Reading 2 thoughts

As mentioned before I had the belief growing up that math is concrete and there is always a right answer. After reading the article involving Hersh I start to think about the nature of mathematics myself. The laws that I learned, growing up and the objects we found the surface area for, well where did all these come from? Who decided a square was a square or a circle a circle? When you really sit down and think about anything in this life, well where did anything come from? After I read this article I start to think and reflect and growing up believing in something, such as math is concrete, then reading an article which questions this is difficult.
In terms of teaching I am going to try to push harder for independance for my students. They do enjoy it when I am at the board doing examples, but I refuse to do that in my class all the time. The students are responsible for becoming part of the class, for contributing and figuring things out on their own. I will get them up to the board more often then I am already doing and I will make them work harder to learn for themselves, not because they must just get good grades.