The difficulty of critiquing VCAA mathematics exams is capturing the variety and the frequency and the depth of the flaws, and then summing the overall effect, the fundamentally impoverished approach to mathematics and its testing. Documenting straight out errors is not overly difficult, and even non sequitur questions are manageable: the error or weirdness typically speaks for itself. Capturing the ubiquitous awfulness of the writing, and the intrinsic meaninglessness of many of the questions, however, is harder.
Late last year, we took a shot at VCAA’s lesser literary offences, the sentence by sentence absurdities. We did so by considering pretty much every sentence on one VCE exam, Methods 2022 Exam 1. In this post, we shall consider, in similarly painful detail, one of VCAA’s greater literary offences.
A Methods or Specialist (CAS) Exam 2 consists of 20 multiple choice questions followed by five or six long questions, each with many parts. The multiple choice questions, along with the shorter questions comprising Exam 1, provide numerous clear and contained examples of lesser literary offences. These lesser offences also occur on the long questions, of course, but many of these longer questions are also offences as a whole.
A long mathematics question should be long for a reason. If there are many parts then these parts should be related and should be building a deeper analysis. In brief, a long mathematics question should be the framework for a story.
A mathematical story need not be great art, of course. Even less does such a story need a real-world scenario, and even less than that does it need dressing up with character or colour. As such, critiquing a mathematical story is not the same as critiquing fiction. But there is overlap.
In his hilarious Feminore Cooper piece, Mark Twain lists eighteen rules of storytelling. The final eight, “little” rules were the focus of our lesser offenses post. Of the ten larger rules, most do not readily apply here. But the first two rules, which Twain frames in regard to Cooper’s novel The Deerslayer, are directly relevant:
1. That a tale shall accomplish something and arrive somewhere. But the “Deerslayer” tale accomplishes nothing and arrives in air.
2. They require that the episodes in a tale shall be necessary parts of the tale, and shall help to develop it. But as the “Deerslayer” tale is not a tale, and accomplishes nothing and arrives nowhere, the episodes have no rightful place in the work, since there was nothing for them to develop.
We shall now go through a question from 2022 Methods Exam 2, part by part. The relevance of the above two rules will be obvious.
The exam question contains ten parts and is worth in total 14 marks (= 21 minutes). The question begins:
And, already we’re bored to tears. And confused, since a “binomial random variable” can only be declared once we first declare the number of flips. But the boringness is the main point. Over forty words are used, when seven would have sufficed:
An unbiased coin is flipped five times.
We do not need Mika, and we do not need the random variable X, at least not for a good while.
OK, sure. You could have asked for the probability that the coin comes up heads every/five times, but sure.
Again, words are better than X but, again, OK.
Yes, a reasonable progression of the story, but why “three decimal places”? There are some nice fractions already sitting there, ingredients for a simpler, better, exact answer. What’s the point of the detour into decimals?
This has nothing to do with the earlier three parts, but OK. And now, yes, you need X, so now is when you should introduce X.
Anyway, we are done with part (a). How, then, will part (b) further the story? Well,
Sweet Jesus. What a sentence. What a scenario. What a disjunction.
Just in case we didn’t realise that indicates a definite integral, which thus has a value.
Is anyone else pondering why we might be given that?
Why? Why find r and s? Who could possibly care? What does it tell us about the height of Mika’s flip, or Mika’s binomialling, or anything whatsoever? Where are you taking us? Can we opt out?
On to part (c):
It was always too much to hope for, that Mika might be an only child.
The correct answer is “Who gives a toss?”, for which no justification is required.
We’re pretty confident that three decimal places is pretty pointless.
So, we’re told the sample mean is 0.4, and then we decide how many flips this sample will contain. A miracle.
And thus the story ends. Like The Deerslayer, the story has accomplished nothing and, like The Deerslayer, it ends in air.
VCAA’s story is depressing and painful in its pointlessness. It hurts to read. We did, however, think of an apt name for the story: The Cheerslayer.