatively, no one gave a stuff about the prize, in which case, fair enough.) So, congratulations to Number 8, who wins by default. We’ll be in touch.
A reminder, the competition was to point out the nonsense in Part 1 and Part 2 of the 2017 West Australian Mathematics Applications Exam. As with our previous challenge, this competition was inspired by one specifically awful question. The particular Applications question, however, should not distract from the Exam’s very general clunkiness. The entire Exam is amateurish, as one rabble rouser expressed it, plagued by clumsy mathematics and ambiguous phrasing.
The heavy lifting in the critique below is due to the semi-anonymous Charlie. So, a very big thanks to Charlie, specifically for his detailed remarks on the Exam, and more generally for not being willing to accept that a third rate exam is simply par for WA’s course. (Hello, Victorians? Anyone there? Hello?)
We’ll get to the singularly awful question, and the singularly awful formal response, below. First, however, we’ll provide a sample of some of the examiners’ lesser crimes. None of these other crimes are hanging offences, though some slapping wouldn’t go astray, and a couple questions probably warrant a whipping. We won’t go into much detail; clarification can be gained by referring to the Exam papers. We also don’t address the Exam as a whole in terms of the adequacy of its coverage of the Applications curriculum, though there are apparently significant issues in this regard.
Question 1, the phrasing is confusing in parts, as was noted by Number 8. It would have been worthwhile for the examiners to explicitly state that the first term Tn corresponds to n = 1. Also, when asking for the first term ( i.e. the first Tn) less than 500, it would have helped to have specifically asked for the corresponding index n (which is naturally obtained as a first step), and then for Tn.
Question 2(b)(ii), it is a little slack to claim that “an allocation of delivery drivers cannot me made yet”.
Question 5 deals with a survey, a table of answers to a yes-or-no question. It grates to have the responses to the question recorded as “agree” or “disagree”. In part (b), students are asked to identify the explanatory variable; the answer, however, depends upon what one is seeking to explain.
Question 6(a) is utterly ridiculous. The choice for the student is either to embark upon a laborious and calculator-free and who-gives-a-damn process of guess-and-check-and-cross-your-fingers, or to solve the travelling salesman problem.
Question 8(b) is clumsily and critically ambiguous, since it is not stated whether the payments are to be made at the beginning or the end of each quarter.
Question 10 involves some pretty clunky modelling. In particular, starting with 400 bacteria in a dish is out by an order of magnitude, or six.
Question 11(d) is worded appallingly. We are told that one of two projects will require an extra three hours to compete. Then we have to choose which project “for the completion time to be at a minimum”. Yes, one can make sense of the question, but it requires a monster of an effort.
Question 14 is fundamentally ambiguous, in the same manner as Question 8(b); it is not indicated whether the repayments are to be made at the beginning or end of each period.
That was good fun, especially the slapping. But now it’s time for the main event:
Question 3(a) concerns a planar graph with five faces and five vertices, A, B, C, D and E:
What is wrong with this question? As evinced by the graphs pictured above, pretty much everything.
As pointed out by Number 8, Part (i) can only be answered (by Euler’s formula) if the graph is assumed to be connected. In Part (ii), it is weird and it turns out to be seriously misleading to refer to “the” planar graph. Next, the Hamiltonian cycle requested in Part (iii) is only guaranteed to exist if the graph is assumed to be both connected and simple. Finally, in Part (iv) any answer is possible, and the answer is not uniquely determined even if we restrict to simple connected graphs.
It is evident that the entire question is a mess. Most of the question, though not Part (iv), is rescued by assuming that any graph should be connected and simple. There is also no reason, however, why students should feel free or obliged to make that assumption. Moreover, any such reading of 3(a) would implicitly conflict with 3(b), which explicitly refers to a “simple connected graph” three times.
So, how has WA’s Schools Curriculum and Standards Authority subsequently addressed their mess? This is where things get ridiculous, and seriously annoying. The only publicly available document discussing the Exam is the summary report, which is an accomplished exercise in saying nothing. Specifically, this report makes no mention of the many issues with the Exam. More generally, the summary report says little of substance or of interest to anyone, amounting to little more than admin box-ticking.
