We still haven’t had time to take a proper look at the 2023-2027 VCAA Mathematics Study Design, but it smells very very bad.

A blog-reader has alerted us to a VCAA webinar on Mathematical Methods in the new study design. (**31/01/24** Link updated.) The video can be viewed here, with transcript here (Word, idiots), and PowerPoint slides here (PowerPoint, idiots). The study design is here (Word, idiots). The previous discussion on this blog can be found here.

The video made us nauseous.

### UPDATE (28/09/22)

John Friend has noted there is a companion presentation on Specialist Mathematics. (**31/01/24** Link updated.) Transcript here (Word, idiots), and PowerPoint slides here (PowerPoint, idiots).

*Sigh* Where to start? I will comment only on Methods Units 3/4. And I will limit my comments to the obvious. And I won’t make comments about Assessment (so I’m only commenting on about 1/3 of the presentation).

1. In fairness to the current VCAA Maths Manager Michael MacNeill, he’s inherited this Study Design mess from a [insert appropriate pejorative here], so he’s stuck with making the best of a shambles. But … there’s a bad way and a worst way of making the best of a shambles. And unfortunately, MacNeill seems to have adopted the worst way.

2. “There remains however, no explicit requirement that students need to employ the second derivative in categorising stationary points and locating a point of inflection. ”

So how the frick are students meant to find the coordinates of a PI? I suppose by finding where the derivative has a turning point? OK …

Q: How do we find that turning point?

A: By differentiating the derivative, putting the result equal to zero and testing the nature of the solutions using the sign test. I suppose.

Except there’s one small snag – students aren’t explicitly required to employ the second derivative … So I suppose using it is a secret requirement (unless someone knows a way of doing it without using the second derivative – I’m all ears).

There are several secret requirements, it seems.

“They would transition that across to unit three, implementing CAS as a means of students locating a point of inflection, or alternatively they could be making good use of linked graphs between a function, and it’s corresponding gradient function using the graphical properties of the derivative function graph, to identify those relevant features in particular, the location of a point of inflection, or a stationary point of inflection.”

Does the CAS have a “Point-of-Inflection” button so that students can find it as a black box? Or are students required to use the second derivative that we’re told isn’t required?

“And I’ll reiterate again at this stage that there is no explicit requirement that students need to employ a second derivative, to locate a point of inflection …”

Yep, you’ve gotta use the secret second derivative approach.

3. “And teachers should also be aware that in the key skills for unit one, there remains the requirement for simultaneous equations up to four unknowns, and matrices with CAS would be a most sensible approach to the solution of this kind of system of equations.”

Or, given that the CAS is being used, the equations could simply be typed in and all confusion about matrices (including what they mean and how to use them to solve equations) could be avoided. A definitive statement that matrices are not on the course, will not be required and are not examinable would have been good. This would avoid any hint of stupidly using them piecemeal (so hated and mocked under the old Study Design).

4. “Rectangle rules are no longer written into the study design.”

So the most intuitive and simplest way of approximating area under a curve (as well as calculating a definite integral from first principles using limits) is removed because “The trapezium rule particularly again, lends itself well to pseudocode, and pseudocode familiarity”.

Note that the average of the left and right rectangles gives the trapezium rule. So what’s the gain? If you’re gonna do this, why not use Simpson’s Rule? Or why not include Newton-Cotes methods in general? Given that VCAA is so algorithmic-computational thinking-pseudocode centric.

Algorithmic computational thinking pseudocode bullshit trumps appropriate mathematical content.

5. I quote from Garner’s presentation at the same MAV PD (not linked at this blog):

“Deleted: Median of a continuous random variable. “However, it may emerge for example if a question looks at the 50th percentile”.

No mention of this from MacNeill. Percentiles are not explicitly mentioned in the new Study Design. Is someone full of it? Or is this another secret requirement?

What a mess.

Google “TI point of inflection”

No, I don’t think I will.

Yep, that’s what I figured.

