This post continues on from the two previous posts, whacking VCAA’s internal response to Burkard’s and my critique of 2022 exam questions. This post will consider VCAA’s response to poorly written questions (part 5). It is, thank God, our last post on VCAA’s response.
********************************************************
Preamble
Burkard’s and my critique of the poorly written questions included a preamble:
The questions flagged in Sections 3 – 5 [on major errors, minor issues and poorly conceived questions] already provide many examples of poor writing, but it is important to understand how consistently poor the writing of VCE mathematics exams has become. Most questions could be improved with proper editing, and very many are so poorly written as to be difficult to read or much worse.
Evidently, a low priority has been put on writing questions in as clear and as short and as straightforward a manner as possible. Rather, the aim appears to have been inflexible adherence to a pedantic, overly-prescriptive and hence confusing formalism, and to following established but pointless conventions. Such needlessly confused wording must disadvantage ESL students. Such wording will also disproportionately disadvantage stronger students, who will potentially spend time looking for nuances that are not there. Hence, such wording indirectly benefits students trained not to read and not to consider the words, but rather trained to pick out key words in the salad and guess the intended question. We provide a few examples here, but the list could be much, much longer. The very long, multipart questions are too awkward to quote here, but are worth particular scrutiny. Seldom does the framing and length of these questions offer anything but confusion.
VCAA provided a specific response to the preamble:
The authors’ opinion is not supported by any evidence. The SSV [Study Specialist Vetters] and ESV [Examination Study Vetters] are experienced mathematicians and mathematics educators familiar with contemporary presentations of scenarios for the application of mathematics. Editing processes where subject specific content are present immediately trigger consultation with the CM [Curriculum Manager].
Any conventions followed in the development of examinations and the solutions are the same as those utilized in the Mathematics community. Significant effort goes into ensuring that genuine Mathematics conventions are followed, not bespoke operating procedures developed expresssly [sic] for the purpose of VCAA examinations.
EAL compliance is one of the editing layers. Any issues immediately trigger consultation with EDM [Examination Development Manager] and CM.
There is no psychometric evidence to support this contention.
Once again, VCAA simply does not know the meaning of “mathematician”, nor of “Mathematics community”. Properly solid mathematicians would simply not have signed off on the 2022 rubbish, and VCAA has no awareness of a “Mathematics community” beyond its own little clique. VCAA has no sense that VCAA’s conventions are often and strongly at odds with more widely accepted conventions. As for the claim that Burkard’s and my “opinion” is “not supported by any evidence”, there is not much one can say in response. In the critique, Burkard and I provided and pointed to plenty of instances of atrocious VCAA writing, and one either recognises them for being atrocious or one does not. VCAA did not.
After the introduction, Burkard and I provided a few specific examples of poor writing, noting,
We provide a few examples here, but the list could be much, much longer. The very long, multi-part questions are too awkward to quote here, but are worth particular scrutiny. Seldom does the framing and length of these questions offer anything but confusion.
Which is the case: VCAA writing has been so unremittingly poor, it has always been a shock to come across a well-written exam question. (I have tried to explain the general problem in two posts, here and here.)
For most examples provided in the critique, Burkard and I reproduced the offending text, commented briefly upon it and then suggested an alternative wording. In all but two instances, VCAA’s response consisted of absolutely nothing of substance, simply the chanting of an unaltering mantra:
The authors offer an alternative wording which is equivalent, yet offers no objective or subjective gain in clarity. The alternative wording renders question purpose less explicit.
In these instances, there is no need to respond to the response: I will leave it to the reader to judge.
Specialist Mathematics Exam 1 (exam here and report here (Word, idiots))
Q8
A body moves in a straight line so that when its displacement from a fixed origin O is x metres, its acceleration, a, is –4x ms–2. The body accelerates from rest and its velocity, v, is equal to –2 ms–1 as it passes through the origin. The body then comes to rest again.
Find v in terms of x for this interval.
