The question below is from the first 2020 Specialist exam (not online), which is discussed here.

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# PoSWW 14: Offering Real Choices

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23 Replies to “PoSWW 14: Offering Real Choices”

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The question below is from the first 2020 Specialist exam (not online), which is discussed here.

The answer is a = 8/3, b = 2 and c = -10/3.

No wait a minute … the answer is a = 4/3, b = 8 and c = -10/3. Uh oh … wait a minute … the answer is a = 8/Sqrt[3], b = 6 and c = -20/6 … Oops, nope, wait a second …

(Too easy, Marty. That question is a fish in a bucket and we’re the dynamite.

This is one of VCAA’s dumber “Give your answer in the form …” Laziness again for just not asking to “Find”)

Thanks, John. PoSWW questions are intended to be bucketed fish.

The answer could be a=0, b=0, c = the value of the integral. This would be “an obvious simplification” (JF below).

Could examiners have asked “Prove that …”?

Or, a=value of integral, b=1, c=0.

TM, I love it! The only problem is that it will look just like the answer found using a = 8/3, b = 2 and c = -10/3 …

Re: “Could examiners have asked “Prove that …”?”

No. Just get rid of the ridiculous “Give your answer in the form …” bullshit. It comes across as some try-hard wanker trying to look erudite (probably because it IS written by some try-hard …)

Could examiners have asked someone competent to check the question? Yes.

The lack of competent vetting is something that genuinely puzzles me.

Writing good and clear and error-free exams is always really hard, and for camels like Specialist and Methods it must be close to impossible, and really painful. So, I understand why it is difficult to find good, or even half-way competent, exam writers.

But vetting is not as hard as writing. The exams require the scrutiny of a willing and competent and attentive mathematician, and these people do exist. I understand that VCAA wouldn’t go near me with a bargepole, and that they actively blacklist anybody seen as a fellow traveller. But there are other suitable mathematicians around.

And there’s the problem in a nutshell. Rather than making objective and professionalism decisions on who to choose as exam writers, vettors, SAC reviewers etc, VCAA makes decisions based on nepotism and cronyism. And it’s the students and teachers who pay the price.

Maybe you’re right, that VCAA’s knee-jerk insiderism means they only look to 3rd rate insiders to vet the exams. But it still puzzles me. The exams, if nothing else, are so blatantly amateurish.

Puzzled? Why? You said it yourself: “3rd rate insiders to vet the exams”. And 3rd rate insiders to write the exams.

If they just stopped thinking they were so bloody shit-hot, stopped trying so hard to look erudite and just wrote the bloody questions, the exams would not be nearly so amateurish.

I have wondered if the “required form” nonsense is a consequence of the lack of transparency about marking schemes. Some of the time it feels to me like VCAA is trying to eliminate some of the doubts students might have about whether they’ve “simplified enough” to get an answer mark.

Of course, VCAA are also needlessly pedantic about some of these things, but if at least they were honest and transparent about the ways in which they were pedantic, it seems to me that would be an improvement, and would probably decrease the need for the “required form” provisos in exam questions.

Thanks, SRK. You’re probably right. And, VCAA probably regards the “in the form of” nonsense as being “honest and transparent”. But, even ignoring that VCAA is inept at it, the effect is appalling, just a further concentration of attention on triviality.

Very easy to fix. A statement in the Examination Report, the VCAA Bulletin and the Instructions box at the top of p2 of the exams that

*Any* arithmetically correct answer is acceptable

will remove every student doubt. The whole business of “Have I simplified enough” is toxic thinking that has flourished under VCAA. And the lack of transparency of the marking schemes is something that all teachers need to powerfully criticise at every opportunity. It is a total disgrace.

John, I don’t think this really does it. You do want reasonably simplified answers, and I think such an instruction as you suggest can be interpreted to accept correct but ridiculous answers.

Fundamentally I think the problem is that judging what is a “good” or “proper” answer has unavoidable elements of reason and subjectivity, based upon a solid and accepted culture. That is just reality and, if you ask 10-mark questions where fussing the final form may affect 1 mark, it is not a troublesome reality.

The fundamental problem is that VCAA refuses to contemplate reality. They perpetuate and milk the myth that there is some objective scale for the presentation of mathematical argument. It is idiotic, and it is fucking up everyone.

Concerning asking students to express an answer in a required form, one should ask, “What is the purpose of such a question?” Perhaps it is simply a way to make a 2 mark question into a 4 mark question, but one would hope for a deeper justification.

Is it a typo? Did they mean Q and wrote R?

I suspect they originally wrote Z and then realized that the answer wasn’t an integer so changed Z to R and…

…now we have a WiTCH.

Thanks, RF. It occurred to me that the “real” specification was an error. Error or intentional, it’s pretty damn funny.

And the examiners’ report will probably pretend nothing is wrong.

There’s no unique answer for either Z, Q or R. The best you can do is try and argue that c = -10/3 is unique on the grounds that VCAA has stated in Reports that obvious simplifications must be performed (so values like c = -20/6 are implicitly rejected).

Exactly!

Ha, I didn’t notice this one, I probably just mentally read it as Q.

I found the latter instances of the “required form” in Q8, Q9 more annoying. For instance, in Q8, would it have been acceptable to leave one’s final answer as since and are both real numbers?

Thanks, SRK. Note, as John points out, restricting to Q doesn’t make the form unique. You are probably correct, that the non-uniquenesses in Q8 and Q9 are more confusing. But, Q2 is funnier.

Given any real number , find three real numbers such that .

What is a real number anyway?