I spent a couple of hours today having quality time with my dentist. He was doing some salvage work on my 3-6 using a 10 long and a 23 mesial clamp. As I lay there staring at the ceiling, I began to wonder about the use of numbers in language.
And then I realised, numbers are language.
We use language to communicate - and numbers do the same. Just as my dentist was communicating with his assistant to pass information and tools.
And we do that everyday in the classroom. Maths is part of our language. As I often tell the kids, the numbers came when we needed to do something like count, measure, record, compare or score. Before we had numbers, our language was deficient, it failed to communicate some really important ideas.
If we didn't use numbers, what else could we do?
Well, we could use comparative language, like big, bigger and biggest. This would work if we were comparing three things but any more than that and we would be stuck. Imagine the dentist trying to get the correct tool by saying, "I need the one that is bigger than the big one but not as big as the biggest one." Great, if he only has three tools to work with.
What other elements could we use to distinguish between a variety of objects? Well, the dentist could colour-code his tools but once there are more than seven or eight colours, it starts to get a bit subjective. Have you ever looked at one of those giant tins of coloured pencils? How do you tell the difference between aqua and teal? Or look at paint charts. Can you honestly see any variation between Antique White and American White?
Or maybe the dentist could name all his tools. Perhaps they could be named after Prime Ministers of Great Britain or his friends at school or 70s pop stars. But that would mean learning a whole system specifically for his set of tools. And if his assistant was ever to be sick, take a holiday or resign, he would have to teach his system to a new person.
No - numbers have universal appeal because we can bring some prior knowledge with us when we use them. We know that 23 is bigger than 21, therefore the 23 mesial clamp is going to bigger than the 21 but smaller than the 24½. And if they are all lined up in order, you could probably work out their relative positions.
And the dentist won't have to retrain every assistant that ever works with him.
At least not to the extent of teaching them how to count.