Following on from our previous post, it is worth considering the role of Roman numerals in the new Curriculum. There isn’t one.

The draft curriculum included the following Year 2 elaboration

*comparing numbers written with Roman numerals with numbers written using the base 10 place value system and explaining why the place value system is easier to use*

As noted by commenter Alex, this elaboration was removed for the approved curriculum. It has been replaced by nothing, unless one counts the Year 3 “Japanese numeral system” twaddle, which was addressed in the previous post. In any case, except for a brief reference in the glossary (Word, idiots), Roman numerals make no appearance in the new curriculum.

### UPDATE (20/01/2023)

It’s somewhat off the point of the post, but there’s a nice one-man Roman history site here, with a good page devoted to roman numerals.

Two questions about Roman numerals (not relating to the study design)

1. Why is 8 written VIII and not IIX?

2. Why is the number IV written as IIII on clock faces?

As to why Japanese numerals have suddenly received a mention and Roman numerals are out… maybe more Grade 2 students are studying Japanese than Italian nowadays. (Sarcasm intended).

1. Not always.

Answer: See attached.

2. Not all clocks.

Answer: When Roman numerals were in use by the Roman Empire, Jupiter (the name of the Romans’ supreme deity) was spelled as IVPPITER in Latin. There was a feeling that using the start of Jupiter’s name on a clock dial, and it being upside down where it fell, would be disrespectful to the deity, so IIII was introduced instead.

Marty, of course Roman numerals make no appearance in the new curriculum. If they did, the curriculum wouldn’t be innovative and cutting edge. It would just be recycling the same old stuff. acara would be seen as old-fashioned and stodgy. Out with Roman numerals and in with the “Japanese (sic) numeral” system! Onwards and downwards!

kreinovichIMF1-4-2021-5

Thanks JF. I knew someone here would know the answer.

I don’t buy your second story. Clock dials would have been sundials, and there the number IV would not have been upside down.

Writing numbers subtractively was in use already in ancient Babylonia, where 19 was often written as 20 – 1. There were also different ways of writing 4 and a few other numbers.

Fair enough. Having done further research, it seems that there’s no definitive answer but several theories (some of which may be more likely than others):

IIII or IV on a clock dial face? Why the difference

There is a small book on the subject. Richardson, W.F. (1985). Numbering and measuring in the classical world. Bristol Phoenix Press. The book describes how large numbers and fractions (and much more) were represented in ancient Rome and Greece. Still in print.

A review is here: https://bmcr.brynmawr.edu/2005/2005.02.20/

Let me share a story. A friend told me that when she was in primary school, they were taught about Roman numerals. At breakfast she noticed IXL on the label of the jam jar. With some excitement, she told her teacher about this and she had worked out that it meant 39. Her teacher told her – in no uncertain terms – that she was wrong. She recalled the story to me many decades later.

When my wife had a birthday a several years ago, I ordered her a cake with LXXI on it. I went to pick it up, and the young shop assistant asked me, “Is this the cake for Lexi?” They had written what I asked for but they were concerned that my spelling was incorrect.

And anyway, what did the Romans ever do for us?

BTW, do you get as annoyed as I do when people use “amount” instead of “number”? Or, “multiple” instead of “several”.

That sounds very interesting (except for “the treatment of Roman plumbing and pipe sizes”). Thanks, Terry.

“What have the Romans ever done for us…”

Apart from aqueducts.

It is standard to use Roman Numerals for the quadrants of a graph and they are used to label sections of many math texts.

Yeah, but what kind of argument is that? Why be functional when you can be clever?

I can well imagine a world in which the dominant language is Chinese. But I cannot imagine a world in which the Hindu-Arabic system of numerals is replaced.

Give ACARA a little time.

I also can not imagine them being replaced – they’re too established. But maybe they should be. [Just like the π vs τ circle constant debate]

Even if we keep base ten, using numerals that properly reflect the 2&5 sub-base structure and aren’t confused (eg 6,b; 5,s) with our letters would be nice!

Of course they won’t be replaced. Although we did end up with the metric revolution, including its idiocies.

True – we did manage to replace and simplify a lot of units – except for in one particular superpower. Which particular idiocies are you thinking of?

We could begin by with the switch from Fahrenheit to Celsius.

The Fahrenheit scale has some pretty weird definitions (NH3Cl brine??) in its origin – and the connection to “human scale” temperatures is oversold.

Celsius is convenient definition of temperature. Most people have access to water, so can make their own approximate measures of temperature and convert from a meter length to kilograms. Seems sensible given the time and place of invention. The definition of the meter was botched though… not that it makes much difference in the end.

Nah. Celsius is ridiculous. You’d have to be a physicist or something to think otherwise.

A Chemist might want Celsius. A Physicist would want Kelvin.

An Engineer might want Rankine. A Contrarian would insist on Delisle. A wannabe-intellectual mathematics textbook writer might use Kelvin but would say (and I have seen this) degrees Kelvin.

And getting it back to the Romans … They used a Mercury thermometer.

All irrelevant. The question is, what does someone who wishes to adjust his heater want?

“You’d have to be a physicist or something to think otherwise.” — Yep… that checks out!

Everyone is a “physicist or something”.

You might want to study up on your ellipses.

I think there are many places and reasons for other number systems to be considered in the mathematics curriculum. But maybe not at year 2 or 3…

People get so habituated with Hindu-Arabic numerals they confuse numbers with their representation. Playing with other systems can help remove that confusion – and playing with other bases helps better understand how our system works and how it is connected to things like the addition and multiplication algorithms, divisibility rules, etc. And yes, base-10 blocks also help here.

The removed elaboration “explaining why the place value system is easier to use” is probably tough for year 2. Adding and subtracting Roman numerals is fairly straight forward – multiplication and division aren’t so fun. But year 2 students don’t have enough experience with base-10 operations yet to sensibly “explain” this.

Roman numerals still occur around the place and people should recognise how to read them as a basic life-skill. Traditional Japanese numbers in particular maybe aren’t worth Australian curriculum time – I’m not sure why they are mentioned but Roman numerals aren’t.

Identifying sexagesimals in their continuing modern usage and connecting that to ancient Sumerian and Babylonian history is worthwhile. Maybe worth mentioning is the independent invention of zero and base 20 in Mesoamerica – the Mayan numerals are tidy numerals for positional representation. Finally, the Chinese counting rods are a nice alternative example of how to simply and cleanly represent base 10 numbers – giving nice physical algorithms to complement written ones.

Learning binary and optionally hexadecimal is in the 5-6 & 7-8 Digital Technologies curriculum – and it would be good if that can be connected to learning in Mathematics of other number bases. So, year 5-7 would be a good place to learn some non-Hindu-Arabic number representation in maths.

Finally showing that all positive integers can be represented using a particular base is a nice inductive proof for year 11 specialist maths!

Hi, Simon. I mostly agree with you, although I think its fine and good for young students to have early exposure to different systems. Of course ACARA’s suggestion that students might “explain” the differences or the values of these systems is ludicrous. But young students can still get an intuitive sense of how these systems work, and how some are clunkier than others.

In ancient Egypt, more than 3000 years ago, it was known that all positive integers can be represented as a sum of distinct powers of 2. This was the basis of their method of multiplication; see attached; you did not need multiplication tables – you only needed to know how add and how to multiply by 2. However, I do not know how they came to this conclusion.

2009-PrimeNumber-egypt

@Terry: Yeah – it’s a fun method of multiplication that is basically a hidden use of binary long multiplication (aka “shift and add”).