The first document that addresses Question 3 in detail is the non-public graders’ Marking Key. The Key begins with the declaration that it is “an explicit statement about [sic] what the examining panel expect of candidates when they respond to particular examination items.” [emphasis added].
What, then, are the explicit expectations in the Marking Key for Question 3(a)? In Part (i) Euler’s formula is applied without comment. For Part (ii) a sample graph is drawn, which happens to be simple, connected and semi-Eulerian; no indication is given that other, fundamentally different graphs are also possible. For Part (iii), a Hamiltonian cycle is indicated for the sample graph, with no indication that non-Hamiltonian graphs are also possible. In Part (iv), it is declared that “the” graph is semi-Eulerian, with no indication that the graph may non-Eulerian (even if simple and connected) or Eulerian.
In summary, the Marking Key makes not a single mention of graphs being simple or connected, nor what can happen if they are not. If the writers of the Key were properly aware of these issues they have given no such indication. The Key merely confirms and compounds the errors in the Exam.
Question 3 is also addressed, absurdly, in the non-public Examination Report. The Report notes that Question 3(a) failed to explicitly state “the” graph was assumed to be connected, but that “candidates made this assumption [but not the assumption of simplicity?]; particularly as they were required to determine a Hamiltonian cycle for the graph in part (iii)”. That’s it.
Well, yes, it’s obviously the students’ responsibility to look ahead at later parts of a question to determine what they should assume in earlier parts. Moreover, if they do so, they may, unlike the examiners, make proper and sufficient assumptions. Moreover, they may observe that no such assumptions are sufficient for the final part of the question.
Of course what almost certainly happened is that the students constructed the simplest graph they could, which in the vast majority of cases would have been simple and connected and Hamiltonian. But we simply cannot tell how many students were puzzled, or for how long, or whether they had to start from scratch after drawing a “wrong” graph.
In any case, the presumed fact that most (but not all) students were unaffected does not alter the other facts: that the examiners bollocksed the question; that they then bollocksed the Marking Key; that they then bollocksed the explanation of both. And, that SCSA‘s disingenuous and incompetent ass-covering is conveniently hidden from public view.
The SCSA is not the most dishonest or inept educational authority in Australia, and their Applications Exam is not the worst of 2017. But one has to hand it to them, they’ve given it the old college try.
Following our discussion with Charlie, we sent a short but strong letter to WA’s School Curriculum Standards Authority, criticising one specific question and suggesting our (and some others’) general concerns. Their polite fobbing off indicated that our comments regarding the particular question “will be looked into”. Generally on the exam, they responded: “Feedback from teachers and candidates indicates the examination was well received and that the examination was fair, valid and based on the syllabus.” The reader can make of that what they will.
Determine the errors, ambiguities and sillinesses in the 2017 WA Applications Exam, Part 1 and Part 2. (Here, also, is the Summary Exam Report. Unfortunately, and ridiculously, the full report and the grading scheme are not made public, and so cannot be part of the competition.)
Post any identified issues in the comments below (anonymously, if you wish). You may post more than once, particularly on different questions, but please don’t edit on the run with post updates and comments to your own posts. You may (politely) comment on and seek to clarify others’ comments.
This post will be updated below, as the issues (or lack thereof) with particular questions are sorted out.
Entry is of course free (though you could always donate to Tenderfeet).
First prize, a signed copy of A Dingo Ate My Math Book, goes to the person who makes the most original and most valuable contributions.
Consolation prizes of Burkard’s QED will be awarded as deemed appropriate.
Rushed and self-appended contributions will be marked down!
This is obviously subjective as all Hell, and Marty’s decision will be final.
Charlie, Paul, Burkard, Anthony, Joseph, David and other fellow travellers are ineligible to enter.
Employees of SCSA are eligible to enter, since there’s no indication they have any chance of winning.
All correspondence will be entered into.
Well that worked well. Congratulations to Number 8, who wins by default. Details are here. We’ll attempt another competition, of hopefully broader interest, in the near future.