My proposal to teach a non-Euclidean geometry as a part of the 4D spun DM track (digital math track) is met with ridicule in some circles, as isn't the priority to gain some grounding in Euclid first, before delving into college level topics?
These ridiculers may not appreciate the meaning of dialog and/or dialectic that much, not having studied philosophy maybe. The Platonists, taking a page from the Sophists, continued the tradition of recording conversations, debates. One needed interlocutors, like what we see on listservs today.
In other words, to really "get Euclid" you'll need to contrast his metaphysics with some other's, say that of Democritus (our "patron saint of discrete math" -- as in: "it gets down to atoms" (quanta) vs. continua).
The pragmatists don't so lazily resort to ridicule in the opening frames, but do worry we're muddying the waters. These might be neo-liberals or neo-cons, secretly and somewhat desperately hard at work to shore up some central authority (an imagined monarchy). The idea of young children questioning the existence of "infinite planes" and/or "perfect solids" just sounds like chaos to them. What will they doubt next? The existence of "real numbers"?
One solution in this case is fairly easy to implement: keep these worry wart types teaching along the creaky old analog math track (aka the status quo in 2009), a sequence of connected curriculum segments already well memorialized in any number of textbooks, some better than others (Dolciani gets some respect, also Saxon, whereas some brands of corporate pabulum cut way too many corners, leaving many in the Lower48 with mush for brains, "pseudo-educated" as Dom Rosa would say).
In other words, don't let them muddy these waters they're so worried about muddying -- leave this non-Euclidean stuff to the certified gnu math teachers, properly trained to not botch it. They have a computer at their elbow (know two or more coding languages), have enough linear algebra to teach the neo-Euclideans' XYZ orthodoxies, even as they express skepticism in the face of its more dogmatic apologists (you'll find these zealots in all walks of life).
Just zooming back from an ancient greek geometer, sketching a proof in the sand with a stick, showing it's on a beach, on a ball (ala Google Earth), not something infinitely flat, would be too subversive for some teachers to handle. The space program sort of went over their heads maybe.
But in a school truly committed to diversity (do they have a statement?), students will have some leverage, as will the parents. If you don't have a spanking new DM track, hotly relevant with lots of bright screens, maybe contact your state and/or local representatives. Ask about the new standards, the new K-12 pipeline.
:: question authority ::
