PoSWW 22: A Distant Reality

Please make it stop. This one is a multiple choice question from the 2009 Specialist Exam 2. The examination report gives the answer as A, without comment.

38 Replies to “PoSWW 22: A Distant Reality”

  1. Yeah, that’s pretty bad. Not much more to say about that question.

    My experience with the examiners reports has been that they are “to talk about how students went on the exam, not about the exam itself” (paraphrased). Which is a bit of a cop out.

    1. A bit of a cop out? Ya think? It is ensuring and confirming how ritualistic and meaningless it all is.

      There is no way on God’s green earth that VCAA hadn’t heard about this error years ago. It is absolutely certain that they consciously chose to leave an error uncorrected, and that is simply insane.

      1. It’s likely that VCAA has been reminded of this error more recently but has decided it has better things to do with its time than acknowledge and fix its past mistakes.

        In taking this arrogant attitude, VCAA chooses to forget that many students do these older exams, find these mistakes, look at the Examination Reports and get confused by what they (don’t) see. Then teachers have to waste time cleaning up VCAA’s shit. And then some students start worrying about what will happen if VCAA screws up on the exam \displaystyle they're sitting in a few weeks.

        1. It’s not just VCAA papers – the time I have spent this year cleaning up some of the commercial papers – and the kids who are full of self doubt because of the issues on those papers.
          But then, VCAA should be producing higher quality and more reliable assessment tasks than some underpaid and overworked casual employee of one of the commercial paper mills.

          1. Of course VCAA exams should be of higher quality. But don’t waste your sympathy on the con artists getting paid thousands of dollars for writing shit. Simon, these “underpaid and overworked casual employee[s]” make a shit load of money from writing exams for commercial organisations. Which is ironic given that what they write is shit.

            I’ve commented elsewhere on the pathetic standard of commercial exams (and the ‘solutions’), particularly noticeable this year. I told my school not to buy any but of course it bought them anyway. Big mistake, waste of money. What they bought was shit. Staying away from The Shit Shit Mathematics requires no insight but schools keep wasting their money.

            The probability and statistics questions are always particularly bad. I’ve commented on this elsewhere. Most of the writers don’t understand this stuff but are happy to get paid for writing dodgy questions on it.

            1. Fair enough – I’ve only known a couple of people who wrote commercial tasks and they weren’t paid enough to spend the time to do a good job… but I guess it depends on the company?

              And yes – the probability and statistics questions are shocking in some papers. Literally the people writing them don’t know what a confidence interval is.

  2. Last I recall, a metric has the property of being non-negative, something the intended answer of A does not have. If z=-2 the distance should be d(-2,-(-2)) = 4 and not 2\text{Re}(-2) = -4…. Out of curiosity, what part do differential equations and slope fields play in this?

  3. Wasn’t there a Paper 1 question with a similar issue, also the topic of a blog post more than a year ago?

    OK, there are some issues here that z is not defined in any way; more recently they would probably write z=x+yi where i^{2}=-1 and so forth.

    Similarly, distance is a tricky concept in the complex plane, depending on how one views it (although I can only assume from the answer that VCAA considers the Argand diagram as a quasi-Cartesian plane not the “cut-plane” which would make measurement of distance more of a challenge, quite possibly beyond Specialist 3&4…)

    1. RF, I’m not sure of the blog post to which you’re referring.

      In terms of “defining z”, the question is better as is, to not have the standard z = x +yi or whatever. z is a complex number, just like x is a real number, and no further notation should be introduced unless it is actively used.

      The concept of distance in the complex plane is absolutely clear, although how familiar students are with it is another question.

        1. Ah, two years ago. How time flies when you’re having a pandemic. Yeah, they’re not related. The 2018 one is probably worse: it’s not even wrong.

    1. For these multiple choice questions where “no answer is correct”, if they were not multiple choice, would there be a correct answer, in some cases?

