What Does “Technology” Mean?

To be more precise, what does “digital technology” mean and, precisely as possible, how is Digital Technology X used in Year Y of schooling?

It is now impossible, of course, to write a document on education without genuflecting to the God of Technology. The repetitious chanting of “technology”, like a wired Tibetan monk, is the way people with no sense of the past or the present indicate how hip they are with the future. But, what do they mean? What technology are they talking about? It is a serious question, of which we only vaguely know the answer. We want help.

Of course by “technology”, the Education Experts are never intending to refer to something like blackboards and chalk. They would not even recognise such primitive devices as products of technology, although of course they are. No, what the EE mean by “technology” is electronic devices, mostly computers and computer programs, and preferably devices that are internetted. So, calculators and electronic whiteboards and Mathletics and Reading Eggs and iPads, and so forth.

The question is, precisely how are these devices used in specific classrooms? For example, are calculators used in Year 5 to perform arithmetic calculations, or to check calculations that have been done by hand? Is Mathletics used in Year 7 to teach ideas or to test knowledge and/or skills?

The same question applies to all subjects. Are word processors used in Year 6 to check and/or teach spelling and grammar? Are iPads used in Year 8 to check the definitions of words?

We want to know as much as possible, and as specifically as possible, what electronic gizmos are being used, and with whom and how.

RatS 10: Adam Curtis’s CGYOoMH

Well, to be more accurate, this is a WatS, since it’s a BBC series.

Adam Curtis is a unique, brilliant filmmaker, exploring the psychology and politics of modern society like no one else. Two previous series, The Power of Nightmares and The Century of the Self, are musts. Curtis now has a new series, Can’t Get You Out of My Head: an Emotional History of the Modern WorldIt is viewable on BBC iPlayer (with VPN trickery) and, at least for now, here. It is great.

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.


  • 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.



  • 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.



  • 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.

PoSWW 17: Blessed are the Cheesemakers

This one is old, which is not in keeping with the spirit of our PoSWWs and WitCHes. And, we’ve already written on it and talked about it. But, as the GOAT PoSWW, it really deserves its own post. It is an exercise from the textbook Heinemann Maths Zone 9 (2011), which does not appear to still exist. (And yes, the accompanying photo appeared alongside the question in the text book.)

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.

RatS 9: The Campus as Factory

Jacob Howland is an emeritus professor of philosophy at the University of Tulsa. For the last couple of years Howland has been watching the demise of his university, and the perversion of other American universities from the same anti-academic forces. (Of course, Australian universities are entirely immune from such anti-academic perversions.) This has come together in Howland’s article,

The Campus as Factory: corporatist progressivism and the crisis of American education.

Richmond, Drugs and the Injection of Bullshit

Just a word about Richmond West Primary School, which has been in the Melbourne news for all the wrong reasons in the last couple days. What follows is obviously our point of view, and is not intended to represent the School or any other person.

Our daughters go to RWPS and, with the caveat that all primary schools are screwed up by the Australian Curriculum and modern education nitwittism, we and our daughters love the school. We commute very non-trivially for our daughters to go there. In particular, we have regarded the school as perfectly safe.

Notoriously, RWPS is next door to the North Richmond Community Health Centre, which houses Richmond’s safe injecting room. The injecting room is there because the drugs and the druggies are there. It was a dodgy area long before the injecting room, and it still is, although if anything our understanding and perception is that it’s probably less so. One is watchful, and it is not unusual to see a down-and-outer, drugged or otherwise. But before this week, for four years, we did not see or hear of anything remotely extreme or threatening near the school. What our daughters have experienced more than anything is lessons in empathy, to think compassionately about people who are doing it much tougher than themselves.

The incidents at RWPS this week were obviously much more serious. What is not obvious, however, is what exactly the incidents were, or whether they carry any deeper meaning. The incidents do not appear in any way linked, and we’ve read nothing to suggest that they’re in any way linked to the injecting room. We’ve seen nothing to suggest that such incidents are likely to recur. It is natural to question what is going; two such incidents in a week demands it. But it should be kept in mind that perhaps nothing is going on, that, accepting the area is dodgy, the incidents may have been coincidental and rare.

What doesn’t help is shopping misinformation and fear-mongering, in particular by shit-stirring Murdoch stooges and their fellow travellers. We’ll be reading and looking to find out more. But, we won’t be reading nasty, populist fuckers, and we suggest others avoid this as well.

UPDATE (24/03/21)

And more populist bullshit today. Fuck Tom Cowie and fuck David Estcourt and fuck Anthony Piovesan, and fuck you TV vultures around when school lets out. All of you, either you have no fucking clue, or you’re lying through your fucking teeth.

UPDATE (29/03/21)

And further “Fuck you”s, to the Age’s Rachel Eddie and ABC’s Zalika Rizmal. And a special “Fuck you” to pompous Liberal toad, Matthew Bach.