What math is and is not

Robert Lewis has a great essay on math, as the most misunderstood subject.  I couldn't agree more! 

In addition to an analogy with sports training similar to one I have here, I especially liked his parable of the hostile party goer.  He is confronted by a man complaining that he was forced to memorize the quadratic formula, and yet has never had to use it.  Lewis compares this to the absurd notion that we should complain to our first grade teachers that we have not once had to recall the details of the ever popular Dick and Jane books.  Why would we need to spend so much time reading the books if the information contained within them can be so easily forgotten?  Of course, the answer is that we used the books to learn to read well.  Similarly, we practice (even memorize) math to learn to think well.

Lewis has captured exactly the problems most Americans have with mathematics and the ways they misunderstand the subject.  But what's next?  How can we correct this error for future generations?  I suspect it all starts with us: college math professors, especially those of us who get to teach future K-12 teachers.  We need to teach with an understanding of what math is, so they will have that understanding, so they in turn can teach in a way that their students appreciate what math is and what it is not.  I am not calling for a change in K-12 math curriculum.  That is too early to teach the nuances of math.  Instead, the teachers must present the mathematics in a way which respects the subject and prepares students to uncover the hidden richness of mathematics as they mature.