Date: Oct 30, 2012 5:10 PM
Author: kirby urner
Subject: Re: Fw: Why?

On Tue, Oct 30, 2012 at 1:41 PM, Clyde Greeno <clydegreeno@cox.net> wrote:

<< snip >>

>> # Your scenario is interesting, but seemingly not what I meant. What I
>> meant was that all children early learn to think and talk in "combos" ...
>> "linear" combinations of things.


OK, I get it. It's obvious with money as we have X, Y, Z of nickels,
dimes, dollars or whatever the denominations in some available
currency.

We take inventory in terms of scalar quantities of a tuple, as in
so-many of each type of supermarket shelf item.

I call this "Supermarket Math" in my heuristics for teachers at
Wikieducator, one of four (allusion to tetrahedron) that "covers
everything" (but only within a specific Digital Mathematics
curriculum, not saying universalist or catholic).

>> Each "combination" of rods can be perceived as a combo --- using whole
>> numbers as "scalars" for counting all rods of a single (length/color) kind.
>> Each "scale" is the succession of same-kind *quantities* ... as with
>> 0-R(eds), 1-R(ed), 2R, 3R, ....
>>


Yes, and different combos add up the "the same amount" whether working
with coins or volumes (polyhedrons as volumes).

I'm open to "money" in connection with "energy" and encourage seeing $
as relating to joules and calories (not the element Au -- Paul jeers
at the Gold Standard people, like William Jennings Bryant was into
Silver, i.e. currency used to relate very closely to metals, still
does in some forms of banking).

>> Such (poly-namial) combos can be scalar-added/subtracted and
>> multiplied/remainder divided by whole numbers. But yours seems to go the
>> further step ... of imposing equivalence classes (e.g. 2 of kind-a ~ 3 of
>> kind-b). Such "ratio" perceptions are crucial not only for rod-fractions,
>> but also for child-measurements and for Arabic arithmetic: in Roman, 345 =
>> 3C+4X+5I ... where 1C~10X and 1X~10I. Vector algebra does not *necessarily*
>> invoke equivalence classes of combos, but it certainly does allow them.
>>


What I'm imagining as a cartoon or animation is this fanning out of
rivulets from the Nile, irrigating the Egyptians fields, from which
grains are harvested (a solar powered industry) and put in vessels.

These vessels will have canonical volumes relative to each other based
on the system of Egyptian fractions, which Milo Gardner writes about
on Math 2.0 (mathfuture, a Google group).

http://planetmath.org/EconomicContextOfEgyptianFractions.html

Board games and/or videogames etc. will feature these "flasks" or
"urns" of various sizes. They come as empty or full, but when full
have the added value of the grain inside. The price of the grain is
another variable -- of the same grain over time, and of different
grains.

As the kids get a little older, we'll talk about wine more, other
oils, pepper. You may have played these trading-based games. Oregon
Trail was popular with my students on Marine Drive (bussed there by
the district).

Actually, I haven't stipulated this is a game for kids (not exclusively).

The Coffee Shops Network idea is to stock a huge variety of didactic
games that one plays for entertainment, but perhaps with ulterior
motives.

Advancing in one's chose fields of study being a leading motive-- but
also helping various nonprofits and the business model lets you share
winnings with a menu of charities you champion (like a knight in
shining armor).

Kirby