A Scaffold for Nothing

It’s been fun VCE times down here in Victoria, but reportedly there have also been issues up north. While our students have been lamenting their inability to calculate the area of a 20 x 20 square (Murdoch, paywalled), New South Wales’ HSC students have been struggling with projectiles subject to air resistance. Same same.

About a week ago, the Sydney Morning Herald contained an op ed by Scott Lankshear, head of mathematics at SCEGGS, a prestigious Sydney school. Titled HSC maths exam gets an F for failing our students, Lankshear expressed his anger with the “unreasonable and inaccessible” mathematics exams, and indicated his concern for the “devastated” students. Lankshear took particular aim at the exam for Extension 1 mathematics, a half-subject ostensibly comparable to VCE’s Specialist Mathematics.* Lankshear also connected the “disillusioned” students to “Australia’s falling numeracy standards”, suggesting such papers will “impact upon attitudes towards mathematics for years to come”.

Maybe Lankshearshear is right about all this. I doubt it.

I haven’t looked closely at the HSC exams, and perhaps they are more difficult than was reasonably expected, or were otherwise unfair. Perhaps even after scaling some students will be short-changed. But for a Victorian looking at the NSW mathematics exams the most striking aspect is that the exams contain some mathematics. And Lankshear’s fundamental argument for changing the exams was disturbing, potentially directing NSW down the road to Victorian mediocrity.

Lankshear placed the blame for the exams’ alleged flaws on NESA, the NSW curriculum authority. Lankshear begins by quoting from NESA’s advice on the mathematics curriculum introduced in 2019. Here is the entire passage from which Lankshear excerpts, in which NESA explains the purpose of items (i.e. questions) worth larger marks:

Why has NESA specified that there will be a certain number of items that are worth 4 or 5 marks?

Items worth larger mark values (eg 4 or 5 marks) provide opportunities for students to demonstrate depth of knowledge and application of skills. Students are presented with a substantial problem to solve with less scaffolding than a similar question broken up into smaller mark value parts. In these larger mark value items, students will be required to make more decisions about the method(s) that they use to solve the problem. [emphasis added]

Lankshear responds to NESA’s advice with disbelief:

“I would like to know what is wrong with scaffolding.”

It seems that a horse can lead himself to water and still not drink.

What’s wrong, and which is plenty clear from NESA’s advice, is that if you scaffold every damn time then you don’t ever test whether students can solve a substantial problem.

It is still possible that Lankshear has a point. Perhaps Lankshear is correct in claiming the HSC exams contained “too many of this style of question”. I doubt it, but it is possible.

Lankshear seems blissfully unaware, however, of the insidious flip side, of purportedly serious exams degenerating into the testing of nothing but trivial steps of a pointless scaffold. Lankshear should take a look at Victoria’s VCE nothing exams, together with their inevitable consequence of a culture of anal-retentive nitpicking and fearful rule-following, where proper mathematical thought is irrelevant when it is not actively punished. Lankshear might then acknowledge and be thankful not just that the NSW grass is greener, but that NSW has any grass at all. We Victorians would kill for some grass.

In Mathematics in Hell I devoted a little time to comparing the 2019 Specialist Mathematics Exam 2 with the 1979 Victorian HSC Applied Mathematics Exam (beginning at 35:45). I showed the 10 mark question on the Applied exam, contrasting it with the 5 mark question on the Specialist exam, which was as high as Specialist went. I then gave the following as the complete mark breakdown for the Specialist exam (including the twenty multiple choice questions):

(20 x 1) + (12 x 1) + (18 x 2) + (2 x 3) + (1 x 5)

Now, the 2022 Specialist Exam is even worse:

(20 x 1) + (12 x 1) + (18 x 2) + (4 x 3

Such numbers cannot tell the whole story, but neither do they lie.** The truth these numbers tell is that VCE mathematics is now little more than the testing of trivia and adherence to dogma. And the trend to trivia is clearly much more general, extending beyond Victoria and beyond Australia.

If NSW’s NESA is bucking, or even reversing, this trend, then thank God and all power to them. Scott Lankshear might stop whining and be quietly grateful for what NSW has.


