One of the real challenges in teaching math has nothing to do with teaching methods of calculation or analysis. I happen to feel an overwhelming responsibility to try to help students understand math in context. What do these numbers mean? What are they good for? Why would you need or want to solve a problem?
The problem is that while people have some intuitive understanding that numbers are an abstract concept, they still invest them with a level of precision and accuracy which they do not necessarily deserve. Numbers may be very good for measuring things, but that doesn't magically imbue those measurements with meaning or value. There's an interesting column in the New York Times today that made me more aware of how our vastly increased access to data has the potential to warp our behavior. The article is here. It also points to and interesting blog post called "Online Status Anxiety" about how online measurements (numbers of Facebook friends or Twitter followers, for example) affect our behavior.
I need to give this more thought and will share what I come up with if I do in fact come up with anything.
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