What Kind of Thing is a Number?

When I first started reading this article, I was thinking to myself that this guy way thinking WAY too much into mathematics and why this was that and why things were how they were. I often find it hard to sit back and be philosophical about things. After I continued reading on for a bit, the article reminded me of the philosophical thought of "If a tree falls in a forest and no one is around to hear it, does it make a sound?" that raises questions about observations and knowledge of reality (Wikipedia, Oct.12, 2011). Hersh says "There's no math without people. Many people think that ellipses and numbers and so on are there whether or not any people know about them; I think that's a confusion" (Brockman, 1997, p. 1). I'm one of those people who would say that yes the tree makes a noise because if there was someone there they would hear it. The same goes for the math, I believe the math still would exist if people were not around, it just would not have a name. All humans have done is name it. However, it certainly makes me think more about the philosophy of math, that's for sure.

There are three philosophical attitudes towards mathematics: Platonism - some abstract entities; Formalism - calculations only, there is no meaning; and Humanism - mathematics is part of human culture (Brockman, 1997, p. 4). Hersh feels that humanism is the only educational friendly philosophical attitude of education and that it "brings mathematics down to earth" (p. 4). In other words, it is just what we have been calling making math real for children. We have been saying for years that we have to relate math to the real world for children in order for them to have a connection to it and find it meaningful to them. Having only been teaching for 4 years, I am finding myself more and more heading in this direction. My first year out, brand new to the whole thing, I resorted to the way I was taught with notes and questions, maybe a scattered activity. As each year went by, I felt more comfortable allowing children to discover formulae and why certain things happened the way they did. The children enjoy the math more this way and then they are much more likely to remember it.