This is our post for discussion of the 2021 NHT Mathematical Methods exams (here and here). See also the accompanying 2021 NHT Specialist exams post, here. See also the relevant Witches: here, here and here.
Our final 2021 NHT WitCH is the final question from the Specialist Exam 1.
Sigh. We really hate updating WitCHes.* We have about a hundred of these things to do, and we’re generally thinking of the updating as a task for retirement or, better, for a reincarnation. However these NHT WitCHes, and this one in particular, have highlighted a degree of confusion. So, alas, it seems worthwhile sorting out the issues while the issues are in mind.
We’ve looked a little more closely at VCAA’s Draft for the new mathematics VCE subjects. Yes, the time for feedback has ended, unless it hasn’t: the MAV are offering a Zoom session TODAY (Thursday 25/3) for members. God knows how or why. But in any case, it’ll be a while before VCAA cements the thing in place: plenty of time to ignore everyone’s suggestions.
The following are our thoughts on the Draft and Overview. It will be brief and disorganised, since there is no point in doing more; as we wrote, the content doesn’t matter as much as the fact that, whatever content, VCAA will undoubtedly screw it up. Still, there are some clear and depressing points to be made. We haven’t paid much specific attention to what is new nonsense, and what is the same old nonsense; nonsense is nonsense.
GENERAL POINTS ON THE DRAFT
- The draft looks like a primary school book report. Someone at VCAA really should learn .
- “Computational Thinking” is meaningless buzzery, and will be endemic, insidious and idiotic. It will poison everything. Every step of Methods and Specialist is subject to the scrutiny of Outcome 3:
“On completion of this unit the student should be able to apply computational thinking and use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in practical situations requiring problem-solving, modelling or investigative techniques or approaches.”
“Statistical functionalities of technology”. And, there’s way more:
“key elements of algorithm design: sequencing, decision-making, repetition, and representation including the use of pseudocode.”
“use computational thinking, algorithms, models and simulations to solve problems related to a given context”
“the role of developing algorithms and expressing these through pseudocode to help determine and understand mathematical ideas and results”
“the purpose and effect of sequencing, decision-making and repetition statements on relevant functionalities of technology, and their role in the design of algorithms and simulations”
“design and implement simulations and algorithms using appropriate functionalities of technology”
This will all be the same aimless, pseudo-exploratory, CAS-drenched garbage that currently screws VCE, but much, much worse. Anybody who signs off on this idiocy should hang their head in shame.
- CAS shit will now be worse than ever.
- There should be no CAS exam, at all.
- There should be no bound notes permitted in any exam.
- Don’t write “technology”. It is pompous and meaningless. If you mean “CAS” then write “CAS”.
- SACs have always been shit and will always be shit. The increased weight on them is insane.
- The statistics is the same pointless bullshit it always was.
- The presence of “proof” as a topic in Specialist highlights the anti-mathematical insanity of VCAA and ACARA curricula: proof has zero existence elsewhere. Much of what appears in the proof topic could naturally and engagingly and productively be taught at much lower levels. But of course, that would get in the way of VCAA’s constructivist fantasy, now with New and Improved Computational Thinking.
- Not including integration by substitution is still and will always be the most stupid aspect of Methods.
- Dilations must be understood expressed as both “parallel to an axis” and “from an axis”? But not in terms of the direction the damn points are moving? Cute.
- The definition of independent events is wrong.
- The demand that, for the composition , the range of must be a subset of the domain of is as pedantic and as pointless as ever.
- “literal equations” is the kind of blather that only a maths ed clown could think has value.
- The derivative of the inverse is still not in the syllabus, and everyone will still cheat and use it anyway.
- “trapezium rule” is gauche but, more importantly, what is the purpose of teaching such integral approximation here? Yes, one can imagine a reasonable purpose, but we’ll lay odds there is no such purpose here.
- The killing of mechanics is a crime.
