Not convinced that there are cultural nuances in how we understand and define math? Watch the following short video (see http://www.culturecognition.com/ for the source) in which a child explains the number system his culture uses to another child.
There are other areas in which we understand mathematical concepts differently depending on our culture. For example, this recent study suggests that something like ‘numbers come in a certain order’ may be a cultural representation, and not one of which most of us are aware.
One wonders, if we can see such dramatic differences between different cultures in terms of understanding something fundamental like number, how likely is it that there are other differences within our own culture?
My wife, for example, tends to rely on landmarks for navigation, but I tend to rely on an internal map based on the names and numbers of the roads. She and I therefore have a different understanding of how one should navigate. I can remember meeting people who could not read a map (but who were otherwise able to navigate with ease) suggesting that our representations of geographical information may differ greatly between different people.
How does this influence how we should teach?