The wording of this very standard kinematics question is not formally wrong, but it is crowded and disordered. More clearly, one could ask,
A body moves in a straight line, and at the origin O has a velocity of –2 ms–1. The acceleration of the body is –4x ms–2, where x is the displacement of the body from O in meters.
Find the velocity of the body in terms of x until the body comes to rest.
Mantra.
Specialist Mathematics Exam 2 (exam here and report here (Word, idiots))
MCQ6
Given z = x + yi, where x, y ∈ R and z ∈ C, an equation that has a graph that has two points of intersection with the graph given by |z − 5| = 2 is …
This is a very common phrasing, where a fussy pile of standard framing comes before the critical information, in this case the equation for the relation. An alternative:
Consider the relation |z − 5| = 2, where z = x + yi, and x, y ∈ R. A second relation for which the graphs of the two relations intersect at two points is …
The VCAA continues to seek to reduce ambiguity through the application of layers of editing to ensure that clear phrasing in common vernacular framing subject specific content and command terms will lead to examination questions that do not invite misinterpretation.
Huh?
MCQ18
The time taken, T minutes, for a student to travel to school is normally distributed with a mean of 30 minutes and a standard deviation of 2.5 minutes.
Assuming that individual travel times are independent of each other, the probability, correct to four decimal places, that two consecutive travel times differ by more than 6 minutes is
This is needlessly dense and tangled. The information and instruction should have been arranged so that the final sentence was simply “The probability that two consecutive travel times differ by more than 6 minutes is … ”.
Mantra.
Mathematical Methods Exam 1 (exam here and report here (Word, idiots))
Q2(a)
Find the rule for an antiderivative of g(x).
The phrase “the rule for” is, always, unnecessary and muddying, and is ubiquitous in VCE mathematics. Also, and astonishingly, it appears that the intention of “an antiderivative” is the literal meaning, that any antiderivative would have been accepted as an answer, with or without +c, with or without +59. However, the expression “the antiderivative” in VCE triggers that +c is required in the answer. To concern students with such micro-interpretation is absurd. It could all be avoided by simply, always, asking for the general antiderivative of the function.
The conventional mode for these question is that “an antiderivative” does NOT require the constant of integration. Teachers have been made well aware of this expectation in NTS [?] and external assessor reports in most years.
That teachers may be well aware of VCAA’s idiotic conventions does not make VCAA’s conventions any less idiotic.
Q6
The graph of y = f(x), where f : [0, 2π] → R, f(x) = 2 sin(2x)−1 is shown below. On the axes above, draw the graph of y = g(x), where g(x) is the reflection of f(x) in the horizontal axis. Find all values of k such that f(k) = 0 and k ∈ [0, 2π].
Such convoluted ordering, and the inclusion of fussy and often gratuitous detail is ubiquitous. An alternative:
Consider the function f(x) = 2 sin(2x) − 1 on [0, 2π]. The graph of f is shown below.
Let the function g be the reflection of f across the x-axis.
Draw the graph of g on the axes above.
Solve the equation f(x) = 0.
Mantra.
Q8
Part of the graph of y = f(x) is shown below. The rule A(k) = k sin(k) gives the area bounded by the graph of f, the horizontal axis and the line x = k.
The phrase “Part of” is unnecessary and distracting: if there is any other part of the graph, it is never considered. The second sentence is a tangle, including the needless “The rule”. An alternative:
The graph of the function f is shown below. The area bounded by the graph of f, the x-axis and the line x = k is given by the function A(k) = k sin k.
Mantra.
Mathematical Methods Exam 2 (exam here and report here (Word, idiots))
MCQ5
The largest value of a such that the function f : (−∞, a] → R, f(x) = x2 + 3x − 10, where f is one-to-one, is …
At minimum the “where” should be “for which”, but the entire sentence should be restructured, and would be best split into two. In general, preliminary information for a question should be clearly separated from and come prior to the final statement of the question, and this is too rarely done in VCE mathematics exams.
