I was humbled to read the awesome work done in Xitsonga about Mathematics Terminology, and inspired to write this blog. I’m still researching different ways of talking about geometry and rates of change, but numbers are things with which I am familiar.

I teach the same lesson in many different ways, depending on whom I’m teaching. That’s a fairly obvious statement, and could come from any teacher. But there are a few things I’ve honed to the point where I end up teaching them the same way each time. The title of this blog is one of those.

I like to start with a basic concept-map around numbers ngesiZulu.

The Zulu number system is a compound animal. It is a combination of three different number systems – an archaic one {enumeratives}, a base-five system {adjectives} and an enlarged nominal system to accommodate decimal or base-ten counting.

 

From this basic map, I launch into the explanation of number by asking my students to hold out their arms in front of them and make fists with their hands. I tell them that counting begins with the pinky finger of the left hand, moving towards the thumb of that hand.

-nye : some, other, one

-bili

-thathu

-ne

-hlanu

These numbers are true adjectives, which I am at pains to point out because the concords used with them are different from those used with the numbers above 5.None of these numbers exists without describing a certain thing. The word for “two” can be different depending on what you’re describing – amabili, ababili, ezimbili, emibili.

Discussion usually ensues about why this first base-five system used only the left hand. Basically, it’s because your right hand was usually too busy holding something.

I also point out that isiZulu is one of those languages where the word for “one” is actually more often “(an)other” or “some”. And this is when I glance at the archaic number system hidden under the base-five one.

-nye: one

-mbe: different one, another one

-ni?: what sort of one?

-phi?: which one of two?

These are called ‘enumeratives’ by linguists, and also have different concords from the ‘adjective’ numbers. Again, these enumeratives do not exist on their own – they must describe something. Thus, a different person would be umuntu mumbe, whereas a different day would be ilanga limbe.

At this point I explain that some languages have a counting system consisting ONLY of these sort of basic measurements. I vaguely mention South American languages where the only words for numbers are ONE, TWO and MANY.

Having looked at the Adjectives, and with the left hand splayed out in front of them, I know show the learners how to continue the counting. At this point, the counting moves from the left thumb to the right thumb. This move is significant because everything from here on is a noun, and so can be spoken of in concrete terms.

isithupha: the thumb of the right hand; the number six

isikhombisa: the index finger of the right hand; the ‘pointer’; the number seven

isishiyagalombili: the number of “two limbs left behind (from ten)”; the number eight

isishiyagalolunye: the number of “one limb left behind”; the number nine

ishumi: the number ten

I ask my students to look at their hands out in front of them, and encourage them to situate the numbers physically. As as aside, this physical situation of numbers in the body ngesiZulu is a possible source of much of the misunderstanding in Foundation Phase Mathematics – if a teacher stands up and, using the right index finger, begins to talk about the number “one”, then a class composed of isiZulu-speakers will experience cognitive dissonance as their association of the index finger is the number “seven”.

In order to describe seven somethings or ten whatchamacallits, you first need to turn the nouns into copulatives, and secondly need to attach the appropriate concord. It’s fairly complex, but not impossible to understand. For example:

isikhombisa >> yisikhombisa >> abayisikhombisa >> bayisikhombisa

seven >> it’s seven >> seven people >> they are seven / there are seven of them

Anyway, not to put too fine a point on it, this pattern means that there are numerous combinations of the numbers depending on what you’re wanting to say.

From ten to ninety-nine, the numbers are filled with amashumi, the word for ‘tens’. This decimal system is very similar to other languages, and a lot clearer than many. By the time one gets to 99, this is what you have:

amashumi ayisishiyagalolunye nesishiyagalolunye

tens that-are-nine and-nine

Which is followed by ikhulu (the BIG number) – one hundred- then inkulungwane (the swarm of flying ants) – one thousand – and isigidi (the countless patterings of footsteps signifying a multitude of animals or humans) – one million.

Add into those words the concept of isigamu, meaning ‘a half’ and you’re on your way.

The same patterns are repeated, just with more nouns all brought into agreement. What follows are some examples:

12 – ishumi nambili

50 – amashumi amahlanu

783 – amakhulu ayisikhombisa namashumi ayisishiyagalombili nantathu

1453 – inkulungwane namakhulu amane namashumi amathathu

2016 – izinkulungwane ezimbili neshumi nesithupha

2.5 million – izigidi ezimbili nesigamu (sesigidi) / izigidi ezimbili nezinkulungwane ezingamakhulu amahlanu

4.6 billion – izigidigidi ezine nezigidi ezingamakhulu ayisithupha

At this point, I draw ridiculously complex numbers on the board and wait for learners to stutter and splutter their way through them. I think it’s important to understand how they work, mostly because they are an insight into a different psychology of number – quite unlike the everyday decimalism of English.

Coming soon: Mathematical Terms ngesiZulu.