So why add point of inflection if there’s no calculus involved? Just button pressing. I wonder what VCAA’s thoughts on the pseudocode for finding the point of inflection are? (As an aside, Mathematica has no ‘Point of Inflection’ command, so I wonder how those students using Mathematica are meant to write code for finding it when the second derivative is not required (*) ?)

It’s a great pity that the [insert pejorative term] responsible for this mess was not forced to publicly explain and answer questions from teachers. Or, in his absence (an otherwise very welcome and long-overdue absence where he can hopefully cause no further damage), it’s a pity that the writing panel can’t be lined up against the wall *ahem* I mean sat down and publicly interrogated by teachers (**). Under a nice hot lamp. But that would require accountability, and when it comes to accountability, VCAA can’t count.

The Study Design never makes it clear that it’s referring to non-stationary points of inflection. A serviceable Methods teacher would assume that the SD statements refer to stationary points of inflection (I wonder how many Methods teachers know that stationary points of inflection are simply a special type of point of inflection?) This needed to be explicitly stated in the Study Design. And the natural language of concavity is not mentioned in the Study Design or the MAV presentations (and not mentioned in Specialist either) – admittedly a minor quibble compared to the explicit advice that calculus is not required for finding PI’s.

I dislike how MacNeill has responded to the new Study Design. Nevertheless, I accept that:

1) It’s not his curriculum.

2) He’s forced to toe the VCAA party line (regardless of what his personal opinion might be) and pretend like there’s nothing wrong with it.

I just really wish MacNeill would give more clarity. A detailed supplement would be an enormous help.

I find it morbidly fascinating that despite VCAA’s algorithmic pseudocode computational thinking fetish, at the end of the day all it really wants is students pressing buttons. Point of inflection is exhibit alpha (English alphabet is exhausted).

* Many students will probably (unnecessarily) buy Mathematica code that sings and dances and finds points of inflection and requires no mathematical understanding.

** Although my understanding is that the Study Design was presented to the panels as pretty much finalised, and that most members of the panels were purely tokenistic. Only an idiot would go on one of those writing panels thinking that they would be part of a genuine process and that their input would be taken seriously.

I’m not sure I can be so charitable. This is utter garbage, and the buck stops with MacNeill.

Ideally, MacNeill would have told VCAA that the Study Design was a mess and that it needed to be retracted and re-written. Re-written by people that had a clue, not VCAA stooges and patsies.

But that was never gonna happen.

What should have – realistically – happened (and it’s not yet too late to happen) is that a supplement got written that provided all of the missing details and gave clarity. Top of the list would be that the double derivative IS required for finding a point of inflection. And examples given. MacNeill should be actively promoting the calculus behind the point of inflection, not pretending that the second derivative is not required.

MacNeill inherited the content of the new Study Design from a [insert pejorative term]. No buck. His interpretation and clarification of that content is where the buck stops. On that score, I have zero charity. I think he means well, but he’s made a mess of things so far. Including his allowing of Garner’s idiotic and

supercilious statement that ‘median is deleted but 50th percentile may still appear’.

1/3 of his presentation was on content, 2/3 was on assessment. That’s beyond stupid. 95% of the presentation should have been on the content (clarification and interpretation), 5% on assessment.

I cannot open the PowerPoint transcript. At 45:10, MacNeill implying that decomposition was just a part or technique of algorithmic thinking is not palatable. Do these guys just think of divide-and-conquer algorithms? What about even such basic topics as polar decomposition of a complex number? Or, a bit more advanced, paving, at least not obstructing, the students’ path towards understanding the idea of a bivariate function that only depends on the distance from the origin? Pure and applied mathematicians alike, I imagine, would be offended.

If you depend on the VCAA Study Design for your understanding (which many teachers do, because it comes from the ‘Authority’) you could be forgiven for thinking that mathematics is simply algorithmic/computational thinking and pseudocode.

Mathematics is a disease, VCAA (and ACARA) is the cure.

