From: kirby urner Sent: Tuesday, December 04, 2012 2:21 PM To: Robert Hansen Cc: firstname.lastname@example.org Subject: Re: Treatment of Negative Numbers
On Tue, Dec 4, 2012 at 5:45 AM, Robert Hansen <email@example.com> wrote:
I think it boils down to the fact that most people are much more aware of the development behind all of this than you will admit. They realize that you can't just walk into a class and put on a show and expect any real achievement. Not that shows are all bad. A distraction once in awhile is a good thing, even a required thing, and it can be inspiring. I am quite certain that teachers don't do as you suggest, and clutter up a lesson with a bunch of tangents and shifting points of perspective because they recognize that lessons are supposed to lead to a moment of clarity for the students. Not leave them more confused than when they started.
Left and right handedness leaves kids confused sometimes and I didn't see much in this class to help them with that.
Part of the reason the featured curriculum is weak is there's no awareness of viewpoint.
We don't talk about where "we" are relative to a line (aka "road") on the blackboard.
If you nail one end "to the left" and the other "to the right" then you're forgetting the first rule of theater (or maybe it's the second) which is that "stage left" is the actor's left when facing the audience and "house left" is the audience's left when facing the stage. http://en.wikipedia.org/wiki/Blocking_%28stage%29
So there isn't one "true left" which is why using those terms is problematic.
If "positive" means "to my right" then it matters which side of the road I'm standing on and/or which way I'm facing. He never mentions that explicitly.
Also, when you focus on a single radial and point in the directions "into town" and "out of town", you're not acknowledging the asymmetry. A planet in space (e.g. Earth) has a convergent "in" or "center" and "out" is divergently away from this center in all directions, not just one.
"Away" and "out" are divergent in the way Earth-powering sun energy is divergently broadcast.
Then there's "around" or axial motion. This is where latitude comes in, and the equator. Time zones.
Of course none of this in-out-around context is important to this teacher because in the back of his head is the real number line going to infinity in both directions (nothing like any "road" we've ever seen), an antiquarian concept inherited from Greek metaphysics that is core to how some subcultures organize their thinking about mathematics.
Rather than be up front with students and give them overview, a sense of where they're heading, they're just led by the nose. There's no historical perspective, no lore, no storytelling about how, where and what people came up with these ideas and how they've been used.
It's inculcation without awareness of history, very typical of math curricula, but nothing to be admired or celebrated in my book. It's mind numbing, and the adults we get out of it tend to be over-specialized and less able to think for themselves than they could be, had their educations been wasteful and weak.