This one may be of little interest to others, but it’s been bugging us.
A peculiar puzzle of writing mathematics is deciding when to use names and when to use numerals: should we write “two” or “2”? There is no one (1?) answer, and there are conflicting principles. Along with other rules, English style guides instruct that names should be used for small numbers, and numerals for large (with varying interpretations of “small” and “large”).
Reasonable enough, but there also appears to be a semi-conflicting mathematical principle to follow (unless we made it up): if the scenario explicitly or implicitly contains arithmetic then numerals seem preferable. So, writing “6 is an even number” feels correct, and the more explicitly arithmetic the context, the stronger the case for numerals. By contrast, if we are simply noting the count of something then, at least if the count is small, names seems better: “Marty committed five cardinal sins”.
Of course the distinction is not always so clear or constant. We might note there are fifty-two cards in a deck, for example, but with the immediate intention of dividing up the deck, or of calculating some probabilities. Moreover, the context and the audience should always be considered. For an exercise or test question, one should typically use numerals, particularly if the students are young or weak. The proper concern, always, is for clarity and for style, in that order.
The rule is there are no rules, but the principle is there are principles. Or at least there should be. Which brings us to the Australian Curriculum.
The Curriculum is very numeral-heavy. That includes plenty of judgment calls, where we would have gone for names but numerals also seem reasonable. But it also includes plenty of instances where there is no arithmetic in sight, where the use of numerals feels plain wrong. For example,
investigating sufficient conditions to establish that 2 triangles are congruent (AC9M8SP01)
It is even more jarring in instances where there is arithmetic nearby, but the numeral is not relevant to this arithmetic:
building a rectangular prism out of unit cubes and showing that the measure of volume is the same as would be found by multiplying the 3 edge lengths or by multiplying the area of the base by the height/length (AC9M7M02)
recognising the features of circles and their relationships to one another; for example, labelling the parts of a circle including centre, radius, diameter, circumference and using one of radius, diameter or circumference to determine the measure of the other 2; understanding that the diameter of a circle is twice the radius, or that the radius is the circumference divided by 2π (AC9M7M03)
Then there’s the possibility of switching mid-stream:
using a tree diagram to represent a three-stage event and assigning probabilities to these events; for example, selecting 3 cards from a deck, assigning the probability of drawing an ace, then a king, then a queen of the same suit, with and without replacing the cards after every draw (AC9M9P01)
The Curriculum contains dozens of other such usages, many just as clunky.
Of course there are many smellier fish to fry: any numeral-name screw-ups pale in comparison to the Curriculum’s other failings. But such misuse of numerals is incredibly aggravating, at least for us. It is inelegant and, more importantly, it makes the reading awkward, almost demanding a double-take.
It amounts to one more instance of ACARA’s inability to manage even the small aspects with a minimal competence.