Mantra.
QB(1)(b)
State the derivative of f with respect to x.
This is literally using seven words where one would have sufficed: “Find f'(x)” is all that was required. Such verbiage is standard.
Mantra.
I have been following this stuff at a distance with interest, and generally agree with the criticisms (one thing that makes me gag in both the original question and the proposed amendment is “g(x) is the reflection of f(x) …”; is this just asking for the curve that is the reflection of the graph of f(x)? I am not aware that “g(x) is the reflection of f(x)” is standard mathematical terminolody. it might be more useful to ask for the function g(x) whose graph is the reflection…. )
This begs a few questions: who are the “mathematicians” involved in setting the questions? what teachers are involved — are they currently active in the classroom? what are the validation procedures? are the names of people on the examination committee publicly available? how are they chosen? to what extent are practising teachers engaged in the grading of the solutions?
I am not a teacher, but have served on committees to create and grade competitions with wide circulation, and am aware that setting problems is a ticklish issue and sometimes can lead to quite a struggle to get it right.
If I were the Victoria officials, I would invite Marty to serve on the examination committee. As the old saying goes, one should keep one’s friends close and your enemies even closer.
Concerning “This begs a few questions”.
Traditionally to beg the question is to use the conclusion of an argument as a premise. For example, I might offer a proof that God exists as follows.
Assume that God exists. etc …. Therefore God exists.
Most examples of this fallacy are more subtle.
The first examinations for school leavers in Victoria were held in the 1850s and were 3 hours long and the Mathematics exams (there were a few different ones) were usually less than two pages, 10 or so questions.
Even allowing nowadays for cover pages and diagrams, the two papers a Methods student (the same argument goes for Specialist) will need to work through in three hours will be closer to 50 pages worth of questioning.
This is the difference between having papers set by a university (and Mathematicians) as compared to papers set by a community of mathematics educators (basically teachers with a few auxiliaries maybe thrown into the mix).
well, there is also the point that the current exams have space for answers. But your point stands. The mincing of every question into tiny little fragments is insane.
Somewhere between 1930 and 1980 (depending on the state, the specific subject and your opinion about what constitutes major change) the format and structure of examinations for school leavers changed.
The CASification accelerated this in Victoria and caused a few other changes as well, but I believe the issues were present before this and as others have suggested in comments in the past, the VUSEB (which meant teachers rather than university academics writing a lot of the questions) seems to have been a major factor.
In a way, if you squint sideways and have had a few beverages, you can see some logic in the move towards having schools write assessments for school students. I’m not saying the logic is valid, nor that it is based on correct premises, but you can sort of see some path of reasoning that may have been taken.
I understood “this begs the question” as to the situation being such that one needs to get to the bottom of it, as opposed to a situation where one can take the situation for granted. To riff off Terry’s example, it I try to argue for morality on the case that God commands it, many individuals make take this as conclusive. But some may say, “This begs the question: ‘is there really a God?’ or ‘Does God really give a damn?'”
In the case of the examinations, in the past, most teachers probably accepted that they originated from a competent body whose membership they were only dimly aware of, but considering the trenchant criticisms on this site, it seems fair to look into the credentials of who actually is doing the job.
Thanks, Ed. What do you think the credentials, of either the teachers or mathematicians, would tell you?
Thanks, Ed. Possibly “graph of” is better added in, and I’m not fussed. There is room for differing conventions, and the points still stand. The points: VCAA has some weird-ass, and bad, conventions; and, even given their weird-ass, and bad, conventions, VCAA’s writing really really sucks.
I tend to pare down as much as possible, as long as the meaning is clear. In this instance, I think of “function” and “graph of function” as the same thing: the set of ordered pairs. Of course it is also reasonable and common to have language specifically for the drawing/picture. But I often find in school mathematics that this geometric language adds a layer of specifier that auto-muddies every sentence and really doesn’t add anything that cannot be added by the reader. It simply becomes ritual of language.
