Foundation Stoned

The VCAA is reportedly planning to introduce Foundation Mathematics, a new, lower-level year 12 mathematics subject. According to Age reporter Madeleine Heffernan, “It is hoped that the new subject will attract students who would not otherwise choose a maths subject for year 12 …”. Which is good, why?

Predictably, the VCAA is hell-bent on not solving the wrong problem. It simply doesn’t matter that not more students continue with mathematics in Year 12. What matters is that so many students learn bugger all mathematics in the previous twelve years. And why should anyone believe that, at that final stage of schooling, one more year of Maths-Lite will make any significant difference?

The problem with Year 12 that the VCAA should be attempting to solve is that so few students are choosing the more advanced mathematics subjects. Heffernan appears to have interviewed AMSI Director Tim Brown, who noted the obvious, that introducing the new subject “would not arrest the worrying decline of students studying higher level maths – specialist maths – in year 12.” (Tim could have added that Year 12 Specialist Mathematics is also a second rate subject, but one can expect only so much from AMSI.)

It is not clear that anybody other than the VCAA sees any wisdom in their plan. Professor Brown’s extended response to Heffernan is one of quiet exasperation. The comments that follow Heffernan’s report are less quiet and are appropriately scathing. So who, if anyone, did the VCAA find to endorse this distracting silliness?

But, is it worse than silly? VCAA’s new subject won’t offer significant improvement, but could it make matters worse? According to Heffernan, there’s nothing to worry about:

“The new subject will be carefully designed to discourage students from downgrading their maths study.”

Maybe. We doubt it.

Ms. Heffernan appears to be a younger reporter, so we’ll be so forward as to offer her a word of advice: if you’re going to transcribe tendentious and self-serving claims provided by the primary source for and the subject of your report, it is accurate, and prudent, to avoid reporting those claims as if they were established fact.

Implicit Suggestions

One of the unexpected and rewarding aspects of having started this blog is being contacted out of the blue by students. This included an extended correspondence with one particular VCE student, whom we have never met and of whom we know very little, other than that this year they undertook UMEP mathematics (Melbourne University extension). The student emailed again recently, about the final question on this year’s (calculator-free) Specialist Mathematics Exam 1 (not online). Though perhaps not (but also perhaps yes) a WitCH, the exam question (below), and the student’s comments (belower), seemed worth sharing.

Hi Marty,

Have a peek at Question 10 of Specialist 2019 Exam 1 when you get a chance. It was a 5 mark question, only roughly 2 of which actually assessed relevant Specialist knowledge – the rest was mechanical manipulation of ugly fractions and surds. Whilst I happened to get the right answer, I know of talented others who didn’t.

I saw a comment you made on the blog regarding timing sometime recently, and I couldn’t agree more. I made more stupid mistakes than I would’ve liked on the Specialist exam 2, being under pressure to race against the clock. It seems honestly pathetic to me that VCAA can only seem to differentiate students by time. (Especially when giving 2 1/2 hours for science subjects, with no reason why they can’t do the same for Maths.) It truly seems a pathetic way to assess or distinguish between proper mathematical talent and button-pushing speed writing.

I definitely appreciate the UMEP exams. We have 3 hrs and no CAS! That, coupled with the assignments that expect justification and insight, certainly makes me appreciate maths significantly more than from VCE. My only regret on that note was that I couldn’t do two UMEP subjects 🙂


WitCH 29: Bad Roots

This one is double-barrelled. A strange multiple choice question appeared in the 2019 NHT Mathematical Methods Exam 2 (CAS). We had thought to let it pass, but a similar question appeared in last’s weeks Methods exam (no link yet, but the Study Design is here). So, here we go.

First, the NHT question:

The examination report indicates the correct answer, C, and provides a suggested solution:

\Large\color{blue} \boldsymbol{ g(x)=f^{-1}(x)=\frac{x^{\frac15}-b}{a},\ g'(x) = \frac{x^{-\frac45}}{5a},\ g'(1) = \frac1{5a}}

And, here’s last week’s question (with no examination report yet available):

WitCH 27: Uncomposed

Ah, so much crap …

Tons of nonsense to post on, and the Evil Mathologer is breathing down our neck. We’ll have (at least) three posts on last week’s Mathematical Methods exams. This one is by no means the worst to come, but it fits in with our previous WitCH, so let’s quickly get it going. It is from Exam 1. (No link yet, but the Study Design is here.)

