The Evil Mathologer is out of town and the Evil Teacher is behind on sending us our summer homework. So, we have time for some thumping and we’ll begin with the Crap Australian Curriculum Competition. (Readers are free to decide whether it’s the curriculum or the competition that is crap.) The competition is simple:

**Find the single worst line in the Australian Mathematics Curriculum.**

You can choose from either the K-10 Curriculum or the Senior Curriculum, and your line can be from the elaborations or the “general capabilities” or the “cross-curriculum priorities” or the glossary, anywhere. You can also refer to other parts of the Curriculum to indicate the awfulness of your chosen line, as long as the awfulness is specific. (“Worst line” does not equate to “worst aspect”, and of course the many sins of omission cannot be easily addressed.)

The (obviously subjective) “winner” will receive a signed copy of the *Dingo* book, pictured above. Prizes of the Evil Mathologer’s *QED* will also be awarded as the judges see fit.

Happy crap-hunting.

I would like a meet Pi for lunch. Hello Pi.

Um, is that in the curriculum?

Line: Mathematics has a central role in the development of numeracy

Location: on the numeracy page under numeracy in the learning areas

Why is it crap?

The Australian Curriculum defines numeracy as mathematics used in everyday life and states mathematics as the main teacher of it. This impacts the design of the mathematics curriculum to focus on facts and procedures rather than mathematical reasoning (just read all their content descriptions – the main proficiency strand that surfaces is fluency). This then impacts how mathematics is taught as teachers accountability is measured (in part but a decent part) by how students do in tests which are assess content from the curriculum. It then becomes increasingly burdensome for teacher to judge teaching mathematical reasoning skills (which are the other proficiencies: understanding, problem-solving and reasoning) and meeting obligations for students to do well in tests.

So while this line is not a mathematical blunder, it has profound impacts on the rest of the mathematics curriculum. That’s while I chose it to be the worst line.

Marti,

I would doubt this is the worst line in the glossary mentioned above but it s certainly incorrect

SKEWNESS the 3rd central moment

“…when the distribution of a set of data values is symmetric about the mean it is said to have a NORMAL distribution…??”

Gauss would object to this definition of the Normal I think

Symmetry is defined clearly here https://en.m.wikipedia.org/wiki/Symmetric_probability_distribution

Regards

Steve R

Agreed. This line really establishes one of the “rules” (which should never have been allowed) which then justify so much of the other crap that is allowed to flow freely in multiple AC publications. Will be hard to find something worse, but knowing the amount of crap out there, it may exist…

Thanks, Potii. I’ll ponder your post tomorrow, though picking on the Curriculum’s “numeracy” focus can’t be wrong. I assume you’d prefer me to delete one of your posts here; you can let me know which one.

Can you delete this one you commented on? I didn’t realise it got posted as it didn’t show after a while. Thanks.

Thanks, Potii, Steve R and jrfitz66, and sorry to be slow to respond.

Potii and Steve R, they’re both great, awful lines. They’re also evidently awful in very different ways: the numeracy line opens the door to the systemic dilution and corruption of the mathematics curriculum by pointless, brain-boring pseudo-application; in contrast, the skewness line is isolated but starkly, moronically wrong. (Potii, we seem to disagree on whether a focus on “facts and procedures” is a positive or a negative, but that is a discussion for another post.)

Notably, neither line was quoted accurately and completely, and in each case the original line is worse. The numeracy line in the Curriculum reads:

The Australian Curriculum: Mathematics has a central role in the development of numeracy in a manner that is more explicit and foregrounded than is the case in other learning areas.That is stunningly bad writing, with bonus points for the needless and inaccurate use of the wanker word “foregrounded”.

The skewness line reads

When the distribution of values in a set of data is symmetrical about the mean, the data is said to have [a] normal distribution.This is careless and clunky, noting that Steve R has included the missing “a” and has corrected “symmetrical” to the mathematically (and universally) preferable “symmetric”. One could also more directly and clearly write “If the data is symmetric about its mean …”.

