Bill,
At least, from my experince of reseach in Nepalise Bazaar,
in commercial activity, calculation of shopkeepers can be often
regarded as a kind of social display of calculation process
for customers and themselves.
If the researcher focuses only on the calculation strategies
of shopkeeprs in the test session or similar session, it is not
observable.
However, I have observed that a shopkeeper showed a way of
street math like verbal calculation for diplaying calculation for
customers. In that case, that shopkeeper could do written math
and he also had a calculator. However, depending on a customer,
and trade, he changed his way of caluculation.
In the same case, for socially observable, accountable
calculation, it took over 30 minutes probably partially because
of a big trade.
In the trading activities, commercial activities, many artifacts
for calculating and recording trades are constituted and used
for social observability and accountability.
This discussion is very related to "inscriptions" of Latour.
If I use the term making thinking visible, it is quite natural
in commercial activities although I do not agree with dichotomy
of thinking inside and outside.
In classrooms, students have to make their calculation socially
visible (or making their thinking visible) in quite different ways
and different reasons.
I think the point is the nature of langauge game where making
calculation (or thinking) visible games are embedded.
Without considering the nature of organized langauge game,
only emphasizing making thinking visible games does not
make a sense.
Naoki Ueno
NIER, Tokyo