WitCH 26: Imminent Domain

The following WitCH is pretty old, but it came up in a tutorial yesterday, so what the Hell. (It’s also a good warm-up for another WitCH, to appear in the next day or so.) It comes from the 2011 Mathematical Methods Exam 1:

For part (a), the Examination Report indicates that f(g)(x) =([x+2][x+8]), leading to c = 2 and d = 8, or vice versa. The Report indicates that three quarters of students scored 2/2, “However, many [students] did not state a value for c and d”.

For Part (b), the Report indicates that 84% of students scored 0/2. After indicating the intended answer, (-∞,-8) U (-2,∞) (-∞,-8] U [-2,∞) or R\backslash(-8,-2), the Report goes on to comment:

“This question was very poorly done. Common incorrect responses included [-3,3] (the domain of  f(x); x ≥ -2 (as the ‘intersection’ of  x ≥ -8 with x ≥ -2); or x ≥ -8 (as the ‘union’ of x ≥ -8 with x ≥ -2). Those who attempted to use the properties of composite functions tended to get confused. Students needed to look for a domain that would make the square root function work.”

The Report does not indicate how students got “confused”, although the composition of functions is briefly discussed in the Study Design (page 72).

Monash Extends a Backhander

One of the better offerings for Victoria’s senior students is Extension Studies. Corresponding roughly to America’s Advanced Placement program, ES permits a school student to undertake a university subject as part of VCE, albeit as a lower weighted, fifth or sixth subject.

The extension studies program is not without its flaws. In particular, there are no externally defined curricula or standards, with, rather, each participating university shaping their ES subjects to match their own university subjects. Consequently, there is significant variance in the content, quality and difficulty of the ES subjects offered. This also creates issues for the AP aspect of the program; on occasion, students aligned with one university have had difficulty receiving credit from another; this subject mismatching has also been exacerbated by the arrogance of some university administrators. It can also be a non-trivial task finding keen and competent teachers for ES which, as always, means the wealthier private schools benefit much more than public schools. And, some weirdness from VTAC hasn’t helped matters.

Nonetheless, extension studies functions reasonably well overall and can be of genuine value to a keen or strong student. Apart from the immediate reward of richer study while at school, ES can give a student a jump on their university education and effectively lower their uni fees. (The fees, one is always obliged to mention, which were introduced by this Labor asshole.)

Which is why Monash University’s decision this year to cease offering extension studies is so disappointing, and so annoying. This has created the ridiculous situation where the John Monash Science School, which is, you know, Monash University’s science school, is having to look elsewhere for their extension studies. And of course it is not just future JMSS students that are being screwed around.

What was Monash’s reason? All they wrote to ES subject administrators was, “In recent years, there has been a consistent decline in the number of students taking up this opportunity due to a range of factors.”

Yeah, well, maybe. Maybe numbers have declined, although enrolment in mathematics (with which we’ve been associated) has been healthy and stable. And, Monash might have mentioned that amongst the “factors” in that “range” are Monash’s relatively high cost for a participating student, combined with Monash’s effective discouragement of the participation of smaller schools.

It’s difficult to tell what is really going on, what is the real reason for Monash’s decision. The obvious suspicion is it has to do with money, although the program is not administratively heavy and ought to be pretty cheap to run; indeed, it’s the individual departments that have to pay for the academics to teach and administer and grade the subjects, almost certainly at a loss. The Mathematics Department has always lost money on the deal, and has never whined about it.

The other suspicion is that Monash’s extension program wasn’t attracting sufficient school students to study at Monash, whatever “sufficient” might mean. In contrast, the Mathematics Department has never worried about whether the program attracts more students to do mathematics at Monash; they’ve just accepted that that’s what a principled Department should do.

So, what was it? Was it Monash engaging in particularly obtuse neoliberal bean counting? Or, was it Monash disregarding any notion of community obligation? We’re not sure. But, we’re guessing the answer is “Yes”.

WitCH 24: The Fix is In

We’ve finally found some time to take a look at VCAA’s 2019 NHT exams. They’re generally bad in the predictable ways, and they include some specific and seemingly now standard weirdness that we’ll try to address soon in a more systematic manner. WitCHwise, we were tempted by a number of questions, but we’ve decided to keep it to two or three.

Our first NHT WitCH is from the final question on Exam 2 (CAS) of Mathematical Methods:

As usual, the NHT “Report” indicates nothing of how students went, and little of what was expected. In regard to part f, the Report writes,

p(x) = q(x) = x, p'(x) = q'(x) = 1, k = 1/e

For part g, all that the Report provides is the answer, k = 1.

The VCAA also provides sample Mathematica solutions to schools trialling Methods CBE. For the questions above, these solutions are as follows:

Make of it what you will.