My regular readers know that as of September, I will be a college student again. I will be attending the University of Southern Maine in an effort to become a math teacher in our nation's public school system. In preparation for this, I have decided to brush up on my math a bit. I went to the used book store, and for under $20 I got textbooks covering Algebra, Plane Geometry, Trigonometry, and Calculus. I began with Algebra for no other reason than that's where I began the first time around. As I progressed through the disciplines, I began to wonder who has the job of deciding in which order students learn math. Of course, it makes sense to begin with arithmetic. Mathematics began when man started finding and manipulating patterns in the natural numbers. Formalized concepts and conventions like orders of operations and the product of negative numbers must be learned so that we can agree on what exactly we are talking about, and definitions must be drilled so that we have words with which to talk in the first place. All of this I get.
But then comes Algebra. Why is that exactly? Why don't we start with Geometry? Many concepts are necessarily presented in a linear fashion, but there are plenty that are fairly autonomous and are simply shoved in somewhere. Why is the chapter on Probability and Statistics at the very end of the College Algebra text I purchased? It doesn't have any prerequisites as far as I can tell, and I would argue that it is far more important than solving quadratic equations. The average person doesn't need to use very much of formal mathematics. Our brains have such well evolved pattern recognition algorithms that we can instinctively find practical solutions to problems without resorting to calculation. I doubt very seriously whether major league outfielders are solving quadratics to predict the path of a pop fly. Ironically, even though every decision we make is based in some part on probability, it is the area of math that most confounds our intuition. Shouldn't we learn that up front? Why wait until we've mastered more technical courses?
I'm just using Stat as an example here. I can't prove conclusively that is is the most important math skill and should therefore we taught first. All I want to know is who decides the order in which mathematics is presented? Somewhere, deep in the shadows of the mathematics priesthood, sits a little robed homunculus pulling all the strings. I just want to know who he or she is. If anyone out there has any clues to this, please let me know.