It is also worth pointing out another issue with this glossary entry, which begins

Skewness is a measure of asymmetry (non-symmetry) in a distribution of values about the mean of a set of data.This line is pretty much lifted from Wikipedia which, unlike the Glossary goes on to explain there are many related definitions of skewness. Stealing from Wikipedia is a little cheap though it would be ok,

exceptthat “skewness” means nothing of the sort in the Australian Curriculum. In the AC skewness is no more than a qualitative, shape-of-the-picture triviality; it is not in any sense of the word a measure.I think an over emphasis on facts and procedures at the expense of understanding and reasoning is not helpful. Like you said, it is better discussed in a different post.

Also, is more than one submission for worst line allowed? I guess one of the submissions will be the worst line but other lines could also be bad.

Sure, go for it. Just try to make each submission a separate comment, so that any subsequent discussions don’t get tangled.

Marti,

Thinking about my comments a little further and to be fair to the editors of the glossary .

They have not referred to the Gaussian Normal distribution specifically but just said ” normal distribution”

I don’t think they are referring to the 3rd central moment specifically (skewness) but as you say the shape of the pdf

That said it is unfortunate to have a bell curve as an example of “normal distribution” when they could easily

have picked another symmetric distribution about its mean. Eg y = mod x or y = sin-1 (x) etc

Steve R

Nah. Whatever the intended meaning, the line is appalling and the authors/editors should be walloped for it.

I am not convinced that “normal” in the skewness entry is only intended in some semi-technical sense of “not-weird-looking”. I have never seen “normal distribution” used in such a manner. But, even if true, the line is still ridiculous. If one uses colloquial language in a technical setting, the burden of responsibility is on the writer to ensure that such usage is clear. Here, as you have pointed out, the very opposite is true.

From the glossary: “Data is a general term for information (observations and/or measurements) collected during any type of systematic investigation.”

Information is data that has been put in a context, while data is a set of values about a qualitative of quantitative variable. Data and information are related but are different, so the first part is just wrong.

Yep. Not on a par with the numeracy awfulness you flagged, but it’s lazy and dumb.

More from the glossary: “The shape of a numerical data distribution is mostly simply described as symmetric, if it is roughly evenly spread around some central point or skewed, if it is not.”

This sentence is awfully clunky. At first I thought they were talking about the simplest way to describe a data distribution is to say it is symmetrical, which sounds nonsensical. Then I thought they also were implying skewed data distributions can be described as being symmetrical. Then finally after reading a few more times I think they should have just defined symmetric and skewed in separate sentences.

Not the worst but “mostly simply” stupid.

Jesus. That is one hilariously bad sentence. Who could possibly write something like that and say “Yep, that’ll do”?

And this in the glossary entry for Shape? The entire obscurely titled entry is pointless, on pointless junk, and close to unreadable.

Potii, this glossary entry isn’t as fundamental as your numeracy suggestion, but it’s amazing that a single sentence can capture so well the fundamental amateurishness and awfulness of the AC.

Yeah it is for shape, which is a very vague title for what it is about. If you go to Symmetry it is about symmetry of plane figures, nothing on symmetry in data, so navigating the glossary is very hit or miss when finding what you’re looking for.

I find that anything to do with statistics in the syllabus is where errors are easy to find. Maybe the topic is a bit obtuse or it is poorly taught at uni (most common phases I’ve overhead while at uni was “I hate stats”, “I don’t get stats” and “I suck at stats”).

I’m going through the NSW’s new syllabus of senior maths and it section on stats is pretty crap, as well as being crap overall (lots of vague sentences that miss subtleties of the concepts their talking about and errors peppered throughout).

Thanks, Potii. Stats is too difficult to be a school subject. Few if any of the concepts can be properly explained, and few if any of the critical formulae and techniques can be properly justified. So, it reduces to trivial picture-pointing and formula-plugging, all draped up with unexplained jargon. It’s then no surprise that the glossary on stats is shooting smelly fish in a stupid barrel.

NSW has been the Switzerland of Australian maths ed. I’m scared to look at what the idiots have done to it.

A couple more candidates from the glossary

Independent events – perhaps a statistical definition of A and B being independent events iff P(A|B) = P(A) and P(B|A) = P(A) would be better ?

Counting on – a strategy very similar to subtraction

Informal units – uniform squares of any size to measure area seems a tad eccentric

I prefer to Barn and the Firkin mentioned here

https://en.m.wikipedia.org/wiki/List_of_unusual_units_of_measurement

….P(B|A) = P(B) . provided I don’t make a typo ?

Acknowledged typos on blogs are forgiven. Unacknowledged typos on exams are not.

