Thursday, August 23, 2007

The Scrap Heap of Mathematics

My nomination for the scrap heap of mathematics, the rational root theorem. It is a lovely pile of math that is collecting all of the math that is no longer relevant, no longer valued to be a part of the K-12 experience. Upon inspection of the heap we find: calculating square-roots by hand, manipulating a slide rule, and if not on the heap lying right next to it balled up like a piece of used kleenex, long division.

I remember learning the rational root theorem in my Algebra 2 class in high school. I loved it. I wanted to factor everything I could, and I needed something that would help me factor higher degree polynomials. Today, I would hopefully have a great understanding of the connections between zeros of a polynomial and the roots. I would graph the polynomial and use that to find the roots. And moreover, I don't think that the proof/reasoning behind the theorem is so enlightening that students will understand mathematics less if we never speak of it again. The reasoning, I believe, boils down to the fact of divisibility of the lead term and constant term. Students get this by factoring quadratics.

Am I missing something important here, or is this a slam dunk onto the scrap heap of mathematics?