      For instance, this question, I cannot see there being a correct answer, the way it is written.

      1. RF, if this was not a MCQ then there would be numerous correct answers (although there would be a secret form of answer known only to VCAA that would be acceptable).

        The Examination Report reveals that Option A was the ‘correct’ answer. There is no explanation. It’s not correct, of course … It’s clearly gives the wrong result for any complex number whose real part is negative. There’s no correct option.

        @Glen: You’re right 🙂 No amount of abnormal psychology can enter the pinhead and rationalise \displaystyle this error. The writer was an idiot. The vettors were idiots. (But VCAA keeps finding new idiots to replace the old idiots).

        The correct answer is either of

        F. \displaystyle 2 \left| \text{Re}(z) \right|

        (keeping in the spirit of the style options provided by VCAA).

        F. None of the above

        (back to the Hall Pass of the good old days).

      2. RF, there’s always a correct answer in the sense that the distance is the distance. The distance between two complex (or real) numbers \boldsymbol{{z}} and \boldsymbol{{w}} is \boldsymbol{|z-w|}. So, the distance between \boldsymbol{{z}} and \boldsymbol{-\bar{z}} is \boldsymbol{|z-(-\bar{z})|}. That’s a perfectly correct answer. That answer can then be simplified to \boldsymbol{|z+\bar{z}|}, and then further simplified to John’s answer.

  4. The purpose of assessment is to ascertain where a student is in his or her learning. Suppose that a student gives the answer A. What can you infer about the student’s learning?

    1. A. That they’ll end up becoming a VCAA Exam writer or vettor.

      B. They know how to live in VCAA World.

      C. They know nothing and guessed.

      D. They know something and guessed.

      E. None of the above.

      Personally, I think we can infer more about VCAA’s learning …

      1. I agree. Multiple choice is a cheap and nasty way of assessing a students ‘final’ understanding. But I think it has diagnostic value for quickly pre-testing a cohort. VCAA has all sorts of specious arguments for using multiple choice in its final exams. And look at how much money it saves in Further Maths.

    2. What’s in it for the Jews?

      Terry, the idiocy of this question is not an argument for your anti-MCQ stance, whatever the merits of your stance.

    3. Shouldn’t we be more concerned about there being a question with no correct answer that was incorrectly graded? Anything else is secondary.

      1. We are concerned. Problem is there are really only two solutions:

        1. Move to NSW. Maybe ACT – although in fairness I’ve never looked to see if they have different exams to NSW.
        2. Only teach IB.

        Since, for many teachers, neither of these options is a possibility, we go to a far-from-perfect option:

        3. Work out how best to prepare students for exams like this.

        1. OK… for those interested, schools set all the assessment in the ACT and then there is one territory-wide test (similar to the GAT here in Victoria) for all students that assists the BSSS in moderation of school results for the purposes of ATAR calculations.

          ACT separated its schooling system from NSW in 1976 apparently.

          (Marty, if this is too far off topic, just delete)

      2. Glen, I honestly think you’re wrong. I think the 2017 question is the much greater concern.

        The 2009 question above is, of course, disgraceful. It is astonishing that it got through to the exam, even more astonishing that it almost certainly got through the grading (as evidenced by the examination report indicating a “correct” answer, rather than all students being awarded the mark). It is also unconscionable that the examination report has remained uncorrected for 10+ years, despite it being absolutely certain that VCAA would have been told about the error very early on. Nonetheless, although it doesn’t fix the screwing up of the exam, the 2009 error is explicit, undeniable and can be noted. The VCAA, if they give a damn or are yelled at sufficiently (at least one of which I guarantee will happen), can now stop random teachers and students trying make sense of pure falsehood.

        Now, compare that to the 2017 question. The question is pretty much garbage from beginning to end, and it contains absolute lunacy. There is absolutely no question that students who sat the exam were penalised for not being able to comprehend the incomprehensible, much more than the 1-mark 2009 question. Nothing in the 2017 question, however, constitutes a clear, correctable error, and so VCAA will never admit, or be forced to admit, what a truly horrible question it is.

