Quick Notes on the Herald Sun’s Exam Errors Article

There is report today in The Herald Sun (Murdoch, paywalled), titled,

Mistake-riddled VCE maths exams robbing students

Regular readers will know pretty much the lay of the land. However, there may be some non-regular readers in the next few days. So, a few clarifying remarks are probably worthwhile. (This is quick: I’ll adjust as I can through the day.)

First of all, without reflecting at all on the accuracy or the merits of the report, I want to make clear that I had no role in the creation of the report. 

Secondly, at one point the report makes quick reference to this blog:

A Bad Mathematics blog run by a professional mathematician with a PhD in maths has identified more than 90 serious problems with specialist maths exams and 77 in maths methods, including sample exams and Northern Hemisphere exams going back to 2006.

More specifically, this appears to refer to the Specialist and Methods (and there’s also Further) error list posts (and the subsequent links included there). The report refers to “serious errors”. Without rejecting that language, the language I use on these posts is of “major” and “minor” errors:

To be as clear as possible, by “error”, we mean a definite mistake, something more directly wrong than pointlessness or poor wording or stupid modelling. The mistake can be intrinsic to the question, or in the solution as indicated in the examination report; examples of the latter could include an insufficient or incomplete solution, or a solution that goes beyond the curriculum. Minor errors are still errors and will be listed.

With each error, we shall also indicate whether the error is (in our opinion) major or minor, and we’ll indicate whether the examination report acknowledges the error, updating as appropriate. Of course there will be judgment calls, and we’re the boss. But, we’ll happily argue the tosses in the comments.

In recording and characterising such errors, I have made no attempt to determine or guess the effect of such errors on students’ scores. That seems to me to be a very difficult thing to do, for anyone.

Thirdly the report refers specifically to three questions in error on the 2022 Specialist Exam 2. That exam is discussed generally here. (The other 2022 exams are discussed here and here and here and here and here.) The specific questions are discussed here and here and here. These three questions (and others on the 2022 exams) appear to me to be unquestionably in error.

Fourthly, and finally for now, for me the prevalence of errors on the VCE exams is simply the tip of the iceberg. The many posts on this blog concerning VCE and VCAA indicate my more general concerns with VCE mathematics. (My broader maths ed concerns are probably best captured by this post.)

That’s it for now. I’ll update this post if something occurs to me, or if someone suggests in the comments that I somehow should.

New Cur 30: The Complete Pain Words


I am not a good writer. Primarily, I use the monkey-typewriter method: if you rewrite a sentence sufficiently many times then you’ll eventually wind up with something at least serviceable. Then, if you rewrite a paragraph sufficiently many times … And so on. It is not a very efficient method.

Even if not efficient, however, the method works well enough for me. Of course I’m not creating great literature, but I don’t think it’s too boastful to claim that I get my ideas across clearly enough and engagingly enough.

Less monkeyishly, my writing style is fuelled mainly by an undergraduate humour and a stubbornness to rewrite and rewrite and rewrite, steered by the lessons and the spirit of the famous style guides, such as Strunk & White and Gowers. These guides are expressly not about creating great art, but rather about lowering your eyes to a much more achievable goal: recognising your intended readers and getting your ideas across to those readers in a clear, uncluttered manner. The powerful message of these guides is that anyone can write well enough, if they simply recognise the proper goal and work sufficiently hard to achieve it.

In the editions of the The Elements of Style to which he contributed, E. B. White quotes and then comments upon a key paragraph from William Strunk‘s original:

“Vigorous writing is concise. A sentence should contain no unnecessary words, a paragraph no unnecessary sentences, for the same reason that a drawing should have no unnecessary lines and a machine no unnecessary parts. This requires not that the writer make all his sentences short, or that he avoid all detail and treat his subjects only in outline, but that he make every word tell.”

There you have a short, valuable essay on the nature and beauty of brevity — fifty-nine words that could change the world. 

Sir Ernest GowersThe Complete Plain Words has an even pithier summary, in an epigraph, a quotation from historian G. M. Young, to the Prologue:

“The final cause of speech is to get an idea as exactly as possible out of one mind into another. Its formal cause therefore is such choice and disposition of words as will achieve this end most economically.”

In his revision to The Complete Plain Words, Sir Bruce Fraser expressed it about as economically as possible:

Be simple. Be short. Be human.

The Complete Plain Words is even more specifically aimed than The Elements of Style, having famously originated as a booklet for UK civil servants. Which brings us, finally, to the Australian Mathematics Curriculum.



I have already whacked some of the larger aspects of the curriculum writing, as well as some of the structural aspects. Here I want to consider a smaller aspect: the phrasing of the curriculum content descriptors. These descriptors comprise the core of the curriculum, the part that the teachers have no choice but to read and to decipher. It is thus in this part, more than any other, that the writing must be clear and clean. Of course, I have already indicated dozens of poorly written descriptors, in particular in the Awfullnesses post. But the focus was almost always on the poor content; here, I will focus on the poor language.

