VCAA’s Responses to the Minor 2022 Exam Issues

Yes, we’re back in Red Rock West. For months, I’ve been bugged by VCAA’s internal response to Burkard’s and my critique of the 2022 exams. The thing is too unwieldy to warrant publishing as a whole, is replete with non sequiturs, statistical smokescreens and whatnot. Indeed, VCAA’s entire response amounts to a non sequitur Gish. I’ve been struggling to figure out what to do with it and I’ve decided to pretty much just go for it, in three separate posts.

Burkard’s and my critique contained four substantive sections on the 2022 Methods and Specialist exams, on: major errors (part 2); minor issues (part 3); poorly conceived questions (part 4); and poor writing (part 5). VCAA responded to it all, in some depth. I’ve substantially dealt with VCAA’s response to the five major errors, here and here. (There’s a little more in the internal response on the major errors but nothing enlightening or warranting further comment.) VCAA’s response to the other sections, the introduction and such, I’ve dealt with here. In two future posts, I’ll deal with the poorly conceived questions and poor writing. Here, I’ll deal with the minor issues.

Question by question, I will reproduce or paraphrase Burkard’s and my concerns, followed by the substance of VCAA’s response, followed in turn by my thoughts on this response. I will not reproduce VCAA’s responses in full because so much of it is stock nonsense and stock phrases, two in particular that are repeated, with variations, ad nauseam. The first, typically following some statistical voodoo, is

“The authors’ contention is not supported by cohort data.”

We’ve said it, many times, and we’ll keep saying it: psychometrician witch doctors are not the proper determiners of mathematical truth. The second phrase is,

“The question was not flagged by SSV [Study Specialist Vetter] or ESV [Examination Study Vetter].”

For VCAA, this lack of flagging was seemingly compelling evidence that the exam questions were fine. It is, rather, compelling evidence that VCAA’s writers and vetters were simply not up to the job.

Why hammer this now? Why not let sleeping dogs lie, even if flea-infested? Simply, I do not trust VCAA to have learned its lesson. VCAA’s internal response to 2022 was astonishing and appalling, utterly MAGAesque in its in-unison unwillingness to admit to the slightest error. With Kylie White in charge, I had some faith that things were changing, and indeed things did change: having solid mathematicians involved made a significant difference in 2024 and it will make a greater difference in 2025. Nonetheless, and particularly with White now gone, I am not convinced that the clowns of 2022 will not be around and feel re-empowered for 2025. In brief, although I do not believe VCAA will ever again be as idiotic as it was in and following 2022, there is a long, long way to go to make VCAA sane. At the moment, I do not trust VCAA to fix itself.

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Specialist Mathematics Exam 1 (exam here and report here (Word, idiots))

Q6(b)(i)

The question asks for vectors to be expressed in terms of x and y (and other terms), but is ambiguous: y has already been given as a function of x.

While y has been given as a function of x, this is clearly pertainig [sic] to the semi-circle on the diagram. [Then follows long and irrelevant blather about “position vectors” and “relative position vectors”] … 

A simple denial of reality, which also raises a concerning issue with VCAA’s exam report and VCAA’s assessment guide for the exam (obtained under FOI). The report and assessment guide indicate final answers for which the function has been substituted for y, and thus containing no y terms: this directly conflicts with the instructions in the exam question. There is no indication that unsubstituted answers were accepted and they damn well should have been. Either way, the question is fundamentally ambiguous and a silly essay about position vectors does not alter this truth.

Q6(b)(ii)

The question refers to “the vector scalar (dot) product”, which is confusing to the point of meaninglessness.

This is the exact wording from the study design (p.83, AoS4, dot-point 5) …

Here, “exact” is being used in the VCAA sense of the term. The expression used in the (then current) Study Design is “scalar (dot) product of two vectors”. In no sense, anywhere, does the Study Design refer to the scalar product as a “vector product”, which is the issue with the exam question.

Q10(b)

The question asks for the answer to be given in the form , with , and real. … The intended answer was …

This question was algebra heavy. For the first cohort that underwent two years of lockdown significantly impacting particularly their algebra skills in Mathematics, this particular wording provided essential leeway for those students. Where in previous years the final form of the answer was heavily constrained, this year flexibility was permitted.

Flexibility is fine. It is nonetheless important to understand that writing “∈ R” instead of “∈ Z” results in an instruction being meaningless and, thus, confusing.

Specialist Mathematics Exam 2 (exam here and report here (Word, idiots))

QB(4)(d)

“How far does the ball travel during the first four seconds after passing through O?”

The “passing through” framing is unnecessary and distracting: the ball can naturally be considered to have begun its travel at t = 0. The question is also ambiguous, since it is unclear whether arc length or Euclidean distance is being requested.

The question clearly asked “how far does the ball travel”, showing the ball path on a diagram.

The first point is not addressed at all, and the second point is inadequately addressed. Any question involving “distance” requires special attention, which was not exhibited here.

Mathematical Methods Exam 1 (exam here and report here (Word, idiots))

Q6(c)(ii) and (iii)

Part (ii) asks for “the smallest positive value for a”, which is confused: a has already been declared (implicitly) to be positive, and a has a single unknown value, not a set of values. Part (iii) then begins “Hence . . . ”, but this confuses what has been done in part (ii): determining the smallest positive/possible value of a is not the same as declaring a to have that value.

Students need to consider the set of values that “a” may take to decide how far left or right the basic shape must shift, then select the appropriate value. [Some blather on transformations]

[Some blather on “hence” versus “hence or otherwise”] “Hence or otherwise” was used here to provide students with that flexibility because they can use their part (ii) response, OR they can start from scratch and still arrive at the correct response.

The VCAA clowns simply failed to understand, much less appreciate, the concerns raised. They do not know how to write proper mathematics and so cannot see when they get it wrong.

Q8(c)

“Consider the average value of the function f over the interval x ∈ [0, k], where k ∈ [0, 2].”

The inclusion of “x ∈” is meaningless and confusing. The value k = 0 should have been excluded from consideration, since this moves the attention from the continuous to the discrete, and it seems that averages of discrete functions are not within the VCE Study Design.

On balance, Mathematical Methods students require more explicit scaffolding to gain access to questions. It is essential that students recognise that k is a subset of x-values, and that k effectively represents an x-value. …

VCAA really should learn the difference between scaffolding and mud. It is fair enough to want to flag that k is an x-thing, but that was not the way to do it: not only is the “x ∈” wrong, and thus confusing, the double “element of” phrasing of the sentence is extraordinarily clumsy. VCAA fails to address the second point, that k = 0 strays into the discrete, which is needless, potentially confusing and probably illegal.

Mathematical Methods Exam 2 (exam here and report here (Word, idiots))

MCQ9

The question asks for “the shortest distance” between two specific points, rather than simply asking for the distance, which is very badly misleading, suggesting that some max-min computation might be required.

The same rule providing the distance will also provide the shortest distance. These are effectively equivalent names. …

Maybe sometimes, but not properly here. And your name really sucks.

Kids were asked to find the “shortest distance” from (0,0) to (x,y), where x is fixed for the question and (x,y) lies on the graph of a given function. Given this scenario, VCAA really doesn’t believe that some kids, at minimum, wasted time pondering whether this was max-min or something? VCAA are either being unbelievably clueless or they are lying though their teeth. Given it is VCAA, both are live possibilities.