Why Counting Is Not As Easy As It Sounds

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

01 May 2005

Counting is easy. We start from zero, and then go to one, two, three, etc. And writing the numbers is even easier: 0, 1, 2, 3… Why then do young children have so many problems with Number Work? This is probably due to the fact that we don’t write the same way we count.

From zero to nine, we use single word names and single digits for the numbers. From ten to twenty, we use single names (ten, eleven, twelve, thirteen, etc.) but write double digits (10, 11, 12, 13…). The “teens” can be seen to as shortened versions of “three and ten” (thirteen), “four and ten” (fourteen) and so on. However, the names eleven and twelve don’t fit that sequence.

From twenty-one to ninety nine we use double worded names except thirty, forty, fifty etc. But these words are shortened versions of two tens (20), three tens (30) etc. From one hundred onwards, the naming of numbers becomes easy: all we need to know is that hundred means a number with three digits, thousand has four digits and so on.

The system for writing numbers is not as complicated. Every digit represents the number of tens. The choice of grouping the digits in tens probably comes from the fact that we have ten fingers. Similarly, the awkward counting up to twenty is probably because we have twenty fingers and toes (incidentally, these are also called digits!).

Unfortunately, although we are well schooled to write and manipulate numbers in tens, all digital equipment in our homes and offices count in a different system; 0, 1, 10, 11, 100, 101, 110, 111, 1000… instead of 0, 1, 2, 3, 4, 5, 6, 7, 8 etc., respectively. This is because they can only recognise zero (when there is no current) and one (when electricity is flowing). In this format, each digit represents the number of twos – instead of tens. Thus two is 10, four is 100, six is 110, eight is 1000, and so on.

But if that is so, how, for example, is a digital electronic calculator able to display all the numbers. If you look closely at the screen, you will notice that it has the figure “8” written faintly using straight segments. These go on or off depending on which number is displayed.

When the “8” is typed, all the segments light up. For zero, the central section of the figure-8 is switched off while all the rest are on. Thus, by manipulating which segments are to be switched on, the calculator is able to display any digit from 0 to 9. The important thing to note is that each sector is either OFF (0) or ON (1).

The same method is used in the screen of a mobile phone only this time there are very many square dots (also known as “pixels”, which is short for picture cells) which are kept on or off in order to display different characters.

Since everything is going digital, perhaps children should be introduced to the zero-and-one counting system early is school.