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)