As with ACARA, the VCAA fundamentally does not know what mathematics is, and fears the idea that anybody might seek to teach it or to learn it.

What is meant by algorithm? My understanding is that an algorithm is an explicit sequence of steps that can be followed to solve a problem – a recipe. This suggests to me that almost all school mathematics involves algorithms.

Perhaps this is another instance of people changing the language without asking me first.

It is much more insidious than a change of terminology.

Solving a quadratic equation is an algorithm. And yet the necessary algorithmic thinking is deemed too difficult and impractical for a Yr 10 student by ACARA.

You can’t eat your algorithm and have it too.

For those who have the stomach (although it’s not quite as bad as Maths Methods) –

VCAA webinar on Specialist Mathematics in the new Study Design: video, transcript (Word), and PowerPoint slides (PowerPoint):

https://www.vcaa.vic.edu.au/news-and-events/professional-learning/VCE/Pages/VCESpecialistMathematicsWebinars.aspx

Thanks, JF. I’ve updated the post. I haven’t had a chance to look yet.

Thanks JF, I read through the transcript. The comment was made “Maths is an evolving subject.” Yet the sections on logic don’t seem to have moved on since Aristotle. Is this too harsh?

Not nearly sufficiently harsh.

Terry, your mistake is taking the comment on face value. The comment is a weasel worded way of saying

“What gets taught in mathematics depends on the fetish of those in charge at the time”.

I read the transcript just after I wrote the attached for my Year 8 and 9 students. I plan to devote one class to this in a couple of weeks. I have these students for only 1 lesson/week. Comments welcome.

Logic problem

That’s nice, Terry. You always put a lot of thought and effort into what you prepare, from what I’ve seen.

How long is the lesson? I’m guessing somewhere between 40 and 50 minutes. I’m not sure you can do this justice (particularly since you’re dealing with Yrs 8-9) in one lesson.

I assume you’re guiding them towards the idea of a truth table? I’d suggest a minimum of two lessons will be needed (but you might not have any control over this). In the second lesson you could give another (shorter) question where students would be explicitly constructing and using a truth table. I liked the knight-knave questions in Raymond Smullyan (1987): Forever Undecided: A Puzzle Guide to Godel. Perhaps the following simple question would be suitable:

While walking through a fictional forest, you encounter two trolls guarding a bridge. Each is either a knight, who always tells the truth, or a knave, who always lies. The trolls will not let you pass until you correctly identify each as either a knight or a knave.

Troll 1 says that he is a knave but the other troll is not.

What is each troll?

Or a slightly longer one: Taken from Cambridge Specialist Maths Units 1&2.

Every person on an island is either a knight or a knave. Knights always tell the truth, and knaves always lie. Alice and Bob are residents on the island. Determine whether Alice and Bob are knights or knaves in each of the following separate instances:

a. Alice says: ‘We are both knaves.’

b. Alice says: ‘We are both of the same kind.’ Bob says: ‘We are each of a different kind.’

c. Alice says: ‘Bob is a knave.’ Bob says: ‘Neither of us is a knave.’

You could have the powers-that-be in rapture if you then decided to role play this. And then had a cross-curriculum lesson with science where students made circuits with switches and light bulbs to model it. It would be all their educational dreams come true.

Thanks John.

Generally they are students who are better than average; they have 4 mathematics lessons each week, but taken out of their normal class to spend one lesson with me each week. I have four small (n<12) classes of students in Year 8 and 9; two classes of each year level. Each lesson is 70 minutes. My job is to extend the students in some way or other; I have a part-time position.

The rationale is that the school is trying to encourage the better students – in addition to supporting students at the other end of the spectrum.

I plan to introduce the problems; let them get used to them until they understand them; after a while, guide them through a solution to say the first one; then see how they go.

Since I posted this, I too had thought about using the names Alice and Bob. Will change. Great minds etc.

Thanks for the reference to Smullyan.

The cross-curriculum suggestion would have been great for a STEAM festival that we had last term; maybe next year – although my contract is only for this year at this stage.