*) The 2022 HSC Advanced Mathematics exam is here, and 2022 Extension 2 exam is here. Advanced Mathematics plays the role of VCE’s Mathematical Methods. There is nothing in VCE mathematics which is even remotely comparable to Extension 2.

**) Unsurprisingly. the story is significantly worse than indicated by the bare numbers. Still the bare numbers tell a loud story, and here is a little more detail of that story. The Specialist (CAS) exam is 120 minutes and a total of 80 marks; thus a 5 mark question is expected to take about 7.5 minutes. The 1979 Applied (scientific calculator) exam was 180 minutes and a total of 160 marks; a 10 mark question would have been expected to take about 11 minutes. The breakdown for the Applied exam cannot be determined precisely, because a question containing related sub-questions has only a total mark indicated for the question. (This matters. A lot.) Here is my estimated breakdown for the Applied exam: 

(2 x 1) + (14 x 2) + (10 x 3) + (5 x 4)  + (5 x 5) + (3 x 7) + (3 x 8) + (1 x 10

35 Replies to “A Scaffold for Nothing”

  1. Recommendation for people who enjoy teaching:
    Tutor an Extension 2 student.
    Since the advent of Zoom and Teams this means that people outside of NSW can actually enjoy teaching non-trivial things to excellent students. I have had 2 students in each of 2021 and 2022. It has saved my sanity and gave me hope that someone still has a clue about education

    VCE is dross and should be regarded as such

    Typical of someone to want to wreck it on a pointless and counterproductive equity crusade. Shame on you Scott Lankshear.

  2. Attached is my lesson for a class on probability this week. This is for students in Years 8 and 9 who have only just stated probability (again – probably they started it in year dot). I think that this illustrates scaffolding – as I understand the meaning of the term.

    PS I don’t know the answer to Q3 although I have asked several experts questions like this. But is generates considerable discussion. In the last lesson I asked similar questions about Victoria; but it could have been better. I decided to ask these questions about Germany because many students in the class are studying German.


    1. Sheesh.

      Terry, the argument isn’t whether teaching and exercises should (sometimes) involve scaffolding. The argument is why Victoria tolerates the perversion of exams, which now contain nothing but scaffolding.

  3. I’ve looked through the exam but haven’t sat it under exam conditions. The questions are not overly difficult (*) but I can understand concerns over the exam being too long. I like the lack of scaffolding – it means that students won’t get penalised in a simple 1 mark question that VCAA subsequently decides requires four lines of working, two of which are totally trivial (I can’t recall the exact exam this happened in), or for forgetting units.

    The projectile motion question was routine but long.

    And how damning of VCAA to note that yet again, NESA is able to publish the exams a mere couple of weeks after students sat them. We will be waiting until at least April 2023 for the VCE exams to get published. What a disgrace.

    * But I think many Victorian Specialist Maths students would struggle to correctly answer most of the questions covered by the VCE Study Design. I can imagine an outcry at the first few multiple choice questions (questions which I think are terrific, by the way).

    1. @JF: On multiple choice questions in general: I do not have a copy of the exam. But suppose that I offer the answer C for a multiple choice question. What does C tell the examiner about my learning – which is the main purpose of any assessment?

      1. Terry, I’m happy to answer your question by directing you to Multiple Choice Question 18 of 2022 Specialist Maths Exam 2:

        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

        A. 0.0448
        B. 0.0897
        C. 0.1151
        D. 0.2301
        E. 0.9103

        So you tell me – What does each option tell us about student understanding (assuming students work their way towards a particular option)?

  4. I saw this too. Just very silly and short-sighted. Also, weird. Extension 1 and 2 exams are quite tough on purpose and aggressively scaled. If a student comes out of those exams thinking they have close to 100% on raw marks, they might just get a top 10 in the state.

    So, for an experienced teacher to use student gripes as a reason why an exam is too tough…. quite odd.

    Thanks for positing. Speaking as a NSW-man, everyone is complaining about our curriculum. From both sides. I’m sometimes hopeful that this has the overall effect of inaction.