- The inclusion of logic and proof and the discrete topics could be good. But it won’t be. It will be shallow and formulaic and algorithmised, and graded in a painfully pedantic manner. Just imagine, for example, how mathematical induction will be assessed on exams: “Students often wrote instead of . Students should be aware of the proper use of these variables.”
- There is no value here in “proof by contrapositive”, and it is confusing. Proof by contradiction suffices.
- They’re really including integration by parts? Incredible.
- The inclusion of cross products and plane equations makes some sense.
You have a choice. The two questions below come from different exams:
- The first question was the final (half-)question from the NSW 2020 Mathematics Extension 2 Examination (scientific calculator permitted, plus provided formula sheet);
- The second question was the final question from the Victorian 2020 VCE Specialist Mathematics Examination (CAS calculator permitted, plus provided formula sheet).
Each question was (arguably) last year’s most difficult exam question on the most difficult mathematics subject in that state. Each question was effectively allocated just under 20 minutes to complete (11/100 x 180 and 13/80 x 120).
Now, you must choose: which question is better, in any sense of the word “better”?
NSW (Formula Marking guide and sample solution are here.)
VIC (Briefly discussed here, marking guide and sample solution are in your dreams.)
We’ve been remiss in not writing further on VCAA’s draft for the new mathematics VCE subjects. It’s just, for reasons we’ll explain briefly here and flesh out elsewhere, we’ve struggled to face up to this new nonsense.
But, feedback is due TODAY (midnight? – see links below), and we really oughta say something. So, here are our brief thoughts and then, after that, why we believe none of it really matters:
- “Computational thinking and algorithms” is pure snake oil. Inevitably, it will be nothing but wafer-thin twaddle for the training of data monkeys.
- The increased weight on these meaningless, revolting SACs is insidious.
- If we read it correctly, more weight will be placed on the non-CAS Methods/Specialist exams; it is not remotely close to enough, but it is good.
- Statistics was and is and will always be an insane topic to emphasise in school.
- Foundation Mathematics: Who Cares?
- General Mathematics: Who Cares?
- Mathematical Methods: same old swill.
- The deletion of mechanics from Specialist Mathematics is criminal, but the topic had already been so bled to meaningless that it hardly matters.
- In principle, the inclusion in SM of “logic” and “proof and number” and “combinatorics” is a good thing. We’ll see.
- Similarly, in principle the making of SM12 presumed knowledge for SM34 is good; in practice, it is almost certainly bad. Currently, a good teacher at a good school will take the freedom in SM12 to go to town, to show their students some genuine mathematics and real mathematical thought. In the future, that will be close to impossible, and SM12 will likely become as predictable and as dull as MM12 (and MM34 and SM34).
And now, why doesn’t any of it matter? Because, fundamentally it doesn’t matter what you teach, it matters how you teach. What matters is the manner in which you approach your subject and your students, and none of that will change in other than a microscopic manner. Nothing in VCAA has changed, nothing in the general culture of Victorian education had changed. So, why the Hell would twiddling a few dials on utterly insane subjects assessed in an utterly insane manner make any meaningful difference?
Everything VCAA touches, they will turn to shit. That will continue to be true until there is a fundamental cultural shift, in VCAA and generally.
I hate this place.
This combo WitCH comes courtesy of mystery correspondent, tjrb. They flagged three multiple choice questions from the 2018 Algorithmics exam (here, and examination report here), and we’ve added a fourth. tjrb also remarks, “There are probably a lot more errors in this paper (and the other algorithmics papers), but these were the most strikingly incorrect”.
For Q2, the examination report indicates that 41% of students gave the intended answer of A. By way of explanation, the report then remarks,
“Cobham theorised that problems that are feasibly computable (also known as easy problems) are those that are decidable in polynomial time.”
For Q6, the report indicate that both A (51%) and C (33%) were “accepted”, but is otherwise silent.
The report is silent on Q12 and Q16, except to indicate the intended answers: C (94%) and A (66%), respectively.