Does the the function have a gradient at a point, or is it “the tangent to the graph of the function” at that point that has the gradient? I prefer the former language. Am I permitted to say “stretching in the vertical direction” or do I have to say “dilation from the x-axis”? I believe VCAA demands the latter, even though it’s not the x stuff but the y stuff that is changing and thus the language routinely confuses the hell out of kids. The latter is much clearer, and is unambiguous as as long as every single dilation is from a coordinate axis, which in VCE it is.
I’ll respond to your other stuff later.
Thank again, Ed. I’ll try to answer your questions.
First, on your suggestion that VCAA invite me on the committee(s), that is never going to happen and it also never should happen. I’ve simply alienated too many people for me to be reasonably part of any such committee. I think that alienating was necessary, in order to expose VCAA’s systemic madness, but that it was necessary doesn’t make it any less true. But VCAA is not unaware of me and is not currently totally hostile to me (or vice versa). I did not have close ties to Kylie White, the previous CEO, but when we met we got along and I hugely appreciated her efforts, and her staff’s efforts. And while I think Kylie was probably never quite sure what to make of me, she definitely didn’t regard me as the enemy.
At the moment, I think VCAA is schizophrenic: it has some increasing hold on reality, but not a strong hold, and I have no faith that the reality function is monotonic. It would not be difficult for VCAA to return to its long-established cult practices. If nothing else, VCAA has poisoned a generation of teachers, who know no better than what VCAA (and ACARA) have taught them. Even a decade ago, kids were being taught CAS crap by teachers who at least knew what was *not* CAS crap. Now, kids are being taught by teachers who have seen nothing else. Once you lose a culture, of mathematics or of reading or of manners or of whatever, it is very difficult to get it back.
Now to your questions.
*) VCAA doesn’t know what a “mathematician” is. For the last thirty years, the writing and vetting has been dominated by teachers, but there were always “mathematicians” in some weak sense of the term. Evidently, they were not performing the role of “mathematicians” in any proper sense of the term. The big change with the Bennett review and Kylie White was that Monash signed on to supply mathematicians (plus there has been some fishing for solid mathematicians at other unis.) Monash’s name on it means they will take the whole thing very damn seriously, and they have been: Warwick Tucker, the HoM, has been outstanding. (The University of Melbourne has been woeful.)
*) The teachers involved are, I think, pretty much always active teachers (although not in the subject for which they are writing/vetting). But the whole thing has been a cult for decades: the same people, with very little variation, making the same idiotic mistakes. The reality is, there are very very few teachers in Victoria of sufficient strength and sense to write good mathematics exam questions. Even so, the writing of VCE exams has been pretty much owned by a cult. This may also be changing now, but probably much more slowly.
*) There are not “validation procedures” as such. Teachers apply and the VCAA chooses the “best” people, where “best” means “mates”.
*) I do not believe the names are public. Warwick Tucker indicated in a radio interview that he was one of the last-minute vetters in 2024, but I think that was an unusual declaration.
*) Currently, I do not know how teachers are chosen. One hopes that the clowns responsible for 2022 are not still involved but, as I wrote above, VCAA doesn’t have a lot to choose from.
*) Teachers grade the exams, under the direction of a Chief Assessor or something. The grading has often been nasty and idiotic, but this is not the fault of the teachers.
The VCAA response to Spesh 2 MC6 is next level word salad. Which is almost amusing given the context. Or at least, it would be if it weren’t so depressing. Far out.
I agree. It had occurred to me to do a separate PoSWW on that one question and response.
i posted a thread at https://community.boredofstudies.org/threads/complex-numbers-question.412344/ on it. They are more interested in nsw hsc but this got their attention. just a suggestion. when you say Word, idiots perhaps it would be better without the comma.
Thanks, Ty. I use “Word, idiots” to be short for “They used Word, they are thus idiots”. I think the comma is fine.