3 Is Not Three
... the art of digit dancing
If 3 is not ‘three’ then what, exactly, is it? That isn’t a trick question.
In our culture we make this mark... 
to communicate a very specific idea about quantity. In China, the same idea might be represented by this mark... 
, while the ancient Mayans’ mark looked like this... 
.
You can find lots of different examples of culture-specific marks established as the convention for communicating this particular quantity; although they appear quite different, they all represent an identical idea.
All of these have something in common... ‘three-ness’. We want to be able to communicate this quantitative idea to others in a way that is efficient and eliminates ambiguity, so we assign a word and a special mark to it that distinguishes it from ‘twoness’ or ‘four-ness’ or any other ‘-ness’. Since both the word and the mark can vary across cultures, we have to conclude that they simply represent an idea, and that they are not the idea itself any more than the map of a territory is the territory itself.
Over time, brilliant mathematical minds have developed progressively clever ways of using the mark to communicate other profound ideas related to quantity. Each new discovery allowed us to better cope with an increasingly complex world.
Consider:.. 
To bring us any one of these powerful tools, they had to have understood that this science we call Mathematics follows patterns and that, if the same rules are applied to other situations sharing a similar idea, it ‘works’ every time!
What does this have to do with your classroom tomorrow? Everything!
