On Tue, Oct 30, 2012 at 1:41 PM, Clyde Greeno <firstname.lastname@example.org> 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).
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).