Hmmm. Maybe I’ll have to start a glossarycrap.com blog.

Thanks, Steve. Your barn and Firkin link is hysterical! And yes, defining two events as independent if “knowing the outcome of one event tells us nothing about the outcome of the other event” is not particularly mathematical or particularly helpful. As for “counting on”, I guess that’s a thing, and so I guess it can have a definition, but somehow “addition” doesn’t seem to have a definition. And yes, the “informal unit” entry is pretty weird.

I followed the link back from the more recent competition and decided to make an entry in this one, which will be most likely misinformed, because I haven’t read the entire curriculum so maybe I’m missing something. This has led me to make perhaps an odd choice (based on maybe not understanding how curricula work).

Year 4Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076)

Recently I needed to explain what was to my six year old. And it struck me immediately that there are two quite conceptually different ways to think of division: e.g., when you do you can think “if you divide 14 into 3 equal parts, how big are those parts?” OR “how many times does 3 fit into 14?”.

It takes a bit of thinking to see them as the same (I think but maybe I’m wrong). So I wondered how they bridge the gap between those two ways of thinking about division in primary school. I didn’t find a clear answer, because reading the curriculum is hard. I would kind of appreciate it in the form of a conceptual flow-chart or something.

But it seems like they make the leap from no-remainder to with-remainder between Year 4 and Year 5? Because the corresponding statement in Year 5 is:

Solve problems involving division by one digit number, including those that result in a remainder:* using the fact that equivalent division calculations result if both numbers are divided by the same factor.

* interpreting and representing the remainder in division calculations sensibly for the context.

The wording on the first part is quite opaque to me and it turns out to be related to things like

.

For all I know they use various other topics (fractions, decimals, area models, arrays). I guess I am submitting the Year 4 line in as stupid, not because it says any egregious thing, but rather because it was completely useless to me. Which efficient mental and written strategies? What digital technologies are appropriate at this (possibly) crucial bridging point between two different ways of conceptualizing division? Because if they’re not getting the concept of division from some other topic area in a much more nuanced way than this one line, then how are they going to make sense of the strategy-focus in Year 5: “You maybe don’t know what division means right now because we just subtly changed how we describe it to you, but did you know you can cancel common factors?”

I am writing from a position of complete ignorance here, so I would be happy to be enlightened by people who understand much better

Student-teacher the only thing you write that is ignorant is that you’re writing from ignorance. You’ve landed on a huge issue. Back to you soon, once I’ve pondered how to respond to your comment on the other post …

And, I still owe you a reply about number systems, on the other other post!

No, you replied. You don’t owe me any replies! I’m getting of plenty of interesting reading from here.

Hello student-teacher,

I enjoyed your authentic post (from a position of CI, or not).

Does this help or … ?

Hi Storyteller. Thank you. Yes, it does. Now I know the different ways of thinking about division are called “sharing division” and “measurement division” (in MuS5), so they do talk about them.

s-t, it is mentioned in elaborations too, but all the critical stuff seems to be hidden. I am not sure how to find what I mentioned above – without the help of Google. I suppose one can, but I tried a little and …

What do you think of the names – and moreover the language used in that page?

I think the language used on that page is pretty good. Some things I had to Google to make sense of, but it seems like these are just the words people use for them.

One thing that stood out to me was that all the examples on the Multiplicative Strategies page are whole numbers, and there’s no mention of the commutative property on the pages about Fractions or Decimals. I guess that means that the extension of multiplicative strategies to fractions and decimals is not taught in primary school?

Maybe that should be in MuS6/MuS7 because fractions get recognized as numbers in level 6 of the Fractions page.

(I’m training to become a high school teacher so I am trying to understand which parts are taught where.)

I do not think there is a definitive answer to the question you ask.

Re which parts are taught where, in many cases that will likely be determined by the text book employed by the school.

Good luck with your studies.

Hi, S-T. I won’t write much here, but I think some sort of reply is in order, particularly since storyteller is being very coy.

Whatever secret layers there may be to the AC, I very much doubt that division and fractions is in any official sense covered sufficiently. In practice, it’s a disaster. In particular, it is one thing to have both notions of division explicit, it is another thing for students to practice either sufficiently to be confident with them, let alone understand the relation between the two.

There is much to write on this (and better written by storyteller), but it’ll have to wait for another day.