Discussion of the 2021 NHT Methods Exams

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.

UPDATE (08/10/21) The exam reports have reappeared, as PDFs, here and here. The exam 2 report has important updates, and important non-updates; see the comments in blue, below.

UPDATE (22/09/21) The exam reports are now out, here and here (VCAA-Word-Stupid). We’ve added a couple comments below, in green.

Continue reading “Discussion of the 2021 NHT Methods Exams”

WitCH 64: Decreasing Intelligence

Just in case anybody got the wrong impression and hoped or feared we’d turned over a new leaf, we’ll be posting a number of WitCHes in the next few days. We’ve finally had a chance to look at the 2021 NHT exams (although the exam reports have still not appeared). As usual, the exams are clunky and eccentric, and we’ll be posting a brief question-by-question overview of the exams. But, first, some highlights. Continue reading “WitCH 64: Decreasing Intelligence”

PoSWW 20: Unconventional Wisdom

This one comes courtesy of frequent commenter, John Friend. It is an example from Cambridge’s Mathematical Methods 34.

UPDATE (19/08/21)

It amazes me at times what does and does not concern some commenters. That’s not intended as a criticism. Well, it is, but it isn’t. And, it is. It’s complicated.

Continue reading “PoSWW 20: Unconventional Wisdom”

MitPY 13: Trigonometry and Wolfram Alpha

This MitPY comes from frequent commenter, John Friend:

Dear Colleagues,

I gave a CAS-FREE question to my Specialist students whose first part was to solve (exactly) the equation \boldsymbol{\cot 2x = \sec x}. I solved it two different ways and got two different answers that are equivalent. I’ve attached my calculations.

I checked my answers using Mathematica, which lead to my question: Mathematica gives a third different but equivalent answer (scroll down to real solutions). How has Mathematica got this answer?

It may be that Mathematica ‘used’ my Method 2, got my tan answer and then for some arcane reason ‘manipulated’ this answer into the one it finally gives. If so, I can ascribe the answer to a Mathematica quirk. But it may be that Mathematica is using a method unclear to me that leads to its answer. If so, I’m curious.

Any thoughts are appreciated.

Click to access Calculations.pdf

The VCAA Draft and its Third Rail

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 \LaTeX.
  • “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.

 

MATHEMATICAL METHODS

  • 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 \boldsymbol{f\circ g}, the range of \boldsymbol{g} must be a subset of the domain of \boldsymbol{f} 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.

 

SPECIALIST MATHEMATICS

  • 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 \boldsymbol{n} instead of \boldsymbol{k}. 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.

WitCH 58: Differently Abled

Like the previous post, this one comes from Maths Quest Mathematical Methods 11, and is most definitely a WitCH. It can also been seen as a “contrast and compare” with WitCH 15.

Subsection 13.2.5, below, is on “differentiability”. The earlier part of chapter 13 gives a potted, and not error-free, introduction to limits and continuity, and Chapter 12 covers the “first principles” (limit) computation of polynomial derivatives. We’ve included the relevant “worked example”, and the relevant exercises and answers.

WitCH 57: Tunnel Vision

The following is just a dumb exercise, and so is probably more of a PoSWW. It seems so lemmingly stupid, however, that it comes around full cycle to be a WitCH. It is an exercise from Maths Quest Mathematical Methods 11. The exercise appears in a pre-calculus, CAS-permitted chapter, Cubic Polynomials. The suggested answers are (a) \boldsymbol{y = -\frac{1}{32}x^2(x-6)} , and (b) 81/32 km.