[ from math-teach archive, hyperlinks added ]
On Tue, Mar 16, 2010 at 9:52 AM, Joe Niederberger wrote:
> What of old decrepit terms like "imaginary numbers"?
> (Apologies to Euler.)
> Come to think of it, is "complex number" unnecessarily
> frightening our kids?
> Shouldn't some of these be rechristened?
> Joe N.
I say keep "imaginary numbers" handy (as a synonym) and don't touch "irrational" either.
It's important to our storytelling, our lore, that irrationals were a big challenge for greek philosophers.
Also, having roots of negative numbers was considered radical in its day.
Remember Lewis Carroll and Alice in Wonderland if you ever worry about math being too wild 'n crazy. It's supposed to be a refuge and source of solace for those seeking like-minded Harry Potter types or whatever.
"Do not sanitize if you know what's good for ya" might be the motto, and read Alice in Wonderland and some Wittgenstein while you're at it. Here's a useful crossroads, where these paths meet:
Irrational numbers (and hence "the reals" as rationals + irrationals) and imaginary numbers were basic innovations, akin to "tetrahedral mensuration" in their day. As such, they took hundreds of years to percolate outward, to where we're now worried about whether we're frightening little children.
Until we had roots of negative numbers, lots of modeling was out of reach. The polynomials forced us into them, or that's one way to tell the story. We should focus on how we got to them and what they gave us in return (the ability to model electrical phenomena for example).
Given the highly conservative anti-innovation climate we're seeing today (citing this recent post by Gary **), I'm wondering if our age will be known for any risk taking at all. Mostly, people hunkered down and denied that change might be advisable, even necessary.
You actually had people calling themselves "math teachers" who refused to share about Mites, Sytes and Kites! So much elementary math was "verboten" in early 2010. Makes ya wonder what they were thinking (if anything) eh?
Ben Franklin was a radical, and also an "off your duff" mathematician, sitting out there with his kite, waiting for lightning to hit.
That's a role model for children (he took wise precautions remember -- two strings to that kite), so lets make sure Ben Franklin and his kite keep getting some airplay.
I'm encouraged that NCTM has kites as a motif this year, as that's a hook for Alexander Graham Bell and his kites as well.
The NCTM lesson plan on Tetrahedral Kites is a buried gemstone amidst a lotta schlock IMO, as it's daring to question the authority of cubist thinking, even if only just a little. It's a chink (crack) in the armor.
Maybe Texas and Alaska are withholding support because everyone else is such a wuss?