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Topic: Let's meet Haim's challenge!
Replies: 8   Last Post: Feb 25, 2009 10:59 AM

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Kirby Urner

Posts: 4,713
Registered: 12/6/04
Re: Let's meet Haim's challenge!
Posted: Feb 24, 2009 9:00 PM
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>
> Kirby's generous note said a lot, inclluding:
>
> "K-4 lacks overview, really OK to preview and do a
> heads up. So yeah, we'll be doing these concentric sets,
> somewhat recapitulating phylogeny (teachers' notes):
>
> "N < W < Z < Q < R < C
>
> "Those'd be naturals, wholes, integers, rationals,
> reals and complex."
>
> I love this stuff. The first course I was allowed to
> teach on my own, in 1966, was the foundations of the
> number systems. I was told to use Stoll's quite good
> book, but I went off in my own way.
>
> I started by working backwards from C > R > Q >Z > N,
> where, for me, N included zero, so was what math ed
> folk call W. I then started from N and went up,
> first to the infinite cardinals and then looked at
> them as special infinite ordinals. If I were to
> teach such a course now, I would include quaternions,
> infinitessimals, and non-standard real numbers.


I prefer chrono order and telling history as we go i.e.
what pushed the envelope at each step in the game to
enlarge the scope. Why weren't rationals sufficient?
What motivated "imaginary" i.e. "complex" and so on.
This helps keep Polynomial objects in play, even as we
give more limelight to Polyhedra than before.

I'm fine with including other objects, have Quaternions
going at Oregon Curriculum Network, no problemo, also
some 4-tuple objects called Quadrays or Chakovians, like
XYZ but no linear independence or negative numbers, lots
of precedents in the literature ("simplicial coordinates").

Yes, very esoteric but students sometimes enjoy getting
off the beaten path. grunch.net/synergetics/quadrays.html

We market through coffee shops, knowing most schools have
no patience for private industry and its mathematics
(way better than "schoolish math", much closer to real
engineering, less mired in stultifying arcana). "Self
school and come work for us" is our subversive message,
but then we also run schools, have a footprint in the
public system (as business associates, sponsors, para-
teachers of various kinds).

>
> For kids K-2, I'd do N and W "counting numbers", then
> introduce real numbers. I'll say much more about
> this on the measuring number thread.


Again, stories matter, so telling how Liber Abacci helped
open Europe's eyes to the Abacus Way, a real leap from
the imperial domination of idiocratic Roman Numbers, made
the Renaissance possible. There's a temptation to
prohibit math teachers from doing this segment, as they
tend to botch everything to do with math. But that's to
get tangle up in semantics. Of course math teachers
teach math, by definition right?

I think the better way of saying it is we Amerish
(a-MER-ish) speakers have no intention of waiting for some
Math Czar in DC (a fantasy) to give us a green light.

We're already off and running, many laps into it, with
students getting it about the DOM (Document Object Model),
the importance of XML. Don't call it "numeracy" if it
has "too many letters in it" (like algebra?) but do call
it basic literacy (or how about "alphanumeracy"?),
"what any kid should know" (if you want to play in
places like CubeSpace -- generic office cubes I blog
about (i.e. more websites, some more on Gattegno, other
constructivists, Karplus especially (physics, more
successful at reform, better managed in many ways))).

>
> Kirby also says: "You're maybe not tracking the tilt
> towards Gattegno in the UK..."
>
> I'd like to. If you have a few good websites, I'd
> greatly appreciate getting them. I don't have easy
> access to a good library. I'll more about what I am
> learning about Gattegno's ideas in the early linear
> algebra thread. The attachment to my first note
> there will also mention some use of computers.


Yeah, definitely the Web is where it's at. Start with
tizard.stanford.edu, a cosponsor of Python for Teachers
at Pycon this year.

Kirby



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