## Wednesday, November 14, 2012

### Zero is an Even Number

There was a neat, short article in the NYT this past Monday (thanks VBJ) about the dilemma posed by whether 0 was an odd or even number. It was a high stakes decision because it determined when you could get gas during the gas rationing imposed in the wake of hurricane Sandy. After consulting a number of mathematicians Mayor Bloomberg correctly called it as an even number so that owners of cars with license plates ending in 0 knew exactly when to fill up. The article also went on to describe how the French police in Paris just ignored the issue during a smog alert in 1977. While odds and evens drove on alternate days 0s could drive whenever they wanted to.

I grew up calling 0 nought and played the game noughts and crosses which seems a much more logical name than the tic-tac-toe used in the US. The name has 3 parts yet there are only two options - very illogical. The name also gave rise to the early (2000 - 2004) and late (2005 - 2009) noughties in the UK. The word also features frequently in British history, literature and lore while Zero for me, growing up, was the name of a Japanese fighter plane.

The recent inclusion of 0 as the starting number in teaching counting in elementary school math is, however, a serious issue. When we teach children to count these days we teach them to begin with zero. The reason for this is that researchers have discovered that it makes fractions much easier to teach, and for student to learn,  if students realize that there is a space on, say, a number line, between 0 and 1. Fractions are introduced as parts of a whole using a variety of different models. One of these models is a linear model such as a ruler. This is really useful because rulers are usually marked with fractional parts beginning at the 0 or origin.

This idea of counting from 0 also helps young chidlren learn about measurement. Life begins at 0 as does time, distance, weight, volume, capacity and angles. Since all measurement is the repetition of the referent unit it is important for children to realize what that referent unit is; what is the one or the whole of the referents being counted.

The really interesting thing, though,  about the numbers on the license plates is that they weren't even being used as counting numbers but as naming numbers so it didn't matter at all if it was odd or even in a cardinal or counting sense. The fact that it was called an even number just made everything tidy and mathematically correct.