I had not thought about role playing – an excellent idea – Mathematics and Drama! I will change the lesson with this idea in mind.

Thanks very much.

I’ve now watched it. It is nauseating con-man nonsense. And MacNeill’s

que sera seraburial of mechanics was dishonest and disgusting.I’m doing methods unit 3/4 next year and I’m honestly feeling a bit scared.

I find methods too be an easy subject, and I’ve even started doing methods 3/4 exams but what has me scared is this introduction of pseudocode and algorithms.

I don’t believe it will be properly taught, and in some schools may not be taught at all due to math teachers, teaching math and not algorithmics.

This quote in the transcipt seems to imply that it will be assessed on the external exams, but for some reason has no indication of how the fuck it will be assessed and it’s pissing me off.

“Pseudocode, is it going to be examinable? From next year, yes, it will be, it does form a part of the course, and it is part of the study design. However, as I’ve alluded to, it is not the entirety of the study design, and a teacher should be mindful of the proportion of the key knowledge and key skills within which pseudocode sits”

Should I be worried, what resources should I be looking at if my teachers don’t actually teach pseudocode? I want to aim for a high study score but I deadass got no idea what the fuck VCAA means by pseudocode, maybe I’m dumb but they seem to be very vague about what they expect from students.

Language, Charlie …

Others here will be better placed to advise you, but I think the practicalities of coping with the pseudocode in SM may not be as difficult as you fear.

VCE does things ritualistically, and the less coherent and/or more obscure/unknown the topic, the more ritualistic it’ll be. In that sense, my guess is that the pseudocode will be akin to the hypothesis testing topic: unexplained and meaningless, but easy enough in the join-the-dots manner. But again, I’m not a good judge, and others here are likely to be more reliable fortunetellers.

Pseudocode is a plain English description of how an algorithm works. However, there are many different conventions for what this ‘plain English’ looks like. I’m still waiting for VCAA to publish its convention. VCAA has a moral and legal requirement to do this. (*) Until then, I’m not going to worry too much about it. Having said this:

1) From what I’ve seen, the new textbooks are having a decent stab at setting out some conventions. It’s likely VCAA will acquiesce to what’s in the textbooks.

2) Without defining a convention (and even with a convention), it’s very hard to see how VCAA could possibly mark a question that asks a student to write some pseudocode that does something. Given that there are so many different ways of writing it … With this in mind, my guess for how it might be assessed (at least in the short term) would be:

a) Giving some banal code and asking a student what the output would be for a given input.

b) Asking a question that might require writing some code (and hence using pseudocode as the first step) that solves a particular problem. Eg. Find the first twin primes greater than 1000.

I agree with Marty that:

“VCE does things ritualistically, and the less coherent and/or more obscure/unknown the topic, the more ritualistic it’ll be. In that sense, my guess is that the pseudocode will be akin to the hypothesis testing topic: unexplained and meaningless, but easy enough in the join-the-dots manner.”

The whole pseudocode computational algorithmic thinking crap is a bog-filled cesspool. We can thank a total prick for giving us this as their parting ‘gift’ (as well as the spineless ignorami and sycophantic goons who sat on the Study Design panels and gave it a Hall Pass). (**) But something to keep in mind (as a student) – VCE is a ranking system. If something is crap for everyone in a ranking system, then it’s a level playing field and so its at least ‘fair’ for everyone.

(Cold comfort for teachers trying to make sense of this crap. And in the meantime you have fools in high places scratching their heads wondering why there’s a shortage of maths teachers and what should be done about it).

* It’s a big ask because after 5 years of Algorithmics, VCAA still has not defined its convention for pseudocode.

** Especially since there’s already a subject on algorithmic and computational thinking. Called ALGORITHMICS: https://www.vcaa.vic.edu.au/curriculum/vce/vce-study-designs/algorithmics/Pages/index.aspx

I’ve updated my VCAA SD post with a bunch of links to new VCAA materials for the new SD.