And if there's some domain-specific application, like in carpentry, then let those people use their own units.
* Scientists and engineers culturally select tasteful units of their choice to represent time, like 1300 milliseconds or 134 hours... and everything else as well: $1.34 billion or $1.34 dollars, not $1 billion and 340 million or $1 dollar and 34 cents.
* When the number representation get too big, people just do X * 10^n where n is a tasteful choice.
* In business, days and hours are distinct concepts and should not be mixed together or confused. A person who worked for 5 days did not work 120 hours.
* Mathematicians could care less.
* Many culturally common units of time are bigger than 12 * 12.
* Calculations that are big are working-memory bound. This is the biggest point. Working memory is probably the strongest factor to large and fast calculation of any kind.
* The bigger the calculation, the more people tend to 10^n multiplicands with the distributive property, rather than 12^n, since most people work in base 10. Some engineers use 2^n or 3^n (I offer that 3^n is efficient without further explanation).
I propose the hypothesis that children who memorized up to 10 * 10 are no more likely to join or do well in the STEM fields than those who memorized up to 12 * 12.
I argue that calculations are working-memory bound, and that common uses of time go beyond 12 x 12.
For time, we often go by units of 5, 10, 15, 30, 45, 60, of these only 60 can find 12 as a divisor. You don't get to claim usefulness for all time. For the rest of these units, it's working memory doing arbitrary integer computation for us.
If we're talking about months in a year -- what's the use case for fast mental calculation? Is this the little sphere where we say 12 * n is useful?
We're talking about a policy for education for all children here. Your use cases sound really limited, if it at all impacts later cognitive performance outcomes.
It's working memory that's going to be the differentiating line between "fast mental math" and "busting out calculator" or "punching in numbers into SAS or SPSS". It's difficult to believe that Taiwanese children are going to have trouble versus American children in time based operations, if that at all continues to be a practice under the common core.
I can't imagine asking some Taiwanese business man, "Quick, what's 6 * 12 in a business context", and he goes, "Let me quickly grab a calculator."
Can you do 15 * 14? I think you can. Why can we do it? Is it because we learned 12 * 12? No. It's working-memory bound. We're doing capricious calculations with distributive property via 10^n multiplicands.
How about 24 * 17? I think you can do that too. Why can we do it? Working memory. Not because we learned 12 * 12 when we were little.
In business? In the STEM fields?