        The damage of the 2009 question is close to done, and was probably always limited. The 2017 question will actively poison teaching for many years to come.

        1. Ah Marty, I agree with you there. I’m responding to Terry — I was trying to compare the concern about using MCQ in general versus the concern in having wrong questions. Not comparing specific wrong questions to each other.

  5. Hi,

    Curiously …

    Given the empirical evidence in this blog shows that it is possible that there may be no or many correct answers to a MCQ

    What should the practical candidate do here?

    Pick the intended solution A for non negative Re(z) or write no correct solution (assuming this is possible)

    Steve R

    1. You can’t write “No correct solution” because the multiple choice questions are marked electronically, not by a human. No-one would see it. However:

      1) I’d alert the invigilator to the error.

      2) I’d leave a note in Section B (which DOES get read by a human): No correct solution to Section A Q6.

      3) At the end of the exam I’d demand a signed note from the invigilator that I’d raised the alert. I’d follow up with my school’s VCE coordinator and Assistant Principal.

      4) Once results came out, I’d pay the fee to see my exam booklet, including the breakdown of my results for Section A, with a trusted and competent teacher. If I didn’t like what I saw, VCAA’s ass is grass and my solicitor is the lawn mower. And I contact as many media outlets as possible with the story of VCAA’s dishonesty and deceit.

      If students did this (or schools did it on behalf of their students), I guarantee VCAA’s standards would rise very quickly.

      1. As a student, would have you done this? It seems like a lot to ask of someone stressing about their marks at this time of the year. However, do you think a parent or school has standing to push this forward without representing a particular student?

        1. Question 1. A: If I was a student in today’s environment, I like to think I’d have enough activist spirit in me to say yes. Particularly if I was taught by teachers I respected who had opened my eyes to how thoroughly reprehensible VCAA is.

          Question 2. A: Yes. Particularly if that parent or school is capable of bringing this to the attention of mainstream media. I think the public would be shocked at how thoroughly reprehensible VCAA is, particular the younger members of the public that have endured the VCAA system. I’d love to see VCAA held to public account. But errors in maths exams are not nearly as glamorous as

          1) a giant fighting robot in a History exam helping revolutionaries in Russia defeat the Czar, or

          2) plagiarism in an English exam, or

          3) defamation in the 2018 English:
          “A Melbourne cafe owner whose business was inundated with hundreds of negative online reviews following the VCE English exam is taking legal action against the state’s curriculum authority. Tara Conron, who owns the Calmer Cafe in Aberfeldie, is still assessing the fallout from a blunder in Wednesday’s exam, which asked students to analyse a scathing review of a cafe that shared an almost identical name to hers.”, or

          4) etc.

          “Maths multiple choice questions with no correct option”

          “Probability density function fails to integrate to 1”

          “Maths Examination Report has wrong answers”

          “Maths Stupid Design content is a farce”

          are not quite attention grabbing headlines for most people. Yet.

          1. Maybe a bit of creativity is needed.

            “Students sabotaged by faulty exams”

            “Math questions with no right answer test students mental limits”

            “Duty of care, mental health, and mathematics exams: BLAH”


            1. Glen, I really like your first headline. I’d read that!!

              (Aside: Apparently we’re genetically programmed to be feel outrage, just like we are to like sugar, fat and salt)

              And your third one is particularly poignant in these current times. I’d read that too. And your second one’s not too shabby either. You’re much better at this than I am!!

              What maths students really need in the exam are giant robots fighting on their side …

              (But the headline and subheading I’d \displaystyle really like to see – not that the public would be much interested – is:

              “VCAA to face IBAC
              Former Mathematics Manager forced to explain historical wrong-doings”

              I’d pay good money to read \displaystyle that article).

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