      1. As in, there are people that want the curriculum to have less content and there are those that want it to have more. More of the former than the latter. But still enough of the latter to count. Last thing I heard from education was that they want to make a new subject between general and “advanced”. There is actually some merit to this but I’d say it is better to shuffle the topics between general-advanced-extI than make a new subject.

    1. Glen, I understand this may be asking a bit much, but could you outline what those complaints are; or perhaps mention where one could read more about these complaints? Thanks

      1. Hi SRK, my info is from talking to teachers and education people, as well as the local mathematicians. Not much is written down to refer to. One example is the handling of limits has been somewhat ruined in advanced, it used to be ok, now it is superficial pointlessness. That would be one example from people lamenting the weakening of the curriculum. An example from those opposing would be on integration, where there are a million ways taught to evaluate an integral and several of these we re-teach at uni. So this is taken as supporting the idea that these topics are possibly too advanced.

  5. I moved from NSW to Victoria, and I think Extension 2 is equivalent culturally to Specialist. It’s a subject no one needs to do as a prerequisite, so people usually only do it if they like maths. At public schools, you get little classes with 5ish students doing them. They seem similar in that way, regardless of the exam and the content.

    On the other hand, I don’t think there is an equivalent to General/Further up north, because there’s no equivalent (I don’t think) to the bound reference. If you judge a course by what it makes students think about and focus on, then from my observations, VCE General Maths seems to be about bound references.

          1. Oh, sometimes people ask “did you do Specialist at school?” I’ve always said: “no, I’m from NSW, but I did the NSW version.” I didn’t realise.

            1. Compare the exams. I take what you get that both subjects are primarily done for other than prereq reasons. But macramé also isn’t a prereq. Specialist is closer to macramé than Extension 2.

              1. I’ll comment to clarify what I mean by culturally equivalent, and also to say I agree that they aren’t the same subject. I think if you took a student in NSW that was inclined to take Extension 2, and transplanted them to Victoria, then they would most likely take Specialist Mathematics; and vice versa. I’ve interpreted people asking “did you do Specialist?” as a kind of short-hand for “did you enjoy maths at school and want to take the highest level that was readily available to students at an ordinary school?” and Extension 2 would be that too. Perhaps that means Victorian students are being let down. Opportunities to learn some interesting stuff are being missed.

                1. Thanks, wst. Yes, the two subjects are serving the same role. One is doing that well, and the other is offering macramé.

        1. One part I disagree with is
          “It’s a subject no one needs to do as a prerequisite, so people usually only do it if they like maths.”

          You will find many students do it purely for the scaling, which they think will help them get into medicine.

          I also disagree that Extension 2 and Specialist are culturally equivalent. You only have to look at curriculum documents and exams to see the vast cultural difference between the two.

          1. NSW Extension 1 and 2 is a glimpse in to a world that Victorian teachers can only dream of (unless they teach IB HL)

  6. From what colleagues tell me on NSW facebook pages teachers were complaining something similar to Lankshear. The main gripe was the questions were testing students what they CAN do with THEIR knowledge, not reproduce what was taught to them.
    Surely that is the point of a good exam, to see if students can think and not just parrot answers. It is a shame that to make things accessible people want to dumb it down instead of building students up to be ready for the challenge.

    1. Marty has made this point before, but it’s an inevitable outcome of the education system being perverted for sufficiently long that the current teachers are inflicting upon their current students the same degraded curriculum /assessment they once received.

    2. The weird thing for me is that this is what the exams are like every year. Or maybe it’s not weird, and I should just realise we are experiencing a typical media cycle for this time of year…

  7. Lis trened to a conversation with Katherine Birbalsingh ( after a tradie talked to me about her/her school).
    Once i hit a section when she mentioned “scaffoldind” about 5 ti mnes i real iised the obvious explanation:
    It is something you build in students gradually, ober the junior/middle(/senior?) years so they are able to construct the solutions to multi-stade, sophisticated problem. They should be able to accomplish it by the examination time. – not scaffolding the examination problems.
    And that would be it.

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