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Topic: Treatment of Negative Numbers
Replies: 12   Last Post: Dec 5, 2012 2:13 AM

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kirby urner

Posts: 1,805
Registered: 11/29/05
Re: Treatment of Negative Numbers
Posted: Dec 4, 2012 3:21 PM
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On Tue, Dec 4, 2012 at 5:45 AM, Robert Hansen <bob@rsccore.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.
>
> Bob Hansen
>
>

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 less wasteful and weak.

Kirby



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