Math Education and Descarte's Rule of Signs

Southern Man is well credentialed in mathematics. He's earned a doctorate in nuclear physics and a masters in computer science and works in the latter field to this day. One would imagine that he's well qualified to help teen daughter with her algebra homework.

One would imagine correctly. However, that is not the point of this rant.

Teen daughter's homework last night involved Descarte's Rule of Signs. You know what that is, right? No? Well, it's an esoteric bit of historical algebra that has absolutely no application to modern life. None. Zilch. Nada. Southern Man, who has worked in physics and mathematics and computer science his entire adult life, has never had any need whatsoever for Descarte's Rule of Signs. In fact, the first (and last) time Southern Man encountered Descarte's Rule of Signs was in high school algebra.

Which begs the question: why the hell are we making high school students learn Descarte's Rule of Signs when they could be mastering concepts that are actually useful and applicable in real life? Like, what's 20% off of 40% off? Is it better to take the instant rebate or the lower interest rate? How is compound interest computed in that furniture-store Rule of 78s loan? Is that "free" cell phone worth committing to a two-year contract? What does it really cost you, per mile, to operate your car? What's the appropriate tip on this tab? Can you double that recipe?^* What, really, does it cost in the long run to carry a balance on that 22%-interest credit card? Is that college worth the expense, and, if so, what sort of loans should we take to attend there? Is it better in the long run to purchase points on your mortgage? Southern Man could think of another dozen things he wishes teen daughter would learn in this, probably the very last mathematics class she will ever take (she's getting college credit for it). With all due respect to the enormous contributions of the mighty René Descartes, his Rule of Signs is not among them.

Now, Southern Man loves math for it's own sake and believes that everyone ought to learn some math. Southern Man uses math every single day. He wishes that people in general knew more math and dies a little inside every time some clerk behind the counter struggles to make change. But there's not much doubt in his mind that our State-regulated education system teaches the wrong kind of math to our children.

^*A reference to a near-disaster some years back when a young relative who shall go un-named complained that doubling the recipe was impossible as the oven temperature dial didn't go high enough.