I will start at the very beginning, as Mary Poppins sang, with Foundation Number. The first descriptor is,

name, represent and order numbers including zero to at least 20, using physical and virtual materials and numerals (AC9MFN01)

Is this OK? Well, adequate, maybe. It’s clear enough that the kids are supposed to learn the numbers from zero 0 to 20. But why not just,

Learn the numbers from 0 to 20.

OK, for ideological reasons ACARA wants to be more detailed and explicit in the descriptors. But “physical and virtual materials and numerals” is very clunky conjuncting, and the three listed activities don’t match the three listed aids: the kids will be “using” none of the aids in naming numbers. Here’s a suggested alternative:

Learn the numbers from 0 to 20, including their names, order, physical representations and representations with numerals. 

Is this not clearly better?

On to the next descriptor:

recognise and name the number of objects within a collection up to 5 using subitising (AC9MFN02)

The preposition “within” is a poor choice, since it distracts from considering the collection as a whole, which is the entire point. Then, “collection of up to 5” hangs there, and it should be “five” not 5. Finally, does one really require the five dollar word “subitising”? Here’s a suggested alternative:

Identify the number of objects in a group of up to five objects.  

On it goes. Here are the remaining four descriptors, and suggested alternatives:

quantify and compare collections to at least 20 using counting and explain or demonstrate reasoning (AC9MFN03)

Identify and compare the number of objects in groups of up to twenty objects. 

partition and combine collections up to 10 using part-part-whole relationships and subitising to recognise and name the parts (AC9MFN04)

Combine and partition groups of up to ten objects, identifying and naming the sizes of the parts and the whole. 

represent practical situations involving addition, subtraction and quantification with physical and virtual materials and use counting or subitising strategies (AC9MFN05)

Represent and analyse problems with physical materials, using counting, addition and subtraction.

represent practical situations involving equal sharing and grouping with physical and virtual materials and use counting or subitising strategies (AC9MFN06)

Represent problems of equal sharing, using number recognition and counting.

I don’t for a minute claim that these rewrites are perfect. But they seem unarguably a damn sight better, and they were the product of about three minutes’ contemplation. And, sure, maybe I skimped a little, with a little detail here or there left out. But it was ACARA’s idiotic idea to shove everything but the kitchen sink into the content descriptors. If that then means the content descriptors are unwritable, it just implies that ACARA screwed up earlier on. Which of course they did. And also later on.

Even accepting the needlessly bloated content, the descriptors are a muddy mess. What are “practical situations”? Is the intention that the kids use counting or (subitising strategies), or that they use (counting strategies) or (subitising strategies)? What even are “subitising strategies”? Isn’t subitising that you either get the number or you don’t? So what could be a strategy for that? To peek when you think the things are not looking?

Every single descriptor is like this. Every descriptor is muddied by vague and inaccurate words, by clumsy grammar, and by imprecise direction and goals. The kids must forever “communicate” and consider “questions” of unstated character, describe “features” and “investigate” god knows what, and “reason” in god knows what manner. The meaningless and excruciating “situations” occurs 136 times.

With absolute honesty, I do not believe the Curriculum contains a single content descriptor that could not be improved with two minutes’ thought from a half-competent mathematical editor. For most descriptors, a monkey with a typewriter would have an even money shot. It is astonishing, and it is a disgrace.

The Curriculum writing is a disaster. There is nowhere a single hint of even an attempt to be simple or short or remotely human. For the writing alone, and for so many other reasons, the Australian curriculum should be discarded.

Peter Dutton’s Broken Home

As soon as Potato Pete and his fellow “No” thugs started whining about the Voice Referendum being “divisive“, we were reminded of a great joke. We had figured the joke was a standard, but seemingly it is not: it took some tracking down. The joke is below, as it appeared on TV. It captures perfectly the hypocrisy and unmitigated gall of these wreckers.

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The Guardian Objects to the University of Sydney’s Considered Voice

We will vote Yes on the Voice Referendum. Twice, if we think we can get away with it.

We did not begin that strongly in favour, but the sleaziness, vacuousness, blatant dishonesty and outright nastiness of the prominent No campaigners has convinced us as nothing else could. That toxic newt John Howard calling for people to “maintain the rage” is as revolting, and as idiotic, a command from an ex-PM as has ever been made. And they are all revolting. They are all lying. None of them believes a single nasty word they’re uttering. Except for Lidia Thorpe who is, instead, a dim-witted, narcissistic separatist. The entire No campaign has been disgusting, without a single ounce of rational thought or human decency. And so we have chosen to attack The Guardian.

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Tom’s Posts Are (Lagrange) Multiplying

Tom has a new post on his Teaching Mathematics blog: Lagrange Multipliers – A Historical Approach? Tom riffs off of a (not uncommon) poor 1960’s undergraduate lecture he had, on the method of Lagrange multipliers. Please support Tom’s blog and check it out.

Continue reading “Tom’s Posts Are (Lagrange) Multiplying”